tag:blogger.com,1999:blog-73428842088359330132024-03-19T05:31:20.909-07:00triKnowBitsRandom topics of potential interest to actuariesMurphy Danhttp://www.blogger.com/profile/02252526252924091700noreply@blogger.comBlogger26125tag:blogger.com,1999:blog-7342884208835933013.post-6498199122513051332020-12-20T21:14:00.000-08:002020-12-20T21:14:54.957-08:00Bayesian priors and posteriors in 3D<div class="separator" style="clear: both;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgPeUxjoLUYjk5aXBYcK9Oc-qCwQTVu6GNY-u9SHsTv2ob_wQ7ShPu7jS9cbtwgKAB0XzhPSNIhbMIirw1XfeJxNAqumFcYY_F-QAndVIs5mHifHI-ggNTYObPKYXg9oMlKux71f4ZUCOrk/s1200/posticon.jpg" style="display: block; padding: 1em 0; text-align: center; "><img alt="" border="0" width="200" data-original-height="1200" data-original-width="1200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgPeUxjoLUYjk5aXBYcK9Oc-qCwQTVu6GNY-u9SHsTv2ob_wQ7ShPu7jS9cbtwgKAB0XzhPSNIhbMIirw1XfeJxNAqumFcYY_F-QAndVIs5mHifHI-ggNTYObPKYXg9oMlKux71f4ZUCOrk/s200/posticon.jpg"/></a></div>
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) 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<h1 class="title toc-ignore">Bayesian priors and posteriors in 3D</h1>
</div>
<p>Once a year you travel on business to New York, always looking forward to lunch with your “year abroad” friend who moved there. Your tradition is to “flip for lunch” using the same tarnished coin you found on a street in Florence that wonderful day the two of you first met.</p>
<p>The opening image above is a visualization of the various probability distributions regarding the fairness of that old coin that could arise after four years of lunches. It presumes significant doubt about its fairness to begin with.</p>
<p>This post visualizes those distributions in three dimensions and asks what insights might have been gained.</p>
<p><strong>Background</strong></p>
<p>In the first Bayesian statistics <a href="https://www.coursera.org/learn/bayesian-statistics">Coursera course</a> <em>From Concept to Data Analysis</em>, instructor Dr. Herbert Lee, UCSC School of Engineering, writes his notes seemingly backwards (!) on a picture window, frequently looking at us through his handiwork to make sure we are getting his point. The effect is attention-grabbing; his windowboards screen-shot-worthy.</p>
<p>In the shot below Dr. Lee summarizes five important aspects of the relationship between a Binomial <em>likelihood</em> (a.k.a, a “Binomial process,” as when flipping a coin and counting the number of heads) and a Beta <em>prior</em>:</p>
<ol style="list-style-type: decimal">
<li>When the <em>prior</em> distribution for the probability <span class="math inline">\(\theta\)</span> of the Binomial process is a Beta, the <em>posterior</em> for <span class="math inline">\(\theta\)</span> is also a Beta (the <strong>conjugate</strong> property)</li>
<li>The mean of a Beta is <span class="math inline">\(\frac \alpha {\alpha + \beta}\)</span></li>
<li>The parameters of the <em>posterior</em> are <span class="math inline">\(\alpha + \#(successes)\)</span> and <span class="math inline">\(\beta + n - \#(successes)\)</span></li>
<li>The <strong>effective sample size</strong> of the <em>prior</em> is <span class="math inline">\(\alpha + \beta\)</span></li>
<li>The <em>posterior</em> mean is the weighted average of the <em>prior</em> mean and the data mean</li>
</ol>
<center>
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2YgP+Jse+VH6V6j8UvEd74W8GzajppAmU4BP0ry79mP/AJiv+8v8q7z46/8AJN7j/e/oaCuh4rof7RXieO6U6lslgJGcnnFfRHg7xdp3j7w8Z41UhhiSPOeor4YjOYTxX0B+zHcyx3N3a7mKZ6E+xoGHxs+E1rpcLa9osRAY/vEAHpXgY9+K+7PHlulz4MvkkUEBM8ivhi6XbeTAdA7D9aBMsaKP+KjsP+uy/wA6+7fDX/Is2H/XFa+E9F/5GPT/APrsv86+7fDf/Is2H/XFaBo+Yv2kR/xWEP8AvD+Zryex41S1/wCui/zr1j9pD/kcIf8AeH8zXk9l/wAhS1/66L/OgD7n8C/8ibp//XIV4J+0z/yFbb6D+de9+Bf+RN0//rkK8F/aa/5Ctt9B/OgXQ8LU5UU6mp90UuaANLw5ZPfeKrGFBnMgNfd2jWwtNFs4R/BCo/SvjP4SW/2z4iWKbd20nI9K+2VAVQB0AwKBo+ZP2mNQM+qW1uh+VcfyrwxRgCvSvjrq39o+PJbdBlYTyc+1ebUCFNJilpKAClFJS0ALRRSUwFptOpKZJ738C/8AkR7z/sIv/wCi46KPgX/yI95/2EX/APRcdFSWtjyHxf8A8jvrn/YRuP8A0Y1Y9bHi8/8AFb65/wBhG4/9GNWNmgkWikzRuoExaUU3dShqBC0UmaM0wFopM0ZoAWkNGaCc0AJRRRTAKKKKAFHWlptOBoAWlpuaM0gFzTw+xajFDcigB+7zKQjFIvyilJoAKKTNGaAFopM0ZoAWikzRmgBaKTNGaAFopM0ZoAWgUmaWgBaKTNGaAFopM0ZoAWikzRQAtFFFABRRSZoAWikzRmgBaKTNGaAFopM0ZoAWgUmaUGgBaKTNGaAFopM0ZoAWikzS0AwooopiClpKM0ALRSZpaQBRRRTAKKKKACiiigAooooAKKKKACiijNABRSZozSAWikzRmgBaUU3NKDQAtFJmjNAC0UmaM0ALSim5ozQIdRTc0ZoCw6im5ozQFh1BpuaWgLBRRRSELRmkooAXNKKbSg00AtFGaM0wCijNGaACg0ZpKGAUUUUhoKKKKBhSikpRQAUUUUEhRRRQAUUUUAFFFFAC0ZpKKAFzRSUooAWlpKM0wFopM0ZoAWkNGaKACiikpALQKSlFAC5ozRRQAZozRRQAZozRRQAZooooAKKKKACiiigAooozQAtJRmigAooooAKUUlKDQAtFJmjNAhaKTNGaAFopM0ZpgLRSZozQAtFJmjNAC0UmaM0xi0UZpM0ALRSZozSGLRSZozSAWikzRmgBaKTNGaAFopM0ZoExaKTNGaBC0UmaM0ALRSZozQAtFJmjNAC0UmaM0ALRSZoJoGhaKbuo3UDHUU3dRuoAdQTim7qCc0ALmjNJRQAuaM0lFAC5pc02lBoELRSZozQIWikzRmgBaUU3NGaAHUUmaM0ALRSZozQAtBpM0maAFopM0ZoAWikzRmgBaKbuo3UDQ6im7qN1AxTSUE0maBC0hozRmgAopKKAA0lKaSgAooooAKKKKAA0lKaSgAoNFITQMKKTNGaAFopM0ZoAWg0maCaAAdaD0puaG+7QVEryHJNRZ5p0h+Y0wUjdDqWkopDFpaSigBaSg0lAwopKUUBcKWkooC4UhoLYpjMTQIUnIphOOtGaQmmICaSkNAagB1JSbqN1Ahc0zdSk8UlADkOasLVaPrVlKBj6UdabThQMdRikzS0hiGnCkooKQ7NGc03NKKBC55pymmGgHNAEtOFRg4p249KCkPoNJmjNAwoFFFAxaKTNFAiCXqaYKkk61EDzQQx9Lnim4pSB2pkiY5ooPFJjFBSFBp4aowaXNILkq9aduxUatxzTXegVyXcKY0mDUBcg0mc0DuSNJnpSh6hNGaBXJS/NODgdagGc0uaAuS76QNUeaAeaBokLYpQ9RE80maAJxIBTvMqtml3UBcsCSpUkzVLdThIQaCrmgJKkVsis8Tc1KkvNIFIug460meaiEgxRv5oLTJs0AnNM3UbsUh3JaMio9+aAaAuShhmnDB6VBnmno3NA7ktJRmgmkMKKTNGaQC0hopCaYCU6m5ozSYDqKaTS5oAWkozRmmIDSUuaQnmgBCaQUuaTNMQtKKaWo3UAONMNKWppNAC0tNzS5oEOBpw4qPdSg0DH0maTdxTc0guOajrSFvWgGmA4jJoPNNLUA8GgBMUtKOlNzQIU0lKORSdqAEPvUZ68U9jxUeaYhaQ8mkzS5oAkTpTwtMSpc4WgZBN8orLnfLVdupKoOd1BnIjX71XoKojhqvW/NBES1nimE4qTotROwoNCJ25qIv6VI1Rkc0yRRyKetMAxTweaoiQ6lptOB4oMmLRSZpSaCUJRRmjNBQGkoJozSAKdGzRzJKhwyMGBpuaAM0Ae2xRnxj8OYdR1C4XztPUGONepxVtbePx34Hjvrb93qWnHhQPmOK88+G2t2um675GrXBW0ccxk8E5rppL+98JePF1OyXZol0cED7pBoGdLF8Y5bDw5DpVjZfaNYX5D8uSO1XLbS/EeqWL694jkayjQbgrHGRWfr8em+F7+LxdpFot0lwA5wuQDXXWFzd/FHR4zfS/YNPjGX52gigYunm11zwzPqHhqRTqFuDnA5OKzvhubrxBrEsurRul5C2Du71jal4l0H4aa5DF4euvPiJxMqnIPar3jTxTqUejw+JvBVpgEBpVQcmgZ6usLtdOg6DjGKr6t4aj1HTJUTHmYyoK968pj+Ld0fB39pXH7q8C8xkc5rhF+PPiKOYOrYB7Y7UCIfFut+KLrXG8O2KSRwxttJBx3xXqnw/8AD0+kaYi6rceb53GxjnFc612PEum2+raKim8fBnOOnrXa/wBj3s3huK6tbjdcIoOwHvQB1F14I0q6tNszKqnnbisSy1Lw7Frg0SztA86fKGxgfnWNH4tlhjS31gvHc9Oc4qn4pSewsF1PwyiSXrDJYdRQBxvi2TxXoHxdjleKWTTGk+VRyoFe7W0qavYRyRx7UZRlcV4jpWreN9S1WL+2LUSxk8sVzgV3finxnc+CNPtTDDvWbAYbc4oA7GDw6YklFowHmdVxSWvhE2tvMrOMS/ewK8p8cfEfVNJ0e21PS2bEgyy5rjV+OfiORk8yX5cjPPagD2m58IWGm2VwzkyRYLOK8/0TVLfW/EUmn+HoRFZQH9++OODVzVPiLc67oMNjocfm3EwxMw5wO9Z9yYvBnh8W2kpvv73/AI+CgyVz1oAg1+aLxj4lTwvY3nlwRvhmDYGa9X0Pw/L4N0VbO+ijurNRhiVzxXnFr8PLTV/DTX3hq/WPXceYy7sNmsiy+LHiLQ0bw94vikaRv3YZgTmgC14+8N+HfE3iSC28PRmMu2ZFTgDmtyTTBGlno2iXIZrQAyxg0zTxY+DtCn1y5TzLi6BMSn7wyP8A69ZUUY0rQrnxTb3W29uBu8pm5oA474ua9Dqt9BaRL5ctqMOFGAa86DbhVvU7+XVNSlu7j/WSHJqoBigQuaQtS103g7wJqPjW4aPTv4M5oA5kNmg5wdp57V6XqfwM8Q6VZy3c/wDqowSeleaSER3EkJ6xsVNAH1B+z5rrXegvZSybmjBxk/Suz+K+hLrngO8TA3xIWXj2rwr9nvUpIfFElsrHYwOfyr6U8QqH8N36t08hv5UAfBmz7LPJC45RippV/wCPmL/fFWdXAXX7wdvNNVlP+kxf74oA+1vhb/yI9r/uj+Qryz9p/wD48bP6j+teo/C5v+KItf8AdH8hXln7TpzY2f1H9aB9D57OfIX6CvrD4Af8igfw/lXyef8AUL9BX1d8AW/4pA/h/KgRH+0P/wAigv8An1r5Vhz5Y+lfVP7Qpz4QX6/418rQ/wCrH0oA6T4e5/4Tmz/3h/Ovt3Tv+QZb/wDXNf5V8RfD7/keLP8A3x/OvtvTm/4ltv8A9c1/lQNHx18bvl+IDH0cfzr3T4A6qL3ww0LNyirXhvxqiZ/iJMCeFIP613v7OerNFqU1i5GNoA/WgEfSPA6V8m/tEH/isU+o/ma+sN1fKH7Q5/4rJfqP5mgTPKR92l7UnaloJO8+Cv8AyUmz/wB1q+u9f/5F6/8A+vd/5V8ifBfj4kWf+61fXGvN/wAU9f8A/XB/5UFI+E9Z/wCRhvP+upqtVnWP+RgvP+uhqtQA1/umvoj9mj/UXX+7/Wvnd/umvof9mo4guv8Ad/rQB6p8Tf8AkSrv/cNfFE//AB8T/wC+f519q/Exv+KLu/8AcNfFM/8Ax8T/AO+f50D6nrf7Nx/4qq4/3v619H+NP+RQ1D/rka+b/wBm848VXH+9/Wvo3xm3/FIah/1yNAdD4bv/APkM3n/XVv51F2qW/wD+Qxd/9dG/nUVBIUopKBQAtevfs6f8jk30P8q8hr139nY48ZN9D/KgZ9H+Mj/xSN//ANcm/ka+Fr3/AJDF2f8Apqa+5vGTf8Ulf/8AXJv5Gvhm8/5C11/10NAMh3UBq0fD+hXHiHWI7C0/1kmcV6NP+z94jgt2lPRVyenpmgR5WDTWqzqNhLpWoS2lx9+M4NVD60AfRH7Mn/MV/wB5f5V3fx0/5JxP/v8A9DXAfsyHC6p/vD+Vd58dDn4cz/7/APSgrofHkXEZr3v9mv8A5C95/n+E14FF/qzXvX7NZxrF3/n+E0CPe/GX/Io6h/1yNfC19xfTf9dG/nX3L4zb/ikb/wD65mvhm+/4/pv+ujfzoBk+jceItP8A+uy/zr7r8N/8izYf9cVr4R0bP/CRWH/XVf5191+Gm/4pmw/64rQNHzN+0gf+Kvh/3x/M15RZf8hS1/66L/OvVP2jufF8P+9/U15VYD/iaWv/AF0X+dAj7m8C/wDIm2H/AFyFeDftMn/ia230H86938CnHg6w/wCuQrwX9pg51a2+g/nQHQ8OX7opTwDTU+6KV/unPAoA9e/Zz0pbzxi92Rny8/yr6suJRDayyH+BC35Cvnr9mbTDEt1dEcfNg/lXuHim7Np4Yv5QeRC2PyoGfGnxEukvPHN/Khzl8VzNS6pcPdeIryVz1lNRUyQooooAKKKKACiiigAooooA97+Bn/Ij3n/YRf8A9Fx0UfAz/kR7z/sIv/6LjopFI8e8X/8AI8a7/wBhG4/9GNWPWt4wP/Fca7/2Ebj/ANGNWMTQSPzSU3NGaYh1KKZmlBoEPzRmmZozSAfmjNMzRmgB+aM0zNKKaAXNGaKKYBmjNFFABmlFJRQwHUU3NGaQDxRTRRQA6jNNoJoAdmjNMzRmgB+aM0zNGaAH5opmaUGgB1FJmjNAC0UmaM0AOpaZmgGgB9FNzRmgB1FNzRmgQ6gU3NGaAQ+imZozQMfSU3NGaAHUU3NANADqKSigBaKSigBaBSUCgB1FJRQAtFJRQAtFJRQAtFFFMQUtJRSAWikoFAC0UZozTAKKM0ZoAKKM0ZoAKKM0ZoAKKM0ZoAKKM0hpALRSUUALRSUUALQKSigB1FNpc0ALRSZozQAtFJmjNAC0UmaM0ALRSZozQAtFJmjNAC0UZozSEFFGaM0AFKKTNANNAOzRmkzRmmAuaM0maM0ALmkNGaM0AFFGaM0gCijNFAwpRTc0oNAC0UZozQIKKM0ZoAKKM0ZoAKKM0ZoAKKM0ZoAKUUmaAaAHUZpM0ZoAXNGaTNGaYC5ozSZozQAtJRmjNIApRSZozQAtFJmjNAC0UmaM0ALRSZozQAtLTc0A0AOopM0ZoAWikzRmgBaKTNGaBC5opM0ZoAWikzRmgBaUGm5ozQA7NGabmjNADs0ZpuaM0AOzRmm5oBpgOzRmkzRmgBc0ZpM0ZoAXNGaTNBNAC5ozTc0ZoGOzRmm5ozSAdmjNNzRmgB2aM03NGaAHZozTc0ZoAdmjNNzRmgQ7NGabmjNADs0ZpuaM0AOzRmm5ozQA7NGabmjNADs0ZpuaM0AOzSE0maM0ALRSZozQMWikzRmgBaKTNGaAFopM0ZoAWikzRmgBaUGm5ozQIdmjNNzRmgB2aM03NGaAHZozTc0ZoAdmjNMzRmgQ/NGaZmjNAD80ZpmaM0APzRmmZozQMfmkzTc0ZoCwtFJmjNAxaKTNGaAFNJSE0ZoAWjNJmjNAC5ozTc0ZoAUmjNITSZoAdmjNNzQDQA6ikzRmgBTSUhNGaAFoNJmkJoAWikzRmgYtFJmjNAC0hozSE0AFI3SikbpSKiVZPvU0U5+tNFBshRRRS8UAApc0lFIYE0ZoNJQAZpM5oNJ0oAKC1JSE0wFzTSaQmkzQIUnFMJpc0hoAbmloooEFFFFABQaKQ0AOTrVlarLVhTxQMdTgabS0DHZozTaWgBc0ZpM0ZoGBOKcDSUUhjs5o6Um7FITnpQIeDk0/NQDipFPHNBVyTNO7VGDTgeKB3HUU3NGaAHUUmaM+lAEcpqFTzUstQZ5oJJsnFLTAcinA0xARTMkVLmmkCkMYTzRnmlPWm5waBMcTTSaKQ8UxCY9aKOaSkUISaO1LQaZLQmaCaRutJyaAHZpM0YNAHNAwJozSEelJzQA7NKDTM0A0APzRmm5ozQA4HFOD4FRiloAmSerKyg1QpyyEUirmkGHWlzmqSzVOsmRSHcmzRu4pgb0o3UDuO34qVWyKgBp6mgq5Nup2aizSbqAuTZpRUO6nhhikO5JkUhx2pmacDSGFFGaSlYBaKTNG6iwC5oBpu4Um6mIcTRmmbqM0xjs03NGabmgQ/rRTQaKBDjSUUlAC0Un40tABRmkNITQA+kzTCabuoFclJzRTM0ZoGSUZpmaCaAHhqTNMzS5oAfnikzTc000AKabilzSc0yRCKUCiloAcDSTSbY6Tdiq08mRQBXlk3Goj0pWGTSEcUzJsYD81Xbc1SHDVdtxSGi1moZMg1IGw3NMmcEUFlctzRmkpwpkgKcOtIaKZDH5paaDRmgyY6im5pSaYhaKbmjNAxxpKQmkzSAdS89qZmlBoACoLqzfwnPWvZdB1K1+Ifhc6E4W3+zJwxPUivGjitDRdUutMvo3tJTHHu+fHcUDPa/BskUmnXfg2++cx5ETvzWC+vaxaX0vg1SbWNmKrJkjP4/jWzHc22uWttc+Gx/p0YBlcCruoWeneLbdbVZ1g1uEDDDgk0Ac9oHwali8Srd+I5mayHzFycj860tb+JOk+FteXRtMKz6Wp2yA88dK17XxNqWl+HbnQPFaFNiEJckdfxryTw/4WtfE/iC8jNyFhViRIzdaBnd+JfCFn4x09dS8L3CgEZaBW7/SuMh+FGsm3kkuwsbL04NZra1f+AfEzWul3DSxK/C54Ne5Lrd74u8CqYovJvSvGB1oA4v4WaNqegzXMOpHybeTow6D869L0i/aK6kRZd8CdCDkVkTeH761+HM8F1MGvnB24PPSvI9N8W+JvCBltdUspZbcucOeeKAPoa7t9D163eS+h2TKMK4wK5XXtBbRPDNzqFrqBMa/dya5qx+JOkX9gI5JPsxYc7jyK1dS1/QJvDZsJ9TR4ZRj71AHS/D65XVPCJvTdK8kROQMc1Y1zRrbxjpixTMEMPOG+tedaF4q0bwjp8lvp0n2mKTqAc0/R/Gmoa94gWy02xljhY8u3NAGR8RtI1K7hg0bTIS0cYxuAzXEWHgPW7zVEsfszKc/M5XgV75PoWsDW7eS1TfCpzI23mue+JnxKtPD0i6Zpdugv2UK745BxQAui22ieBLNrOCaObVJl2nnOCa3/AAZ4Mnt9TuNR1s/aFuASqnB2g14vf+E9St9G/wCErm1AtKxDbSelaXhD416rpU0UeokyICAATnPagCz4vvtY+HPxEGqaY7JZ78tHngj0rSsb+H4p+LIta1G1WG0t8FmxjJFWfEWnXPxMvIby8H2KxGCx6ZFacNzZ2Fmnh7RbcLaY2yXKr/WgA1hZ9X8RrcQxGTRLHgr7CvOviN4rt9U1BYdEcxW8Y2NGprpvF/it/CVg2jaXIssVwDvcc9q8ecBrh5R1c5NAhKKXNGaAEPQ17n+zc22/uP8AgVeGMflP0r2/9m98Xtz9GoA9y8btnwffY/55n+Rr4fuyP7Tux381ua+2PGz58IX3P/LM/wAjXxLcf8hK6/66tQDPTvgFx4yfHof5V9Sa6/8AxT99/wBcH/lXy18Bjjxi/wBD/Kvp3XZP+Kfvuf8Alg/8qBnxBrJz4hvP+upqqp/0iL/eFT6uf+KivP8Aroarj/j5i/3hQI+0fhg//FE2v+6P5CvL/wBpps2Nn9R/WvSfhk+PBdtz/CP5CvMP2lmzZWf1H9aB9DwIn9yPoK+q/gI+PCJ/D+VfKZ/1I+gr6m+A748Jnn0/lQIX9oJ8+EV+v+NfLUJ/dj6V9P8Ax/fPhJee/wDjXy/F9wfSgDpPh+3/ABW9p/vD+dfa+nv/AMS23/65r/KvibwCceNrT/eH86+0NPk/4ltvz/yzH8qBo+TvjM+74g3B9v60fBvVvsHjmJC+3ft7+9M+MfPj2c+x/nXMeD7j7F4utLgnADAfrQI+6o5d0StnqAa+Vf2hmz4yX/e/qa+ldFvBd6LazA53RCvmj9oI58Xqff8AqaAZ5YD8tLmm5+UUZoEd98GTj4j2f+61fWuuv/xT9/8A9cH/AJV8j/Bw4+Itp/utX1hrsn/Egvuf+WD/AMqBo+H9YP8AxUF5/wBdDVarGrn/AIn95/10NVwaAGv9019C/s2NiC6/3f6189MflNfQH7OLYguv93+tAHqvxKfPgu7/ANw18XTn/SJv98/zr7K+JD58G3fP8Br40m/4+Jv98/zoGesfs5HHimf/AHv619F+Mn/4pG//AOuRr5x/Z2bHiif/AHv619D+MX/4pO/5/wCWZoA+Jr//AJDF3/10b+dRVJfH/icXf/XQ/wA6izQSLQDikzQTQApNeufs8HHjFvof5V5DmvW/2fTjxg30P8qBn0b4xf8A4pO//wCuTfyNfDt5/wAha6/66Gvtrxe//FKX3P8Ayyb+Rr4kvP8AkK3X/XQ0DZ2fwj5+Ilj6YavsS+bOn3A/6ZN/Kvjn4SHHxCsvo1fX95J/oM/P/LNv5UAj4n8bj/isr7JyN9YR+7W541OfGV9/v1hn7tAj6C/ZmbEep/7w/lXd/HFs/Dqf/f8A6V5/+zW22PU/94fyrufjc+fh5Nz/AB/0oH0PkSL/AFde8fs3HGr3f+f4TXg8X+rr3T9nM41a7/z/AAmgR7z4xf8A4pK//wCuZr4cvj/p03/XRv519t+L3z4Tvuf+WZr4kvv+P2b/AH2/nQDJtH/5GKw/66r/ADr7l8Nv/wAU1Yf9cRXwzo5/4qCw/wCuq/zr7e8Ov/xTdjz/AMsRQNHzf+0Wc+Lof97+pryuwP8AxM7b/rov869R/aHOfFkX+9/U15bYf8hO2/66L/OgR9weB3/4o+w/65CvCP2lTnVbb6D+de4eCXx4QsOf+WQrwv8AaQbOqW/0H86BniaH5RRJyh+lIv3RUkab5kU/xMB+tAj6r+AFsIfBnm7cFjjP5V0fxZ1Q6d4CvHU4LKR19qPhnYppvgi0RBjcMmuV+PupC38GiFm/1m6gfQ+Wc+ZO8ucl2LGn1GilUGDT+1MkWikzRmgBaKTNGaAFopM0ZoAWikzRmgD3z4F/8iPef9hF/wD0XHRR8C/+RHvP+wi//ouOikUjxzxgf+K413/sI3H/AKMasbNbHjD/AJHnXf8AsI3H/oxqxqCBc0ZpKKAFzSg02lFAC5ozSZozQAuaM0maM0ALmlBpuaUGmA7NGaTNGaYhc0ZpM0ZoAXNGaTNFJgLmjNJRSAcDRmmg0uaYC5oJpM0hNAC5ozSUUhi5ozSUUCFzSg02gGgB2aM0maM0wFzRmkzRmgBc0opuaAaAHUUmfejNAC0UlFAC0ZpKDQAuaM02igY7NFIKKBC0optKKAFopKKQxaKSigBaKSigB1GaSjNAC5ozSZozQAuaUU3NKDTELmjNJmjNAhc0ZpM0lADs0oNMpQaAHZozSZozQAuaM0maM0ALmjNJmjNAC5ozSZozQAuaM0maM0ALmikzRQAtFNopAOoptFADqKbRQA7NGabRQA7NGabRQA7NGabSigBc0ZpM0ZoAXNGaTNGaAFzS5puaM0AOzRmm5ozTEOzRmm5ozQA7NKDTM0oNCAdmjNJmjNMBc0ZpM0ZoAXNGaTNJmgB2aM03NGaQDs0ZpuaM0AOzSg0zNKDQA7NGabmjNADs0ZpuaM0AOzRmm5ozQA7NGabmjNADs0ZpuaM0AOzSg0zNKDQA7NGabmjNADs0ZpuaM0AOzRmm5ozQA7NGabmjNADs0ZpuaM0AOzRmm5ozQA7NGabmjNADs0ZpuaM0AOzSg0zNKDQA7NGabmjNADs0ZpuaM0AOzRmm5pc0ALmjNJmjNAhc0ZpM0ZoAXNGaTNGaAFzRmkzRmgBc0ZpM0ZoAXNKDTc0oNADs0ZpuaM0wHZozTc0ZoAdmkJpM0hNAxc0ZpM0ZpALmjNJmjNAC5ozSZozQAuaM0maM0ALmjNJmjNAC5ozSZozQAuaM0maM0CFzRmkzRmgBc0ZpM0ZoAXNGaTNGaAFzRmkzRmgBc0ZpM0hNADs0ZpmaM0DH5ozTM0ZoAfmjNMzSg0AOzRmm5ozQA7NGabmjNADs0ZpuaM0AOzRmm5oJoGOzRmmZozQIfmjNMzRmgB2aM03NGaBDs0ZpuaM0AOzRmm5ozQA6jNNzRmgY7NGaZmjNAD80ZpmaM0DH5ozTM0ZoEOJozTSaTNAD80mabmjNADs0ZpuaM0AOJpM0hNJn3oAdmlBpmfejNIB+aM03PvRn3pgOJpM03NGaQDs0ZpuaM0DHUUlFAwzS02gmgQ7NIaaDS5oGFIx+WgmoZJcDFBcURv1pBSFs0UGg6ikooAWjNJRQApNJmkzRQMKQ0U0tigB2aaTimlvSkJzQIXNITSGigAzSE0uaTigQgGaXFLmigBMUYpc0ZoATFIRTs0E0ALHU69KhSpqBi07NNBpc0DFzRmkozQAuaQmjNISKQC5pQabmjNAC7qOlIKM0DHbjTgajzmgtjvQBOGFLuqANS780DJs0u6ogacDmgCTNLn0qMGlzQMRxmoCMNUzGomOaBCg0uaZmnA0xDxQaaDS5oGBph4pxNNY0hADRjNNB5p45oEJilwRS45oNA0IBS4zSZpc0xiFRSbcUpakLUCDbSYxS7qXdk80hDCM02paTApgREUAVLikxQBHijFSFaMUgI6KeVpu2mAlJTsUhFIYA4NSLJzUZoFAyyk3OKmD5qhuwamWagLloGnA4qssnPJqQSA9KCkyYNTt1RBs0bqQyXdTs1Bup4fApjJgacDVfzKcJKkLk2aM1D5lL5lA7khNJuphek30BcfmjNM3UZoAeTSE0maSgBc0gozRmgQ7NGabmjNADs0ZpuaM0AOzRmmZozQA8nim5puaM+9MQpNJmkzSUAOBpc0wGlzQA/dS5pmfejNIB9JupuRSZoAkzmkNNzSZpgOzRmm5pM0wH5oPFNzQzcUCFbpVSY81K0hFQMctQJsjpDTjTDQQIPvVbh4FVU+/VpOBmkNCu2KiaTdSyv1qJaYySnD3pmaXNADs80UgNLTIY4UtNFLQZhRmkzRmgQuaM0maM0AKTSZoJpKAFzSim0ooAdSE4GOlFIaBnSeEvF9z4Zuj9nGRKQG+leh3Vvp9/p66toF3jWn+Yord68Y9+laWga3ceH9UF9ATI69FJ4oA9X0nxiupZ8PeP4hDNKCqTMMc9q4rxj4R1bwRqD3GnSs+nzfMsic8fhXRQy6F4+tm1HxFcraX8fEKqQMntW9ot/fQ6XLpniu3NzprjZDKwzgdqAPHtBtJvE3iW3BO4q+WJ+tfTDWzaBpEcykIgTAArz3SdC8K+Ep7jVI71dz8qrMBt+lbGteJ5tY8DvcWrmURtkKDnigZw1/rfjKTxe7KZDbyP+7B6da6u/wBYvdOsoo/ElikhlGF+XNYGjeOj4q13TdNFsIXhYBjjHQ10vii9i1nx1Z6b5qyLDgFRQBjz+BtG1eD7ZKpt1bkKBiqlj4D0G/mMCXTlU4PtXrl1aWLxxwiFQFXBFVodH0zTyzRWygyDk0AcVp3hbQtPmFvaDz2X15rT1291Pw/ppm0rTlj4wrha3tPgsLO7mZ41G/oak1K9gfR5ba7kCxD5lJoA5j4aeMPEzX0kviVGEMrYXPesb41eDFuCNfsUJkbDNjtxXOS+NtavvFEGnaVbl7WCTGQp55r1zUvEWmf8I+lnr5WJpk2kMRxQB84QeIdY1K0XR08yeMkAKB0r0jwl8OrHRbddX8WSqNo3xwuRk9609MtfDHhESXGiIt/dSncowCRVa706+8WZ1TWLpreK3ORb7scdcYoAX+2L7x7qM2k6eh02xiGFkPyhhVLVvFcXhHQ5/Diqstxg/vwc/rWb4o8f2s2lJpuhJ9lmh+V5E4JxXnU9xNcyb7mVpX/vMcmgB89xNcOXnkaQ5zknNRZpA3GDRmgkXNKDTKUUAKx+U/Sva/2dG23lx9GrxMnivY/gBMI9QmGcZ3UDPcPGcmfCV9z/AMsz/I18W3H/ACEbr/rq1fY/jGXPhS9H/TM/yNfHFx/yEbn/AK6NQNnpfwLOPF7/AEP8q+ltbk/4kN7z/wAsH/lXzJ8EW2+LXz6f0r6P1mb/AIkd7/1xb+VAI+MtV/5GC8/66GoB/wAfEX+8Kn1U/wDE+u/+uhquD/pEf+8KBH2F8NZMeDbb/dH8hXmf7SD7rO0+o/rXoXw5lx4Ptv8AdH8hXm/7RT7rO0+o/rQPoeGE/uR9BX0/8C3x4UP4fyr5fP8AqR9K+mPgi+3wsfw/lQIk+PT7vCi/X/GvmWL7g+lfSXx0fd4WX6/4182RH5R9KAOi8BnHjS0/3h/Ovsiwl/4l1vz/AMsx/KvjXwMf+KxtT/tD+dfX1jL/AMS+D/rmP5UDR8vfGBs+OZvof51xWmsRqttg4/eCux+LbZ8bTfQ/zrjdO/5Clt/10FAj7Q8HyY8J2HP/ACyFfPXx9bd4rj+v9TXvfhKXHhWx/wCuQr5/+O7bvFMf1/qaBnmeflpc0n8NGaBHdfB84+IVof8AZavqnW5P+JDfc/8ALB/5V8p/CRseP7U/7LV9Qa1L/wASO9/64t/KgaPjPVj/AMT67/66Gq4NTasf+J5d/wDXQ1ADQIRj8te9/s7Ptguv93+teBsflr3X9n19sNz/ALv9aAPUviLJnwfdc/wGvjyb/j4m/wB8/wA6+ufiDLnwjdf7hr5EmP8ApE3++f50DPU/2fG2+Jp/97+tfQXi+TPhW+5/5Zmvnj4BNt8ST/739a978Wy58LXv/XM0AfHV8f8Aib3f/XQ/zqLNSXx/4mt1/wBdD/OoqCWLmikzRmgBTXq3wCfHi5vof5V5RmvUfgM+PFjY9D/KgD6G8XS/8Utff9cm/ka+LLs/8TS6/wCuhr7I8WS58L3v/XJv5V8a3Z/4mlzj/noaCmdn8Jzj4gWR9mr62vJf9Bn5/wCWbfyr5F+FjhfHlmT6NX1ddzf6FP8A9c2/lQCPjrxm2fGF9/v1iE8Vs+MTnxden/brFPSgR71+zg+2PUv94fyruPjS+74fzf739K4H9nd9seo/7w/lXa/GSTPgKb/e/pQPofKkX+rr3D9nhtuqXf8An+GvDoz8le1/s/Pt1O7/AM/wmgR7l4tkz4Vvv+uZr4rvT/ps3++386+yfFUv/FMXv/XM18a3n/H5N/vt/OgbJtIP/FQWP/XVf519reHpP+Kdsef+WIr4n0rjXbI9hKP519meH5v+Kessf88hQCPn79oI7vFUR/2v6mvMLI41K2/66D+delfHxs+KIv8Ae/qa80syP7Stv+ug/nQI+0fBcn/FJWPP/LIV4j+0W27U7f6D+dex+DZMeFLL/rmK8X/aEfdqNv8AQfzoH0PG1OFFW9KiN1rNrAozukGfbmqijKV0PgC3+1eM7WPbuAYfzoEfYXh5Ba+HrOFeAsYrxP8AaQvHkFlaI3UdP1r223byrdIwMbVxXzP8b9aXUPGBtw3FuSP6UDPNEyEAp3am7l9aXIpiFopKKBC0U0mlFAC0UlFAC0UlFAHv3wL/AORGvP8AsIv/AOi46KT4Ff8AIjXn/YSf/wBFx0Uizx3xgf8AiuNd/wCwjcf+jGrGzWx4wP8AxXOu/wDYRuP/AEY1Y2aZAuaM0maM0ALmjNJmjNAC5ozSZozQAuaM0maM0ALmikzRQAUUUUhCijNIKWgAzRmikoAXNGaTNGaAHA0ZpAaM0ALmjNJmjNMBc0ZpM0ZoAXNGaTNGaAFzRmkzRmgBc0ZpM0ZoAXNGaTNGaAFzRmkzRmgBc0ZpM0ZoAcKWmg0ZpAOopuaM0AOopuaM0AOopuaM0AOopuaM0AOopuaM0AOopuaM0AOoFNzSg0AOopuaM0wHUU3NGaAHUA03NLmgB2aM03NGaBDs0ZpuaM0AOzRmm5ozQA7NGabmjNADs0ZpuaM0AOzQDTc0ZoAfmjNNzRmgB2aM03NGaAHZozTc0ZoAdmjNNzRmgB2aM03NGaAHZozTc0ZoAdmjNNzRmgB2aM03NGaAHZoBpuaAaYD80ZpuaM0AOzRmm5ozQA7NGabmjNADs0ZpuaM0AOzRmm5ozQA7NGabmjNADs0ZpuaM0AOBpc0wGlzQA7NGabmjNIBc0ZpM0ZoELmjNJmjNAC5ozSZozQAuaM0maM0ALmjNJmjNAC5ozSZozQAuaM0maM0AOBozTQaXNAC5ozSZozQAuaM0maM0ALmjNJmjNAC5ozSZozQAuaM0maM0ALmjNJmjNAC5pQabmgGgB2aM03NGaAHZozTc0ZoAdmjNNzRmgB2aM03NGaAHZozTc0ZoAdmlBpmaXNADs0ZpuaM0AOzRmm5ozQA7NLmmZozQA/NGaZmjNAh+aM0zNGaAH5ozTM0ZoGOzRmm5ozQA7NGabmjNADs0ZpuaM0AOzRmm5ozQA7NGabmjNADs0ZpuaM0AOzRmm5ozQA7NGabmjNADs0ZpuaM0AOzRmm5ozQA7NGabmjNADs0ZpuaM0AOzRmm5ozQA7NGabmjNADs0E03NGaAFzRmm5ozQA7NGabmjNADs0ZpuaM0AOzRmm5ozQA7NGabmjNADs0E03NBNAC5ozSZozQAuaM0maM0ALmjNJmjNAC5ozSZozQAuaM0maM0ALmjNJmkJoAdmjNNzRmgB2aTNJmjNAC5ozSZozQAuaM0maM0ALmjNJmjNAC5ozSZpCaBjs0ZpuaM0AKTRmmk0ZoAdmjNNzRmgB2aM03NGaAHZozTc0ZoAdmgGm5ozQMfupM03NGaQ7D91Jmm5ozTELmkLYpjNxULyYFAWJGmxUDPuNRs+aAaRaJRS00GnCgsWijNJmgYc0GikY4FAhCaTfTD1oxQA4vmkJpMUtMBKKWigBKM0tIRQAUUUUhBSZpaKBiGilNJQAUUUUAPQ1LUS1JQA6lzTc0ZFAxc0hPFJmkPNIA34o3etMopgSBsmnCoRTwaAJM0maTNFAC0hFANLQAwmnKaRutJ0pAS5pwNQhqduoGS5p2ahBp2aAHNUZ604nNNoC4ZopKM0wHA4pc02jNILjs0HFJmg0AMYYpyn1oIyKYeKAJgc0Hmog1ODUwHEUhpc0GkA0nFNJpxGaaVoATdRupCtJimA7fSh/WmYNFAiUOKXdUJHpRk0ATbs0oxUINLuwaBkpxTaTdmjNAC4FAApM0uaQCMtN21JRQBGVpNpqWkpgR54p6cd6MUUgJRJxTw1V6erYFA7k26l3VFupQ9A0yUH1pQRUWaM0irk2aM1FmjOKAuTbqM1GWpN1AXJc80u6od1KGoAl3Uoaot1G6gLkm7mjdUeaN1AD93NLuqMtSFqAJC2KN1RZzQDQBLmjNR5ozQBJmkpmaUGgQ+kpuaM0CHE4ozTM0ZoAfmjNN3UbqBjs0Zpu6jNADwaM0zNG6gB2aTNJupM0ALmkLYpCaYWyaYhW5qNuKfmmNQIYaaSKVjiomJJoESJ1qwGwlVYwc1Kz7RQIjY5alHWmFsnilU0DuSg0pNMzS5oAcp5p2aYtOzTIYuaM0maM0EC5ozSZozQIXNGaTNGaAFzRmkzRmgBc0oNNzSg0ALmjNJmjNAxaXrTc0ZoANxEg5wQeCO1d5ofxFnma303WFBso8DecZ9K4HvmkIyKAPXLrw3oPjORzY33kpGuSM45qvollqvheGXdm50pTgjqCK80tr25tEK2szR567TXRW/j/ULXSV0+T95HnJyOtAHdW0+ly3S39lYi2lbkELimLpKjWf7WiudtxnJyax28dadfJZWzQiBUxvYVotqejXd0UhudqBeu49aAOqfVZZYcLeAS461Fp99dwyM1/fh0PQZrmfL0t1YrfYPrupv2XTY7CV21Dc/UDdQBtahcXl5eBob3bCp6A1LLqEc0Yhu5TIgHSsGd9Li0q3kW9+bd843Uy61rRLDUoZoJvNQrhwTmgDZTxDZ2Wm3FxoWlhpouC+znNc/quiXuuWlvr2s3BS3L/NGD0FVJviHBp73MGn2imKbPOK5e/wDFGo3tmbTzD9nJzs9KAPQL7VPDnhRre80dhcsy/MhGcGuH8QeMr/WtQee1draJusanArni7FcE8UgbAwKAHFiZC7cseppM+lIWyKKAFozSUUALmjNNzRmgY7Nd98I9ei0nxQsVwdkcmcGvP80+OV4JlmiYqynIIoEfYmtRHU9DngiOTJGdp9eK+UtZ8M6lYa1dI1s5+ckEKa7vwp8Y57G1S21Ib1UABiDXVf8ACyvDd8PNuoEMncmgDnPgv4dvodakvLqJo0APJB9K9g8X6xFpvhi8kmkC7o2Vc9+K8/ufi3pVhaldOiVT2xXmPjHx/feK28p3McI/hAxQM5a7k86/nm/vuSKjX/Xx/wC8KQLQAVdWb+E5oEfV/wAPJceErf6D+Qrzz9oJ99pa/Uf1rG8N/F/+xdLjtJIQyp7e1YHjzx4PGKxqIwgQjoKBnEn/AFQ+lfSHwXk2+Fz+H8q+cSM8V6D4N+JzeFrH7K8IdfpQI9K+Nkm7wuP8+tfOUf3B9K9D8ZfEw+LLH7L5QRR6CvPgNvFAG74I48XWx/2h/OvrSymxYQf7g/lXx7ouof2Vqsd3jJQg4r1SD46LDbpEbcEqoGcGgZyXxWbd40lPsf51yGn/APITt/8AroK0fFGvf8JDrDXpXbu7YrLt38m5jl/usDQI+vfCsuPC9kM/8sxXg/xwbd4mjPv/AFrV0f40pp+mRWjwAmJQAcGuC8Z+Kh4q1T7Sy7SOgAxQM57tS5ptGaAO1+FLbfHdqfZq+l9Ymzot5/1xb+VfJvhbXR4e1yK/K7tgPFelXvxtS60+aAQKDIpXODxkUAeTaqf+J3df9dDVcGnXc32m9lm/vtmo6BA5+U17d8BH2w3H+7/WvET0rtPAfj0eEN4MYYP1yKAPf/Hsu7wrdD/YNfJ0p/0ib/eP869T8QfGD+2NOktI4VVXBBOK8qkO+VyP4iTQB6b8Cn2+Ipv97+te5+K5v+KZvP8Arma+YfBHipvCWpNcBN4Y5ORnvXdaz8aF1DTZbVIAPMUgnFAzym9P/E0uf+uh/nUNLK5mupJT/GxNNzQSOzRmm5ooAdXY/C7XY9B8ZwyTPtjk4PtxXGUDKyLIpwynIPpQM+zNQCapo8sUbBlmjO0/UV8teK/Bup6PrkwW2dldiQQprovCPxcvtHhW11HE0S4Ckg13C/FPQNQjD3sKFwO+aBnF/CbwlqR8Tx393C0cMY4yp9K938Sa1DpOg3VxO+392wX3OK86n+LukWVuwsolB7AV5j4w+Id94mYx7ysPPygYoA5vV737dq1xcN/G5xVIkYpM0ZoEe3fs/vsj1D/eH8q7L4uy7vAsw/2v6V4l4D8ef8IaLj92H84g4IrZ8WfFceJdDex8kJuOcgUDPMIz8hr2b4CSbdRu/wDPavG16V13gbxv/wAIfdSy+WHEnUEe1Aj6W8UzZ8M3n/XOvkK8P+mS/wC+f516rqnxsGoabNaiADzFxnbXk0snmyu/94k0AOgkMN3DMv8AyzYHFfV/gDxBBq/hW1MT5eNAGHpXyYcEV0XhbxrqHhWZTbOTFnlaAPRvjf4XvtQvItQtIzIo64BrzDQPDOq32rW6i0kUBwclT617BYfGTTb63EepRLyORVpfid4ctDut4EU+ooA9F0GNtP0G1hmOGjjG72r5++M+tQ6v4kENu+Vi6/nWn4m+M09zFJbacu1WGNwFeUXVzJeXLTzMWdjyaAEBAXFd98IbL7V4sSVVJ2EZ4968+BrqvBHi/wD4RK+abbu3UAfWBmPY814j4u+Feo674luL5MlZGOOD60z/AIXqCf8AUKP+A0v/AAvZR/ywX8jQMx/+FKalnp+hpl58HdQtLSSbbwgyeDW5/wAL2X/ngn5Gq998bvtdjLCkCqXXGQDQI8ku7ZrS6khfqjEVCamv7v7ZeSznq7Fqr5oAXNGaSigBaKSimAtFJRQB7/8AAn/kRbz/ALCT/wDoqOij4Ef8iLef9hJ//RUVFIo8c8Y/8jzr3/YSuP8A0a1Yua2PGJ/4rrXv+wlcf+jWrGzTJFzRmkzRmgBc0ZpM0ZoAXNGaTNGaAFzRmkzRmgBc0ZpM0ZoEOzRmm5ozSAcDS5pmaXNMB2aQmkzSZoAdmjNNzRmkA4GlzTM0uaYDs0ZpuaM0AOzRmm5ozQA7NGabmjNADs0ZpuaM0AOzRmm5ozQA7NGabmjNADs0ZpuaM0AOzRmm5ozQA7NGaaDRmgB2aM03NGaAHZozTc0ZoAdmjNNzRmgB2aM03NGaAHZozTc0ZoAdmjNNzRmgB2aXNMzS5oEOzRmm0UAOzRmm0ZoAdmlBpmaAaBj80ZpuaM0CHZozTc0ZoAdmjNNzRmgB2aM03NGaAHZozTc0ZoAdmjNNzRmgB+aM0zNGaAH5ozTM0ZoAfmjNMzQDQA/NGabmjNADs0ZpuaM0AOzRmm5ozQA7NGabmjNADs0ZpuaM0AOzQDTc0A0APzRmm5ozQA7NGabmjNADs0ZpuaM0AOzRmm5ozQA7NGabmjNADs0ZpuaM0AOzRmm5ozQA8GjNMBpc0AOzRmm5pM0APzRmmZozQIfmjNMzRmgB+aM0zNGaAH5ozTM0ZoAfmjNMzRmgB+aM0zNGaAH5ozTM0ZoAeDS5pmaM0APzRmmZozQA/NGaZmjNAD80ZpmaM0APzRmmZozQA/NGaZmjNAD80ZpmaM0APzRmmZozQA/NGabmjNADs0ZpuaM0AOzRmm5ozQA7NGabmjNADs0ZpuaM0AOzSg0zNANAD80ZpmaM0APzRmmZozQA/NGaZmlzQA7NGabmjNIQ7NGabmjNADs0ZpuaM0wHZozTM0ZoGPzRmmZozQA/NGaZmjNAD80ZpmaM0APzRmmZozQA/NGaZmjNAD80ZpmaM0APzRmmZozQA/NGaZmjNAD80ZpmaM0APzRmmZozQA/NGaZmgmgB+aM0zNGaAH5ozTM0ZoAfmjNMzRmgB2aM03NGaAHZozTc0ZoAdmjNNzSZoAfmjNMzRmgB+aM0zNGaAH5ozTM0ZoAfmjNMzRmgB+aM0zNGaAH5ozTM0ZoAfmjNMzRmgB+aM0zNGaAH5pCabmjNADs0ZpmaM0APzRmmZozQA/NGaZmjNAD80ZpmaM0APzRmmE0maB2H5oJpmaM0gHZozTc0ZoAcTSZpM0ZoAXNGaTNGaAFzRmkzRmgBc0uabmjNADs0ZpuaM0DHZozTc0ZoAdmkJ4pM01jQMY71AxJNSMabQNIip45pDQKCh4NOBpgNLmgY6ikzRmgBc0maSigBGFH0opKBC0UUUAFFFFABSGlpDQAUYpKWgAooooAKTFLRQAmKUcUUZoAetOzTRQTQMdmjNNzRmgB2aQ0gPNLigBtFOpNtACU4GkAppNAEmaCaZmlzQA8GlqMGl3UAOIzSEUmaM0AIOtOFJRmgB4NKDUeaXNAEuc0003NLmkMWikooAWjNFJQMdmim5ozTAdTWGaM0ZzQBHShqcRmmlaQhwanB6i6UmaAJ91BqINTg1ADj0pMUuaKYCYppWnUUAM5pDTqQ0ANpaSigBSaXcaZmikA/caNxFNpaAHh/Wl3VHS5oAfmlzUeaXNAD80ZpuaM0wFpd1MzSg0DHZxShs0zNJnFICYNijdUO404GgZJmlDVHmjNAXJs0m7FRbjS5oC5JuozUeaN1AXJQ1LuqPNGaBkm6jdUe6lzQBJmjNM3UZpAPzRmmZozTAfmjNMzRmgB+aM0zNGaAH7qM0zNGaYh2aM03NGaAHZozTaM0gHZpc0zNGaAH5ozUeaXNADs0ZpuaaTQA4tim5puaUc0AOzTWpaaxxQIax4qLqaVnoUZoAeoqOU1OeFqu7ZNAhgNSA1FTgaYiYGlJqNTT80AOWnZpgozQSx4NGabmjNBI7NGabmjNADs0ZpuaM0AOzRmm5ozQA7NLmmZozQA/PvRn3pmaM0DH596M+9MzRmgB2aM03NGaAFz6UdetJmjNACk5XFCExj5GI+hpM0ZoAlWeUcCRvzpDcTcr5j4+tR5ooAkaeRo9hdivpmmdup/OkooAXd607PHWm5ooEKaM0maTNADs0uaZmlzQA7NJupuaM0ALmlzTM0oNAC07IHFMzRQA7IzxTTnrk/nRSUAOXJ6k/nTuKZmlBoAdnHSkyT1pKKAAjNKgANJmjNAD2bHSmHnrSZozQAAbafmmZpc0AKaTauc4ozRmgBc4PtQWpKQ0ALx6c0YXr3pM0ZoGLQaTNGaADPHPWlGMZpM0A0CF+lLSZozTACaQ8jFBNJmkAAY70ucdKTNFADs5PNGBTaXNAxc0ZpuaKBDs0ZpCaTNMB2aM0zNGaAHZpCuTncfzozSUALkjuT+NGc0lGaQDqTNJmjNMANIcelLmjNADgeKQgUlGaAAAemKWkzRmkMXvQ3NJmigQEHHU0gJHc/nS8etFMBSfWkzRmjNACg0uB1PWm5ozQAuBupCozRnmkzzQAu0Uh46UuaTNAC5ozSZozQAuaM0maM0ALmjNJmjNAC5ozSZozQB9A/Af/kRbz/sJP/6Kioo+A3/IiXv/AGEn/wDRUVFIo6G8+F/g/UL6e8u9I8y4uJGllf7TMNzMck4D4HJ7VB/wqTwR/wBAT/ybm/8Ai6KKAD/hUngj/oCf+Tc3/wAXR/wqTwR/0BP/ACbm/wDi6KKAD/hUngj/AKAn/k3N/wDF0f8ACpPBH/QE/wDJub/4uiigA/4VJ4I/6An/AJNzf/F0f8Kk8Ef9AT/ybm/+LoooAP8AhUngj/oCf+Tc3/xdH/CpPBH/AEBP/Jub/wCLoooAP+FSeCP+gJ/5Nzf/ABdH/CpPBH/QE/8AJuf/AOLoooAP+FSeCP8AoCf+Tc3/AMXR/wAKk8Ef9AT/AMm5v/i6KKAD/hUngj/oC/8Ak3P/APF0f8Kk8E/9AX/ybn/+LoooAP8AhUngn/oC/wDk3P8A/F0f8Kk8Ef8AQF/8m5//AIuiigA/4VJ4I/6An/k3N/8AF0f8Kk8Ef9AT/wAm5v8A4uiigA/4VJ4I/wCgL/5Nz/8AxdH/AAqTwT/0Bf8Aybn/APi6KKAD/hUngn/oC/8Ak3P/APF0f8Kk8E/9AX/ybn/+LoooAP8AhUngn/oC/wDk3P8A/F0f8Kk8E/8AQF/8m5//AIuiigA/4VJ4J/6Av/k3P/8AF0f8Kk8E/wDQF/8AJuf/AOLoooAP+FSeCf8AoC/+Tc//AMXR/wAKk8E/9AX/AMm5/wD4uiigA/4VJ4J/6Av/AJNz/wDxdH/CpPBP/QF/8m5//i6KKAD/AIVJ4J/6Av8A5Nz/APxdH/CpPBP/AEBf/Juf/wCLoooAP+FSeCf+gL/5Nz//ABdH/CpPBP8A0Bf/ACbn/wDi6KKAD/hUngn/AKAv/k3P/wDF0f8ACpPBP/QF/wDJuf8A+LoooAX/AIVJ4J/6Av8A5Nzf/F0f8Kk8E/8AQF/8m5v/AIuiigA/4VJ4J/6Av/k3N/8AF0f8Kk8E/wDQF/8AJub/AOLoooAP+FSeCf8AoC/+Tc3/AMXR/wAKk8E/9AX/AMm5v/i6KKAD/hUngn/oC/8Ak3N/8XR/wqTwT/0Bf/Jub/4uiigA/wCFSeCf+gL/AOTc3/xdH/CpPBP/AEBf/Jub/wCLoooAP+FSeCf+gL/5Nzf/ABdH/CpPBP8A0Bf/ACbm/wDi6KKAD/hUngn/AKAv/k3N/wDF0f8ACpPBP/QF/wDJub/4uiigA/4VJ4J/6Av/AJNzf/F0f8Kl8E/9AX/ybm/+LoooAP8AhUvgn/oC/wDk3N/8XR/wqXwT/wBAX/ybm/8Ai6KKAD/hUvgn/oC/+Tc3/wAXR/wqXwT/ANAX/wAm5v8A4uiigA/4VL4J/wCgL/5Nzf8AxdH/AAqXwT/0Bf8Aybm/+LoooAP+FS+Cf+gL/wCTc3/xdH/CpfBP/QF/8m5v/i6KKAD/AIVL4J/6Av8A5Nzf/F0f8Kl8E/8AQF/8m5v/AIuiigA/4VL4J/6Av/k3N/8AF0f8Kl8E/wDQF/8AJub/AOLoooAP+FS+Cf8AoC/+Tc3/AMXR/wAKl8E/9AX/AMm5v/i6KKAD/hUvgn/oC/8Ak3N/8XR/wqXwT/0Bf/Jub/4uiigA/wCFS+Cf+gL/AOTc3/xdH/CpfBP/AEBf/Jub/wCLoooAP+FS+Cf+gL/5Nzf/ABdH/CpfBP8A0Bf/ACbm/wDi6KKAD/hUvgn/AKAv/k3N/wDF0f8ACpfBP/QF/wDJub/4uiigA/4VL4J/6Av/AJNzf/F0f8Kl8E/9AX/ybm/+LoooAP8AhUvgn/oC/wDk3N/8XR/wqXwT/wBAX/ybm/8Ai6KKAsH/AAqXwT/0Bf8Aybm/+Lo/4VL4J/6Av/k3N/8AF0UUBYP+FS+Cf+gL/wCTc3/xdH/CpfBP/QF/8m5v/i6KKAsH/CpfBP8A0Bf/ACbm/wDi6P8AhUvgn/oC/wDk3N/8XRRQFg/4VL4J/wCgL/5Nzf8AxdH/AAqXwT/0Bf8Aybm/+LoooCwf8Kl8E/8AQF/8m5v/AIuj/hU3gn/oC/8Ak3N/8XRRQFg/4VN4K/6Av/k3N/8AF0f8Km8Ff9AX/wAm5v8A4uiigA/4VN4K/wCgL/5Nzf8AxdH/AAqbwV/0Bf8Aybm/+LoooAP+FTeCv+gL/wCTc3/xdH/CpvBX/QF/8m5v/i6KKAD/AIVN4K/6Av8A5Nzf/F0f8Km8Ff8AQF/8m5v/AIuiigA/4VN4K/6Av/k3N/8AF0f8Km8Ff9AX/wAm5v8A4uiigA/4VN4K/wCgL/5Nzf8AxdH/AAqbwV/0Bf8Aybm/+LoooAP+FTeCv+gL/wCTc3/xdH/CpvBX/QF/8m5v/i6KKAF/4VN4K/6Av/k3N/8AF0f8Km8Ff9AX/wAm5v8A4uiigA/4VN4K/wCgL/5Nzf8AxdH/AAqbwV/0Bf8Aybm/+LoooAT/AIVN4K/6Av8A5Nzf/F0f8Km8Ff8AQF/8m5v/AIuiigVkH/CpvBX/AEBf/Jub/wCLo/4VN4K/6Av/AJNzf/F0UUBZB/wqbwV/0Bf/ACbm/wDi6P8AhU3gr/oC/wDk3N/8XRRQFkH/AAqbwV/0Bf8Aybm/+Lo/4VN4K/6Av/k3N/8AF0UUBZB/wqbwV/0Bf/Jub/4uj/hU3gr/AKAv/k3N/wDF0UUBZB/wqbwV/wBAX/ybm/8Ai6P+FTeCv+gL/wCTc3/xdFFAWQf8Km8Ff9AX/wAm5v8A4uj/AIVN4K/6Av8A5Nzf/F0UUBZC/wDCpvBX/QF/8m5v/i6P+FTeCv8AoC/+TU3/AMXRRQFkH/CpvBX/AEBf/Jqb/wCLo/4VN4K/6Av/AJNTf/F0UUBZB/wqbwV/0Bf/ACam/wDi6P8AhU3gr/oC/wDk1N/8XRRQFkH/AAqbwV/0Bf8Ayam/+Lo/4VN4K/6Av/k1N/8AF0UUBZB/wqbwV/0Bf/Jqb/4uj/hU3gr/AKAv/k1N/wDF0UUBZB/wqbwV/wBAX/yam/8Ai6P+FTeCv+gL/wCTU3/xdFFAWQf8Km8Ff9AX/wAmpv8A4uj/AIVN4K/6Av8A5NTf/F0UUBZB/wAKm8Ff9AX/AMmpv/i6P+FTeCv+gL/5NTf/ABdFFAWQf8Km8Ff9AX/yam/+Lo/4VN4K/wCgL/5NTf8AxdFFAWQf8Km8Ff8AQF/8mpv/AIuj/hU3gr/oC/8Ak1N/8XRRQFkH/CpvBX/QF/8AJqb/AOLo/wCFTeCv+gL/AOTU3/xdFFAWQf8ACpvBX/QF/wDJqb/4uj/hU3gr/oC/+TU3/wAXRRQFkH/CpvBX/QF/8mpv/i6P+FTeCv8AoC/+TU3/AMXRRQFkH/CpvBX/AEBf/Jqb/wCLo/4VP4K/6Av/AJNTf/F0UUBZB/wqfwV/0Bf/ACam/wDi6P8AhU/gr/oC/wDk1N/8XRRQFkH/AAqfwV/0Bf8Ayam/+Lo/4VP4K/6Av/k1N/8AF0UUBZB/wqfwV/0Bf/Jqb/4uj/hU/gr/AKAv/k1N/wDF0UUBZB/wqfwV/wBAb/yam/8Ai6P+FT+Cv+gN/wCTU3/xdFFAWQf8Kn8Ff9Ab/wAmpv8A4uj/AIVP4K/6A3/k1N/8XRRQFkH/AAqfwV/0Bv8Ayam/+Lo/4VP4K/6Av/k1N/8AF0UUBZB/wqfwV/0Bf/Jqb/4uj/hU/gr/AKAv/k1N/wDF0UUBZB/wqfwV/wBAX/yam/8Ai6P+FT+Cv+gL/wCTU3/xdFFAWQf8Kn8Ff9AX/wAmpv8A4uj/AIVP4K/6Av8A5NTf/F0UUBZB/wAKn8Ff9AX/AMmpv/i6P+FT+Cv+gL/5NTf/ABdFFAWQf8Kn8Ff9AX/yam/+Lo/4VP4K/wCgL/5NTf8AxdFFAWQf8Kn8Ff8AQF/8mpv/AIuj/hU/gr/oC/8Ak1N/8XRRQFkH/Cp/BX/QF/8AJqb/AOLo/wCFT+Cv+gL/AOTU3/xdFFAWQf8ACp/BX/QF/wDJqb/4uj/hU/gr/oC/+TU3/wAXRRQFkH/Cp/BX/QF/8mpv/i6P+FT+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style="width:60.0%" /></p>
</center>
<p>Also noteworthy but unwritten:</p>
<ul>
<li>“Points 4 and 5 can help a practitioner select <em>prior</em> values for <span class="math inline">\(\alpha\)</span> and <span class="math inline">\(\beta\)</span>.” (Demonstrated below.)</li>
<li>“<span class="math inline">\(\alpha + \beta\)</span> is the <strong>effective sample size of the <em>prior</em></strong> because the sum <span class="math inline">\(\alpha + \beta + n\)</span> forms the denominator in the weighted average formula for the <em>posterior</em> mean.” (Where his pen is pointing. Enlightening!)</li>
<li>The <strong>posterior distribution</strong> is a <em>distribution for <span class="math inline">\(\theta\)</span></em> because <span class="math inline">\(\theta\)</span> is <strong>the determining factor</strong> of the Binomial process of interest.</li>
</ul>
<p>However, the most illuminating point I heard him make was one I’d actually <em>misheard!</em></p>
<p>When Dr. Lee discussed the mathematically natural conjugate relationship between the Binomial and the Beta, I thought I’d heard him say, “The Beta distribution is conjugate to the Binomial <em>likelihood</em>.” From “conjugate to” I imagined “perpendicular to,” picturing the data observations rising at right angles from the <em>prior</em> in the <span class="math inline">\(x-y\)</span> plane, like an <a href="https://forums.aaca.org/topic/319667-identifying-vintage-bumper-jack-help/">old bumper jack</a> whose base forms the <em>prior</em>, whose shaft houses the data, and whose lever, ratcheted by the practitioner, hoists the <em>posterior</em> to sequentially higher planes with each new success.</p>
<p>Let’s graph that.</p>
<p><strong><em>The process</em></strong></p>
<p>Flip a coin <code>n = 4</code> times and count the number of heads (“successes”).</p>
<p><strong><em>The prior</em></strong></p>
<p>Model “coin fairness uncertainty” with Beta parameters <span class="math inline">\(\alpha = 2\)</span> and <span class="math inline">\(\beta = 2\)</span>. A Beta <em>prior</em> with those parameters satisfies two conditions:</p>
<ul>
<li>The <em>prior</em> mean is 1/2, reflecting our <em>apriori</em> expectation of a fair coin.</li>
<li>The <strong>effective sample size</strong> of the <em>prior</em> and the sample size of the data are the same, thereby giving equal weight to the <em>prior</em> mean and the data mean when reassessing our fairness expectation after seeing the data.</li>
</ul>
<p>Using algebra and the formulas in points 2 and 4 above, we can solve for <span class="math inline">\(\alpha\)</span> and <span class="math inline">\(\beta\)</span> – or just guess.</p>
<p><strong><em>The graph</em></strong></p>
<p>Using the base <span class="math inline">\(R\)</span> <code>persp</code> function,<a href="#fn1" class="footnote-ref" id="fnref1"><sup>1</sup></a> the figure below visualizes the <em>prior</em> distribution and the five possible <em>posteriors</em> in three dimensions. It is the opening 2D image, now in 3D.<a href="#fn2" class="footnote-ref" id="fnref2"><sup>2</sup></a></p>
<p><img src="data:image/png;base64,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" width="672" style="display: block; margin: auto;" /></p>
<p><strong>Takeaways</strong></p>
<p><strong><em>A pair of quick observations</em></strong></p>
<ul>
<li><strong>Four heads</strong> in four flips would give us reason to believe the coin is biased towards heads – illustrated by the shifting of the mode from the center of the <em>prior</em> to the right in the red <em>posterior</em> at the top.</li>
<li><strong>Two heads</strong> in four flips would increase our belief in the fairness of the coin – illustrated by the movement of mass away from the tails of the <em>prior</em> toward the center of the green <em>posterior</em> in the middle.</li>
</ul>
<p>Arguably those points could have been made from the opening 2D graph. However, the separateness of the planes seems to lend greater emphasis to the individuality of the <em>posteriors.</em></p>
<p><strong><em>New insight</em></strong></p>
<ul>
<li>Each <em>posterior</em> can be envisioned as a contour on a three-dimensional surface.</li>
<li>The space between the planes suggests the existence of latent factors driving the potential real-life outcomes.</li>
</ul>
<p><strong>Some closing questions</strong></p>
<p>Instead of the top plane being at a height of 4, what if we had 40 or 400 or 4000 data points? How would the surface change?</p>
<p>If we were more confident in the <em>apriori</em> fairness of the <em>Firenze</em> coin, how would the surface change?</p>
<p>Look for answers in a future post.</p>
<hr />
<blockquote>
<p><font size="2">The end of business today, 12/20/2020, marks 251.645 months since the end of the last millenium.<br />
Generated with <a href="https://rmarkdown.rstudio.com/">Rmarkdown</a> in <a href="https://rstudio.com/">RStudio</a>. </font></p>
</blockquote>
<hr />
<div id="r-environment" class="section level3">
<h3>R Environment</h3>
<pre><code>R version 4.0.3 (2020-10-10)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows 10 x64 (build 19041)
Matrix products: default
locale:
[1] LC_COLLATE=English_United States.1252
[2] LC_CTYPE=English_United States.1252
[3] LC_MONETARY=English_United States.1252
[4] LC_NUMERIC=C
[5] LC_TIME=English_United States.1252
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] mondate_0.10.01.02
loaded via a namespace (and not attached):
[1] compiler_4.0.3 magrittr_1.5 tools_4.0.3 htmltools_0.5.0
[5] yaml_2.2.1 stringi_1.4.6 rmarkdown_2.3 knitr_1.28
[9] stringr_1.4.0 xfun_0.14 digest_0.6.25 rlang_0.4.6
[13] evaluate_0.14 </code></pre>
</div>
<div class="footnotes">
<hr />
<ol>
<li id="fn1"><p>Color scheme by <a href="https://personal.sron.nl/~pault/#fig:scheme_rainbow_discrete_all">Paul Tol</a>.<a href="#fnref1" class="footnote-back">↩︎</a></p></li>
<li id="fn2"><p>The image at the top of this post was created from the same <span class="math inline">\(R\)</span> code with two differences – <code>persp</code> arguments <code>phi = 90</code> and <code>r = sqrt(10000)</code> – taking the viewer to a 10000-foot perspective, effectively producing the 2D <em>prior</em>/<em>posterior</em> combination graphs more commonly seen (as <a href="https://stackoverflow.com/questions/54274850/plots-of-prior-and-posterior-distributions-for-different-models">here</a>) – although most of the combination graphs you find will be of multiple priors and only one of the many possible Binomial outcomes rather than, in this post, the other way around.<a href="#fnref2" class="footnote-back">↩︎</a></p></li>
</ol>
</div>
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Murphy Danhttp://www.blogger.com/profile/02252526252924091700noreply@blogger.com0tag:blogger.com,1999:blog-7342884208835933013.post-73503362231528618722020-12-06T10:41:00.015-08:002020-12-12T04:05:43.523-08:00Colorizing points in a base R plot<div class="separator" style="clear: both;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhJuR_k95iWsE319GzkqjEZOi7S2gj-PYLLPFdW6VL2QHCw5xTzzo3XkGsxQ10OOQ0XgvuoGZK6vb988PM9bVJS78yapFpM6oyp8oZOjdHuor1kE8b07r6EbqKP6EMRX0gyjt5RSQGlAOfZ/s600/disc.jpg" style="display: block; padding: 1em 0; text-align: center; "><img alt="" border="0" width="200" data-original-height="600" data-original-width="600" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhJuR_k95iWsE319GzkqjEZOi7S2gj-PYLLPFdW6VL2QHCw5xTzzo3XkGsxQ10OOQ0XgvuoGZK6vb988PM9bVJS78yapFpM6oyp8oZOjdHuor1kE8b07r6EbqKP6EMRX0gyjt5RSQGlAOfZ/s200/disc.jpg"/></a></div>
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) 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<h1 class="title toc-ignore">Colorizing points in a base <span class="math inline">\(R\)</span> plot</h1>
</div>
<p>By default, base <span class="math inline">\(R\)</span> <code>plot</code> uses hollow circles for points, perfectly adequate for a single data set, but less so for multivariate data because the edges are too thin for color to stand out well. My go-to option: set the <code>pch</code> argument to 16 and the <code>col</code> argument to the color of my choice.</p>
<p><strong><font size="3">Background</font></strong></p>
<p><code>pch</code> is the argument that specifies the shape of a point in a <code>plot</code>. The three basic selections for a <strong>circle</strong> shape are:</p>
<table>
<colgroup>
<col width="40%"></col>
<col width="59%"></col>
</colgroup>
<thead>
<tr class="header">
<th>pch</th>
<th>colorizing options</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td><strong>1</strong> (or the default when <strong>pch</strong> is not given)</td>
<td>the edge color can be changed but not the interior</td>
</tr>
<tr class="even">
<td><strong>16</strong> (a so-called “<strong>solid circle</strong>”)</td>
<td>the interior can be changed but not the edge</td>
</tr>
<tr class="odd">
<td><strong>21</strong> (a so-called “<strong>filled circle</strong>”)</td>
<td>the interior and the edge can be different</td>
</tr>
</tbody>
</table>
<p>The <code>pch=16</code> and <code>pch=21</code> <strong>colorizing options</strong> apply to other shapes that also fall into their respective “pch groups”: <strong>15-20</strong> for <strong>solid shapes</strong> and <strong>21-25</strong> for <strong>filled shapes</strong>. To see which shapes correspond to which <code>pch</code> value, check out <code>help("points")</code> as well as many posts on the web <a href="http://www.sthda.com/english/wiki/r-plot-pch-symbols-the-different-point-shapes-available-in-r">such as this one</a>.</p>
<p>Circles and squares are illustrated in light and dark backgrounds below.<a href="#fn1" class="footnote-ref" id="fnref1"><sup>1</sup></a> IMO, points “pop” from their interior, not from their edge.<a href="#fn2" class="footnote-ref" id="fnref2"><sup>2</sup></a></p>
<p><img src="data:image/png;base64,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" 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" width="80%" style="display: block; margin: auto;" /></p>
<p><strong><em>Notice how</em></strong></p>
<ul>
<li>For the default (<code>pch == 1</code>)
<ul>
<li>the interior color cannot be changed and is always transparent so the background always shows through</li>
<li>the default edge color is black so the point virtually disappears on a dark background</li>
</ul></li>
<li>For solid shapes (<code>pch in 15:20</code>)
<ul>
<li><code>col</code> specifies <em>both the interior and edge colors</em>, necessarily the same</li>
<li><code>bg</code> – specified or not – <em>has no impact</em></li>
</ul></li>
<li>For filled shapes (<code>pch in 21:25</code>)
<ul>
<li><code>col</code> specifies the <em>edge color</em></li>
<li><code>bg</code> specifies the <em>interior color</em>, defaulting to “transparent” if unspecified<a href="#fn3" class="footnote-ref" id="fnref3"><sup>3</sup></a></li>
</ul></li>
</ul>
<p><strong><font size="3">Example</font></strong></p>
<p>Here is a bivariate example using the <code>mtcars</code> dataset in <span class="math inline">\(R\)</span> and Paul Tol’s “bright” palette.<a href="#fn4" class="footnote-ref" id="fnref4"><sup>4</sup></a> <a href="#fn5" class="footnote-ref" id="fnref5"><sup>5</sup></a></p>
<pre class="r"><code>green = "#228833"
magenta = "#AA3377"
# build plot title -- see stackoverflow citation in footnote
a = quote(paste("miles per gallon vs displacement (i"))
b = quote(n^3)
c = quote(")")
e <- substitute(a * b * c, list(a = a, b = b, c = c))
with(mtcars,
plot(disp, mpg
, pch = 16
, col = c(green, magenta)[as.numeric(vs)+1]
, main = e
)
)
legend("topright", c("v-engine", "straight-block"), col = c(green, magenta), pch = 16)</code></pre>
<p><img 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" width="672" style="display: block; margin: auto;" /></p>
<p>Not only do smaller engines get better gas mileage, but high-displacement straight-blocks were nonexistent in 1973.</p>
<p><strong><font size="3">Bottom line</font></strong></p>
<p>Use base <span class="math inline">\(R\)</span>’s default black circles to quickly visualize sequential data.</p>
<p>For colored circles use <code>pch = 16</code> and <code>col = color_of_your_choice</code>.</p>
<p>Use <code>pch = 21</code> when it is useful to differentiate a point’s edge from its interior.</p>
<p>Use color-blind friendly colors whenever possible.</p>
<p>Try <code>pch = "."</code> for dots when you have many points but you don’t want lines.</p>
<p><img 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" width="50%" style="display: block; margin: auto;" /></p>
<p><strong>Postscript</strong></p>
<p>The <a href="https://en.wikipedia.org/wiki/Complementary_colors">complementary colors</a> <strong>green</strong> (#228833) and <strong>magenta</strong> (#AA3377) used in this post come from Paul Tol’s color-blind friendly <a href="https://personal.sron.nl/~pault/#sec:qualitative"><em>bright</em> color palette</a>.<a href="#fn6" class="footnote-ref" id="fnref6"><sup>6</sup></a> Tol’s <a href="https://personal.sron.nl/~pault/">“Notes” page</a> is worth visiting for other helpful colorizing advice. This non-color-blind author would be interested in reader feedback regarding the distinguishability of the colors used in this post.</p>
<hr />
<blockquote>
<p><font size="2">The end of business today, 12/12/2020, marks 251.387 months since the end of the last millenium.<br />
Generated with <a href="https://rmarkdown.rstudio.com/">Rmarkdown</a> in <a href="https://rstudio.com/">RStudio</a>. </font></p>
</blockquote>
<hr />
<p><strong>R Environment</strong></p>
<pre><code>R version 4.0.3 (2020-10-10)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows 10 x64 (build 19041)
Matrix products: default
locale:
[1] LC_COLLATE=English_United States.1252
[2] LC_CTYPE=English_United States.1252
[3] LC_MONETARY=English_United States.1252
[4] LC_NUMERIC=C
[5] LC_TIME=English_United States.1252
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] mondate_0.10.01.02
loaded via a namespace (and not attached):
[1] compiler_4.0.3 magrittr_1.5 tools_4.0.3 htmltools_0.5.0
[5] yaml_2.2.1 stringi_1.4.6 rmarkdown_2.3 knitr_1.28
[9] stringr_1.4.0 xfun_0.14 digest_0.6.25 rlang_0.4.6
[13] evaluate_0.14 </code></pre>
<div class="footnotes">
<hr />
<ol>
<li id="fn1"><p>Regarding the color of the default background, the italicised phrases are from <span class="math inline">\(R\)</span> help pages: <em>normally “white”</em> from <code>help("par")</code>, <em>often transparent</em> from <code>help("frame")</code><a href="#fnref1" class="footnote-back">↩︎</a></p></li>
<li id="fn2"><p>Called “border” in <span class="math inline">\(R\)</span><a href="#fnref2" class="footnote-back">↩︎</a></p></li>
<li id="fn3"><p>Per <code>help("par")</code>: “For many devices the initial value [of the plot background] is set from the <code>bg</code> argument of the device, and for the rest it is normally "white".”<a href="#fnref3" class="footnote-back">↩︎</a></p></li>
<li id="fn4"><p>Okabe and Ito have a wonderful site that discusses Color Universal Design: <a href="https://jfly.uni-koeln.de/color/" class="uri">https://jfly.uni-koeln.de/color/</a>. Okabe/Ito and Tol palettes can be displayed with <span class="math inline">\(R\)</span> code downloadable from here: Goedhart, Joachim. (2019, August 29). Material related to the blog “Dataviz with Flying Colors”. Zenodo. <a href="http://doi.org/10.5281/zenodo.3381072" class="uri">http://doi.org/10.5281/zenodo.3381072</a><a href="#fnref4" class="footnote-back">↩︎</a></p></li>
<li id="fn5"><p>Technique for superscript in title from <a href="https://stackoverflow.com/questions/34193276/concatenate-several-math-expressions-in-r" class="uri">https://stackoverflow.com/questions/34193276/concatenate-several-math-expressions-in-r</a><a href="#fnref5" class="footnote-back">↩︎</a></p></li>
<li id="fn6"><p>For additional perspectives on color-impaired visualizations, see <a href="https://thenode.biologists.com/data-visualization-with-flying-colors/research/" class="uri">https://thenode.biologists.com/data-visualization-with-flying-colors/research/</a> and <a href="https://venngage.com/blog/color-blind-friendly-palette/" class="uri">https://venngage.com/blog/color-blind-friendly-palette/</a> and <a href="https://jfly.uni-koeln.de/color/" class="uri">https://jfly.uni-koeln.de/color/</a>.<a href="#fnref6" class="footnote-back">↩︎</a></p></li>
</ol>
</div>
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Murphy Danhttp://www.blogger.com/profile/02252526252924091700noreply@blogger.com4tag:blogger.com,1999:blog-7342884208835933013.post-60661643444277908262020-05-30T14:14:00.002-07:002020-05-30T14:44:11.540-07:00Mimic Excel's Conditional Formatting in R<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjJdGdkGHTGnDYp68ojH9cz7A_xmO3E3qhj4n3berhgkwlSC0Cj5DbUfp8loQjWbmqp_VfZW09aHs12b4FQfQ0G9USyerszHpZAt7PanEXlDwT4mu0vS5-U_fOp5ycJVVglN_92mYUh8f6y/" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="797" data-original-width="1205" height="133" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjJdGdkGHTGnDYp68ojH9cz7A_xmO3E3qhj4n3berhgkwlSC0Cj5DbUfp8loQjWbmqp_VfZW09aHs12b4FQfQ0G9USyerszHpZAt7PanEXlDwT4mu0vS5-U_fOp5ycJVVglN_92mYUh8f6y/w200-h133/GenInsLinkRatios.png" width="200" /></a></div>
<div>
<br /></div>
The <b>DT</b> package is an interface between R and the JavaScript DataTables library (<a href="https://rstudio.github.io/DT/" target="_blank">RStudio DT documentation</a>). In Example 3 (at <a href="https://rstudio.github.io/DT/010-style.html" target="_blank">this page</a>) they show how to heatmap-format a table. This post modifies the example to<br />
<div>
<ol style="text-align: left;">
<li>format each column individually</li>
<li>shade in green rather than red</li>
<li>use base R syntax rather than piping</li>
<li>omit the extra accoutrements of the displayed table (from the answer to <a href="https://stackoverflow.com/questions/44416606/r-datatable-in-dt-the-shiny-filter-none-option-doesnt-work" target="_blank">this stackoverflow post</a>), except</li>
<li>include a title.</li>
</ol>
<div>
Here we generate data similar to that in Example 3, but with average values growing by column</div>
<div>
<pre style="text-align: left;"><span style="font-family: courier;">set.seed(12345)
df = as.data.frame(
cbind(round(rnorm(10, mean = 0), 3),
round(rnorm(10, mean = 4), 3),
round(rnorm(10, mean = 8), 3),
round(rnorm(10, mean = 16), 3),
round(rnorm(10, mean = 32), 3),
sample(0:1, 10, TRUE)))</span></pre>
</div>
<div>
Using the code in the example -- modified to green -- the darker values naturally appear in columns <b>V4</b> and <b>V5</b>.<br />
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh6T-c1zjOPo2aYCbwQTaonZfTtDQ-iT2NKaFsFdJidW9E084tf_7YTAvcIUBUtqY5pi3QFwv5W0GRxWVKYNsZV8D0BiXoCvXH7a5mwo6dF8UvIgZpr1hRxNQ4c4CUFjpXAVQOCa8fDhIdE/" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1148" data-original-width="1180" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh6T-c1zjOPo2aYCbwQTaonZfTtDQ-iT2NKaFsFdJidW9E084tf_7YTAvcIUBUtqY5pi3QFwv5W0GRxWVKYNsZV8D0BiXoCvXH7a5mwo6dF8UvIgZpr1hRxNQ4c4CUFjpXAVQOCa8fDhIdE/s320/Example3.png" width="320" /></a></div>
<div>
<br /></div>
<div>
But that's not what we want.</div>
<div>
<br /></div>
<div>
For each column to have it's own scale, simply apply RStudio's algorithm to each column of <span style="font-family: courier;">df</span> in a loop. The trick to notice is that <span style="font-family: courier;">formatStyle</span> wants a <span style="font-family: courier;">datatable</span> object as its first argument, and produces a <span style="font-family: courier;">datatable</span> object as its result. Therefore, start off with a plain-Jane <span style="font-family: courier;">datatable</span> and successively format each column, saving the result each time. Almost like building a <b>ggplot</b>. At the end, view the final result.</div>
<div>
<pre style="text-align: left;"><span style="font-family: courier;"># Start with a (relatively) plain, unformatted datatable object
dt <- DT::datatable(df,
options = list(dom = 't', ordering = FALSE),
caption = "Example 3 By Column")
# Loop through the columns formatting according to that column's distribution
for (j in seq_along(df)) {
# Create breaks for shading column values high to low
brks <- stats::quantile(x <- df[[j]], probs = seq(.05, .95, .05), na.rm = TRUE)
# Create shades of green for backgrounds
y <- round(seq(255, 40, length.out = length(brks) + 1), 0)
clrs <- paste0("rgb(", y, ", 255,", y, ")")
# Format cells in j-th column
dt <- DT::formatStyle(dt, j, backgroundColor = DT::styleInterval(brks, clrs))
}
dt</span></pre>
</div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgRha9DCHAkNSI9RiisFJtj2_v5feB8TBGyWveO4VqDzm27QaZveSnajxS4RcJ2okQ0qELgZZZsLgP6OAXSjG6yQpgNAzOp5J2ScDfCbaoh90nEFWS9Z3rt5BG1saAaqf2Q3oFZeRSwyVNq/" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="892" data-original-width="1180" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgRha9DCHAkNSI9RiisFJtj2_v5feB8TBGyWveO4VqDzm27QaZveSnajxS4RcJ2okQ0qELgZZZsLgP6OAXSjG6yQpgNAzOp5J2ScDfCbaoh90nEFWS9Z3rt5BG1saAaqf2Q3oFZeRSwyVNq/s320/Example3ByColumn.png" width="320" /></a></div>
<div>
<br /></div>
<div>
Actuaries in the crowd might recognize the image at the top of the post as the table of link ratios from the <span style="font-family: courier;">GenIns</span> dataset in the <a href="https://cran.r-project.org/web/packages/ChainLadder/index.html" target="_blank">ChainLadder</a> package. There do not appear to be any distinctive trends in the ratios by age.</div>
<div>
<br /></div>
<div>
<br />
<div>
<br /></div>
<div>
<br /></div>
</div>
</div>
Daniel Murphyhttp://www.blogger.com/profile/01412558765055222349noreply@blogger.com0tag:blogger.com,1999:blog-7342884208835933013.post-35839158377242369832020-05-15T15:31:00.001-07:002020-05-15T17:18:30.455-07:00How to Add a Vignette to a Package in RStudio<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgy4yTBqaEX2DjvcYjbjsaHabgyI2K6qXF6lbY2Nw9uJ3RBXCEwCKaL65rktjeB5egDZIVDpqRuzZkNbVnaHjqiAscZ2Jh9DX0I_ftUktkcFDSPTFarIrtHCsi0Y-VU9Yvj8PQM5t0wLx-i/" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="2108" data-original-width="2043" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgy4yTBqaEX2DjvcYjbjsaHabgyI2K6qXF6lbY2Nw9uJ3RBXCEwCKaL65rktjeB5egDZIVDpqRuzZkNbVnaHjqiAscZ2Jh9DX0I_ftUktkcFDSPTFarIrtHCsi0Y-VU9Yvj8PQM5t0wLx-i/w194-h200/vignette.jpeg" width="194" /></a></div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
R package vignettes are user-friendly ways to demo your package's capabilities. They can also be helpful documentation for your own reference when modifying the package in the future -- "what was I thinking there?"</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
The easiest way to create a vignette in RStudio is using File | New File | R Markdown | From Template | Package Vignette (HTML). Write your RMarkdown document. {<b>Note</b>: Be sure to copy the "title" of your vignette to where "Vignette Title" shows in the section below:</div>
<blockquote class="tr_bq" style="clear: both; text-align: left;">
<span style="font-family: "courier new" , "courier" , monospace;">vignette: ><br />
%\VignetteIndexEntry{Vignette Title}</span></blockquote>
<div class="separator" style="clear: both; text-align: left;">
</div>
<div class="separator" style="clear: both; text-align: left;">
}</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
After that, build your package. But if you use the typical procedure for developing a package in RStudio, <b>your vignette will not show up</b>. [Pulling hair out] Let me explain.</div>
<div class="separator" style="clear: both; text-align: left;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
My typical procedure for <b>build</b>ing package <span style="font-family: "courier new" , "courier" , monospace;">myPackage</span> in RStudio is to use two menu items in the <b>Build</b> pane</div>
<div class="separator" style="clear: both; text-align: left;">
</div>
<ul style="text-align: left;">
<li><span style="font-family: "courier";">Check</span>, then</li>
<li><span style="font-family: "courier";">Install and Restart</span></li>
</ul>
<div class="separator" style="clear: both; text-align: left;">
<span style="font-family: "courier";">Check</span> makes sure everything checks out correctly. This includes processing vignettes in the <span style="font-family: "courier";">myPackage/vignettes</span> directory, which you can see in multiple areas of <span style="font-family: "courier new" , "courier" , monospace;">Check</span>'s output in that pane:</div>
<blockquote class="tr_bq" style="clear: both;">
<span style="font-family: "courier new" , "courier" , monospace;">...<br />
- installing the package to build vignettes<br />
v creating vignettes (7.4s)<br />
...<br />
* checking files in 'vignettes' ... OK<br />
...<br />
* checking for unstated dependencies in vignettes ... OK<br />
* checking package vignettes in 'inst/doc' ... OK<br />
* checking re-building of vignette outputs ... OK<br />
...</span></blockquote>
<div class="separator" style="clear: both; text-align: left;">
</div>
<div class="separator" style="clear: both;">
</div>
<div class="separator" style="clear: both; text-align: left;">
When <span style="font-family: "courier";">R CMD check succeeded</span> appears at the bottom of that output, click <span style="font-family: "courier";">Install and Restart</span> in the <b>Build</b> pane again and <span style="font-family: "courier new" , "courier" , monospace;">myPackage</span> will be recompiled, reloaded, and ready to go ... all except for the vignettes, because when you look for them, they won't be there:</div>
<blockquote class="tr_bq" style="clear: both;">
<span style="font-family: "courier new" , "courier" , monospace;"><span style="color: blue;">> browseVignettes("myPackage")</span><br />
<span style="color: red;">No vignettes found by browseVignettes("myPackage")</span><br />
<span style="color: blue;">></span> </span></blockquote>
<div class="separator" style="clear: both;">
It turns out, according to RStudio's slightly-outdated <a href="http://r-pkgs.had.co.nz/vignettes.html" target="_blank">online documentation</a> this behavior is to be expected because, presumably, developers don't want to worry about vignettes in the typical <b>code/Install-and-Restart/re-code</b> development cycle [I get that]; to wit: </div>
<blockquote class="tr_bq" style="clear: both;">
<span style="background-color: white; color: #333333; font-family: "helvetica neue" , "helvetica" , "arial" , sans-serif; font-size: 14px;">RStudio’s “Build & reload” does not build vignettes to save time.</span></blockquote>
<div class="separator" style="clear: both;">
{<b>Note</b>: "Build and reload" has been renamed "Install and Restart" in today's RStudio Version 1.2.5042.}</div>
<div class="separator" style="clear: both;">
<br /></div>
<div class="separator" style="clear: both;">
In any event, the correct workflow was pointed out in 2018 by <a href="https://stackoverflow.com/users/2554330/user2554330" target="_blank">user2554330</a> in a <a href="https://stackoverflow.com/questions/49476812/error-in-browsevignettes-no-vignettes-found" target="_blank">stackoverflow post</a></div>
<blockquote class="tr_bq" style="clear: both;">
No. Go to the Build pane, then in the "More" dropdown, choose "Build Source Package". This will create a file with extension .tar.gz, which you can distribute to others. You install it using "Packages | Install | Install from... | Package Archive file". – user2554330 Mar 25 '18 at 19:10</blockquote>
<div class="separator" style="clear: both;">
That worked great. Thank you RStudio for software that tends to simply get it done one way or another, and thank you user2554330 for explaining how to get it done for vignettes.</div>
<div class="separator" style="clear: both;">
<br /></div>
Murphy Danhttp://www.blogger.com/profile/02252526252924091700noreply@blogger.com0tag:blogger.com,1999:blog-7342884208835933013.post-87894754168470786312020-04-24T15:19:00.002-07:002020-04-25T15:43:37.795-07:00New R Package 'foo' -- Updated<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfH-jc9xwi87EYlA2X_cvE59o7RJzm7Gy68e9Pj8ZTeZRx8wB2wuLedrQqe3mZmC7ghV3j5Y9AM-_EnTew4VMYqqqDOhezTs3wUBU7AmQUrcKMAghLTGXICvRIGv_ReBR1X9Rpc_Ni7QB_/s1600/package1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1600" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfH-jc9xwi87EYlA2X_cvE59o7RJzm7Gy68e9Pj8ZTeZRx8wB2wuLedrQqe3mZmC7ghV3j5Y9AM-_EnTew4VMYqqqDOhezTs3wUBU7AmQUrcKMAghLTGXICvRIGv_ReBR1X9Rpc_Ni7QB_/s200/package1.jpg" width="200" /></a></div>
<br />
RUN THESE LINES IN AN R SESSION ...<br />
<hr />
<blockquote class="tr_bq">
<span style="font-family: "courier new" , "courier" , monospace;"># Navigate to where you want your folder to be located<br />
setwd("C:/Users/chief/Documents/Github")<br />
# Run create_package in 'usethis' package and read below what happens<br />
usethis::create_package("foo")<br />
# Messages show up in the console including this line<br />
# ✔ Opening 'foo/' <span style="background-color: yellow;">in new RStudio session</span></span></blockquote>
WHEN SWITCHED TO THE NEW SESSION, RUN THESE LINES / EXECUTE THESE STEPS ...<br />
<hr />
<blockquote class="tr_bq">
<span style="font-family: "courier new" , "courier" , monospace;"># Add a test environment and add your first test script</span><br />
<span style="font-family: "courier new" , "courier" , monospace;">usethis::use_testthat()</span><br />
<span style="font-family: "courier new" , "courier" , monospace;">setwd("R") # this is where you need to be</span><br />
<span style="font-family: "courier new" , "courier" , monospace;">usethis::use_test("firsttest") # edit your first test; close</span><br />
<span style="font-family: "courier new" , "courier" , monospace;">setwd("..")</span><br />
<span style="font-family: "courier new" , "courier" , monospace;"># That will create a file 'test-firsttest.R' in foo\tests\testthat</span><br />
<span style="font-family: "courier new" , "courier" , monospace;"># LICENSE...not necessary, but Check Package will issue warning without it</span><br />
<span style="font-family: "courier new" , "courier" , monospace;"># Open DESCRIPTION -- just click in RStudio</span><br />
<span style="font-family: "courier new" , "courier" , monospace;"># Assuming GPL-3 ...</span><br />
<span style="font-family: "courier new" , "courier" , monospace;"># Replace</span><br />
<span style="font-family: "courier new" , "courier" , monospace;"># License: What license it uses</span><br />
<span style="font-family: "courier new" , "courier" , monospace;"># with</span><br />
<span style="font-family: "courier new" , "courier" , monospace;"># License: GPL-3 | file LICENSE</span><br />
<span style="font-family: "courier new" , "courier" , monospace;">#</span><br />
<span style="font-family: "courier new" , "courier" , monospace;"># Put a LICENSE file in the root. In RStudio, File, New File, Text File</span><br />
<span style="font-family: "courier new" , "courier" , monospace;"># "GPL3 License file"</span><br />
<span style="font-family: "courier new" , "courier" , monospace;"># as the sole contents works for me, or the license here:</span><br />
<span style="font-family: "courier new" , "courier" , monospace;"># <a href="https://www.gnu.org/licenses/gpl-3.0.txt">https://www.gnu.org/licenses/gpl-3.0.txt</a></span><br />
<span style="font-family: "courier new" , "courier" , monospace;"># File, Save As, LICENSE</span><br />
<span style="font-family: "courier new" , "courier" , monospace;"># roxygenise to create help files, run tests, etc.</span><br />
<span style="font-family: "courier new" , "courier" , monospace;">roxygen2::roxygenise()</span><br />
<span style="font-family: "courier new" , "courier" , monospace;"># Your package is ready to be checked.</span><br />
<span style="font-family: "courier new" , "courier" , monospace;"># In RStudio Menu, go to Build, Check (as in "check package integrity")</span><br />
<span style="font-family: "courier new" , "courier" , monospace;"># All should check ok, no errors, no problems.</span><br />
<span style="font-family: "courier new" , "courier" , monospace;"># Write some code.</span><br />
<span style="font-family: "courier new" , "courier" , monospace;"># Then roxygen2::roxygenise() and Build, Check</span><br />
<span style="font-family: "courier new" , "courier" , monospace;"># Repeat</span><br />
<span style="font-family: "courier new" , "courier" , monospace;"># When ready to build the actual package</span><br />
<span style="font-family: "courier new" , "courier" , monospace;"># In RStudio Menu, go to Build, Install and Restart</span></blockquote>
<br />
<hr />
That's it.<br />
<br />
Note: Whenever you add new functionality from another package, don't forget to change the DESCRIPTION file -- roxygen can't do that for you.<br />
<div>
<br /></div>
Murphy Danhttp://www.blogger.com/profile/02252526252924091700noreply@blogger.com1tag:blogger.com,1999:blog-7342884208835933013.post-28457525983539046852019-05-30T17:48:00.000-07:002019-05-30T19:11:51.787-07:00How to start a new package with testing in R<div class="x-el x-el-span c1-60 c1-61 c1-b c1-62 x-d-ux" data-block="true" data-editor="4k8l8" data-offset-key="56ro3-0-0" style="background-color: white; box-sizing: inherit; transition: all 0.3s ease 0s, all 0.3s ease 0s, all 0.3s ease 0s;">
<div class="public-DraftStyleDefault-block public-DraftStyleDefault-ltr" data-offset-key="56ro3-0-0" style="box-sizing: inherit; direction: ltr; position: relative; text-align: inherit;">
<span style="white-space: pre-wrap;"><span style="font-family: "courier new" , "courier" , monospace;"># Navigate where you want your folder to be located
setwd("C:/Users/chief/Documents/Github")
# Assumes usethis is installed
usethis::create_package("foo")
# Say yes or no to next (annoying) popup window, it doesn't matter.
# Add a test environment
setwd("foo")
usethis::use_testthat()
# Add your first test function to at least get something in that folder.
# Go to foo\tests\testthat
# and add this file with a name that begins with 'test_'
context("foo")
library(foo)
test_that("I'm testing something", {
# do something with your code
expect_equal(1:4, 1:4)
})
# After writing a function with roxygen comments, roxygenize your package
roxygen2::roxygenise()
# Then click "Check" under RStudio's Build tab
# You may get a warning about "Non-standard license specification".
# To clean that up, see below.
# Keep changing your code and roxygenizing until your package checks out clean.</span></span><br />
<span style="white-space: pre-wrap;"><span style="font-family: "courier new" , "courier" , monospace;"># Once no errors, click "Install and Restart" next to "Check" and you're done.</span></span><br />
<span style="white-space: pre-wrap;"><span style="font-family: "courier new" , "courier" , monospace;"><br /></span></span>
<span style="white-space: pre-wrap;"><span style="font-family: Arial, Helvetica, sans-serif;"><b>You're Done!</b></span><span style="font-family: "courier new" , "courier" , monospace;">
# Don't forget!
# The only thing roxygen doesn't handle is,
# whenever you add new functionality from another package,
# you have have to change DESCRIPTION.
</span><span style="font-family: "arial" , "helvetica" , sans-serif;"><b><span style="font-size: large;">License</span></b>
Assuming you just go GPL
Open DESCRIPTION
Replace "</span><span style="font-family: "courier new" , "courier" , monospace;">What license it uses</span><span style="font-family: "arial" , "helvetica" , sans-serif;">" with
</span><span style="font-family: "courier new" , "courier" , monospace;">GPL-3 | file LICENSE</span><span style="font-family: "arial" , "helvetica" , sans-serif;">
and put a file named LICENSE in the same directory as DESCRIPTION.
For me, this file content sufficed
</span><span style="font-family: "courier new" , "courier" , monospace;">Something about GPL</span><span style="font-family: "arial" , "helvetica" , sans-serif;">
but the GNU community would probably prefer you used the one here
https://www.gnu.org/licenses/gpl-3.0.txt </span></span></div>
</div>
Murphy Danhttp://www.blogger.com/profile/02252526252924091700noreply@blogger.com0tag:blogger.com,1999:blog-7342884208835933013.post-6024468813233377832017-04-12T13:10:00.000-07:002017-04-12T13:16:19.567-07:00CAS RPM: Installing & running Rattle in RStudioAt the <a href="http://www.casact.org/calendar/index.cfm?fa=eventView&id=1453" target="_blank">Ratemaking and Product Management</a> (RPM) seminar of the <a href="http://www.casact.org/" target="_blank">Casualty Actuarial Society</a> (CAS) in San Diego last month, Linda Brobeck, Peggy Brinkmann, and yours truly gave a concurrent session on a machine learning technique called <a href="https://en.wikipedia.org/wiki/Decision_tree_learning" target="_blank">decision tree analysis</a>. See the DSPA-2 session -- and other sessions -- at <a href="http://www.casact.org/education/rpm/2017/index.cfm?fa=presentations" target="_blank">this link</a>. Technical issues precluded showing the video of installing and running Rattle within RStudio. Thus this post.<br />
<br />
As Peggy notes, installing and running Rattle takes only three "commands" in R:<br />
<div class="MsoNormal">
<span style="color: #1f497d;"> install.packages("rattle",
dependencies=c('Depends', "Suggests"))<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="color: #1f497d;"> library(rattle)<o:p></o:p></span></div>
<span style="color: #1f497d; font-family: "calibri" , sans-serif; font-size: 11.0pt;"> rattle()</span><br />
<br />
Although not necessary, the "Suggests" option above can avoid Rattle's annoying requests for more packages as you click through its GUI; the downside is the time to download and install about 900 packages. Below ("Read more >>") is
a link to a video of me running through the three lines above:<br />
<a href="https://drive.google.com/file/d/0B82rVboXnsUgd1FhRFl0MFRHRUU/view?usp=sharing" target="_blank"></a><br />
<a name='more'></a><a href="https://drive.google.com/file/d/0B82rVboXnsUgd1FhRFl0MFRHRUU/view?usp=sharing" target="_blank">download/install Rattle</a><br />
<div class="MsoNormal">
<o:p></o:p></div>
<br />
<div class="MsoNormal">
For those whose IT departments restrict installing R and RStudio on company equipment, this presentation used the software on a USB drive. The
first minute or so of the video shows me setting up the shortcut on the USB drive so RStudio
runs without a bunch of confusing questions, especially for a newbie. If you have R and RStudio installed
on your computer already, you can fast forward through the first minute. </div>
<div class="MsoNormal">
<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Peggy
put her three lines of code into a script called ‘Rattle.R’. That’s the file I
double-click around the 1:10 mark. You can see the three lines of the script in
the upper left pane of RStudio. <o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
I run
the first line starting at 8:17 am, which finishes at 9:32 am (the 1:42 mark in
the video). Plenty of time to read the newspaper.<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Then I
run the second line which, despite the “Depends” and “Suggests” settings above,
has to download and install yet another package, GTK+. (There are reasons why
that’s necessary, but not important right now.) That takes just a few minutes.<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Then I
run the third line, which fires up the Rattle user interface (GUI). It’s a little
hard to see, but the Rattle GUI shows up as another process running in the
taskbar.<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
At this
point you can start using rattle/rpart per Peggy’s presentation. The links to our three presentations are reproduced here for convenience:<o:p></o:p></div>
<div class="MsoNormal">
<a href="http://www.casact.org/education/rpm/2017/presentations/DSPA-2_1.pdf" target="_blank">Linda Brobeck</a></div>
<div class="MsoNormal">
<a href="http://www.casact.org/education/rpm/2017/presentations/DSPA-2_2.pdf" target="_blank">Peggy Brinkmann</a></div>
<div class="MsoNormal">
<a href="http://www.casact.org/education/rpm/2017/presentations/DSPA-2_3.pdf" target="_blank">Dan Murphy</a></div>
<div class="MsoNormal">
<br /></div>
<br />
<div class="MsoNormal">
Contact me if questions.<o:p></o:p></div>
Murphy Danhttp://www.blogger.com/profile/02252526252924091700noreply@blogger.com0tag:blogger.com,1999:blog-7342884208835933013.post-78240520997880033682016-10-27T11:03:00.000-07:002016-10-27T11:03:04.746-07:00ChainLadder version 0.2.3 available on CRANChainLadder is an R package for actuarial analysis of General / Property & Casualty insurance reserves. <a href="https://cran.r-project.org/web/packages/ChainLadder/index.html">Version 0.2.3 on CRAN</a> is is the first update in about a year. For the most part, the new version expands upon existing capabilities, as illustrated in the News <a href="https://cran.r-project.org/web/packages/ChainLadder/vignettes/NEWS.html">vignette</a>. Two of the most important are<br />
<br />
<ul>
<li>the <i>rownames</i> (origin period) of a <i>Triangle</i> need no longer be numeric -- for example, accident years may be labeled with the beginning date of the period</li>
<li>the exposures of a glmReserve analysis may use names to match with origin period</li>
</ul>
<div>
Comments and contributors (!) are always welcome. Please refer to <a href="https://github.com/mages/ChainLadder">the package's repository</a>.</div>
Murphy Danhttp://www.blogger.com/profile/02252526252924091700noreply@blogger.com0tag:blogger.com,1999:blog-7342884208835933013.post-61134165607752516282016-10-16T19:06:00.000-07:002016-10-16T21:24:56.613-07:00October 2016 BARUG MeetingThe October meeting of the San Francisco Bay Area R User Group held at Santa Clara University consisted of socializing, an intro, and three speakers. In the intro, host representative <a href="http://srdas.github.io/" target="_blank">Sanjiv Das</a> highlighted the curriculum and advisory board of the school's new <a href="https://www.scu.edu/business/ms-business-analytics/" target="_blank">MS in Business Analytics program</a>. The first speaker, yours truly, reenacted <a href="http://www.businessinsider.com/benfords-law-to-detect-financial-fraud-2014-12" target="_blank">Sara Silverstein's Benford's Law post</a> using R and insurance industry data (see previous <a href="http://trinostics.blogspot.com/2016/09/benfords-law-in-r-cont-actual-data.html" target="_blank">posts</a> in this blog). In light of the <a href="http://www.reuters.com/article/us-yahoo-nsa-exclusive-idUSKCN1241YT" target="_blank">yahoo email scandal</a> that broke that same day, it was posed to attendees whether a similar "law" might be found to discriminate between harmless and harmful emails without regard to message content. The last comment from the audience seemed to capture the evening's temperament: "Snooping is snooping!"<br />
<br />
The other two timely talks dealt with election forecasting.<br />
<br />
Mac Roach previewed a new <a href="http://www.alteryx.com/alteryx-election-app" target="_blank">online app</a> from Alteryx to predict U.S. election results at the neighborhood level. Equally interesting was Mac's countrywide display, which was the first time I had seen graphical evidence of the increasing polarity of the American electorate, a disturbing trend IMO.<br />
<br />
The last speaker, Pete Mohanty, spoke about presidential forecasting using bigKRLS. I was struck by the existence of a closed form solution to the problem. Pete's slides can be found <a href="https://github.com/rdrr1990/code/blob/master/mohanty_shaffer_BARUG_Fall_2016.pdf" target="_blank">here</a>.<br />
<br />
For a brief summary of the meeting, see BARUG's <a href="https://www.meetup.com/R-Users/events/234367295/" target="_blank">Meetup site</a>.<br />
<br />Murphy Danhttp://www.blogger.com/profile/02252526252924091700noreply@blogger.com0tag:blogger.com,1999:blog-7342884208835933013.post-21354662774948201122016-09-08T00:11:00.002-07:002016-09-08T00:11:09.156-07:00Benford's Law in R (cont.): Actual Data This is the second post based on <span style="background-color: #fefdfa; color: #333333; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13px; line-height: 18.2px;"><a href="http://www.businessinsider.com/benfords-law-used-detect-fraud-math-forensic-accountants-2016-2" target="_blank">Sara Silverstein's blog on Benford’s Law</a>. <a href="http://trinostics.blogspot.com/2016/08/benfords-law-graphed-in-r_30.html" target="_blank">Previously</a> we duplicated the comparison of the proportion of first digits from a series of randomly generated numbers, and successive arithmetic operations on those numbers, and saw that the the more complicated the operation, the closer the conformance.</span><br />
<span style="background-color: #fefdfa; color: #333333; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13px; line-height: 18.2px;"><br /></span><span style="background-color: #fefdfa; color: #333333; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13px; line-height: 18.2px;">In this post we investigate the conformance with actual data, similar to Ms. Silverstein's investigation of "all the values from Apple's financials for every quarter over the past ten years."</span><br />
<span style="background-color: #fefdfa; color: #333333; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13px; line-height: 18.2px;"><br /></span>
<span style="background-color: #fefdfa; color: #333333; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13px; line-height: 18.2px;">Four different types of financial documents from property/casualty insurance were investigated:</span><br />
<span style="background-color: #fefdfa; color: #333333; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13px; line-height: 18.2px;"><br />
</span> <span style="background-color: #fefdfa; color: #333333; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13px; line-height: 18.2px;">1. An exhibit of estimated ultimate loss using various actuarial methods, and related calculated values</span><br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi0eAKDEj2pGHcnF8pisjb5PeWIQLpLqsC9axBhAU__E4CXsRsWT-Pp1xuhpw41hqMdIToTIfM8AmzpW_FFFU8DC0d8I6CiDFrAONwWe29DcXVWV5XLg9OXB5kAPWjA3d1DxDsyRyj80Xxl/s1600/Exhibits.PNG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi0eAKDEj2pGHcnF8pisjb5PeWIQLpLqsC9axBhAU__E4CXsRsWT-Pp1xuhpw41hqMdIToTIfM8AmzpW_FFFU8DC0d8I6CiDFrAONwWe29DcXVWV5XLg9OXB5kAPWjA3d1DxDsyRyj80Xxl/s320/Exhibits.PNG" width="284" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Exhibits.pdf</td></tr>
</tbody></table>
<span style="background-color: #fefdfa; color: #333333; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13px; line-height: 18.2px;">This exhibit includes financial values as well as some non-financial numbers, such as rows labeled with years, which could skew the results.</span><br />
<span style="background-color: #fefdfa; color: #333333; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13px; line-height: 18.2px;"><br />
</span> <span style="background-color: #fefdfa; color: #333333; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13px; line-height: 18.2px;">2. A Massachusetts insurance company rate filing </span><br />
<span style="background-color: #fefdfa; color: #333333; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13px; line-height: 18.2px;"><br />
</span> <span style="background-color: #fefdfa; color: #333333; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13px; line-height: 18.2px;">In addition to many financial values, rate filings include </span><span style="background-color: #fefdfa; color: #333333; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13px; line-height: 18.2px;">much text and many numbers that are non-financial in nature.</span><br />
<span style="background-color: #fefdfa; color: #333333; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13px; line-height: 18.2px;"><br />
</span> <span style="background-color: #fefdfa; color: #333333; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13px; line-height: 18.2px;">3. An insurance company annual statement from 2009</span><br />
<span style="background-color: #fefdfa; color: #333333; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13px; line-height: 18.2px;"><br />
</span> <span style="background-color: #fefdfa; color: #333333; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13px; line-height: 18.2px;">Annual statements (aka, the Yellow Book) include many, many, many, many, many, many financial values.</span><br />
<span style="background-color: #fefdfa; color: #333333; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13px; line-height: 18.2px;"><br />
</span> <span style="background-color: #fefdfa; color: #333333; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13px; line-height: 18.2px;">4. Schedule P data compiled by the <a href="http://casact.org/" target="_blank">Casualty Actuarial Society</a></span><br />
<br />
Schedule P for six different lines of business for all U.S. property casualty insurers can be found at <a href="http://www.casact.org/research/index.cfm?fa=loss_reserves_data" target="_blank">this link</a>. The six files were combined into a single document. To isolate the investigation to purely financial numbers sans labels, company codes, and the like, the columns investigated are "IncurLoss_", "CumPaidLoss_", and "BulkLoss_".<br />
<br />
Here are the results. The number of non-zero numbers in each document is indicated on the plot.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhUPNzMhSu5NhStllwA6Hwef4y_fSkTVnZqu8fiPh_UDGgTC1cnAg2EhllTa_xFP2f51t-rN9WhMpFAJSgcXu7nUcxn4ma6Ul8TOfsFYVxA41IXPQNMv57AyTTeNjoUugi01Fs4mfOOGMSp/s1600/Results.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="563" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhUPNzMhSu5NhStllwA6Hwef4y_fSkTVnZqu8fiPh_UDGgTC1cnAg2EhllTa_xFP2f51t-rN9WhMpFAJSgcXu7nUcxn4ma6Ul8TOfsFYVxA41IXPQNMv57AyTTeNjoUugi01Fs4mfOOGMSp/s640/Results.png" width="640" /></a></div>
<br />
The Schedule P data is the most purely-financial in nature, and its plot in black matches Benford's Law almost exactly. Perhaps surprising, the Exhibits document is also quite close even though it holds the least number of observations. Perhaps a better job of pulling purely financial numbers out of the Rate Filing and the Annual Statement would improve their conformance.<br />
<br />
<h2>
Appendix</h2>
<br />
For reading PDF documents into R as text strings, I used the readPDF function in the <a href="https://cran.r-project.org/web/packages/tm/index.html" target="_blank">tm</a> package. Look at <a href="http://stackoverflow.com/questions/32472729/pdf-to-text-in-r-in-mac" target="_blank">this link</a> to learn how to download the binary files that make readPDF work easily, and the suggestion of where to store them for expediency.<br />
<br />
To divide strings of characters into individual "words", I used 'scan' in base R. See <a href="http://stackoverflow.com/questions/24741541/how-to-split-a-string-by-any-number-of-spaces" target="_blank">this link</a>.<br />
<br />
For parsing numbers, in all their various forms with commas, decimal points, etc., I used the parse_number function in the <a href="https://cran.r-project.org/web/packages/readr/index.html" target="_blank">readr</a> package.<br />
<br />
<h2>
<u>sessionInfo()</u></h2>
<br />
<div style="border-width: 1px 1px 1px 20px; border: solid #5c7b90; height: 200px; overflow: auto; white-space: nowrap;">
R version 3.3.1 (2016-06-21)<br />
Platform: x86_64-w64-mingw32/x64 (64-bit)<br />
Running under: Windows >= 8 x64 (build 9200)<br />
<br />
locale:<br />
[1] LC_COLLATE=English_United States.1252 LC_CTYPE=English_United States.1252 <br />
[3] LC_MONETARY=English_United States.1252 LC_NUMERIC=C <br />
[5] LC_TIME=English_United States.1252 <br />
<br />
attached base packages:<br />
[1] stats graphics grDevices utils datasets methods base <br />
<br />
other attached packages:<br />
[1] readr_1.0.0 tm_0.6-2 NLP_0.1-9 <br />
<br />
loaded via a namespace (and not attached):<br />
[1] assertthat_0.1 rsconnect_0.4.3 parallel_3.3.1 tools_3.3.1 tibble_1.2 <br />
[6] Rcpp_0.12.5 slam_0.1-38 <br />
<br /></div>
<br />
<span style="background-color: #fefdfa; color: #333333; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 13px; line-height: 18.2px;"><br />
</span>Murphy Danhttp://www.blogger.com/profile/02252526252924091700noreply@blogger.com0tag:blogger.com,1999:blog-7342884208835933013.post-52112903206187411102016-08-30T12:03:00.001-07:002016-09-02T12:10:01.316-07:00Benford's Law Graphed in R<h1 id="benfords-law-graphed-in-r">
Using R to replicate Sara Silverstein's post at BusinessInsider.com</h1>
<br />
A first-year student near and dear to my heart at the <a href="http://www.kellogg.northwestern.edu/">Kellogg School of Management</a> thought I would be interested in <a href="http://www.businessinsider.com/benfords-law-used-detect-fraud-math-forensic-accountants-2016-2">this Business Insider story</a> by Sara Silverstein on Benford’s Law. After sitting through the requisite ad, I became engrossed in Ms. Silverstein’s talk about what that law theoretically is and how it can be applied in financial forensics.<br />
<br />
I thought I would try duplicating the demonstration in R.<a href="https://www.blogger.com/blogger.g?blogID=7342884208835933013#1" name="top1"><sup>1</sup></a> This gave me a chance to compare and contrast the generation of combined bar- and line-plots using base R and <strong>ggplot2</strong>. It also gave me an opportunity to learn how to post RMarkdown output to blogger.<br />
<h2 id="using-base-r">
Using base R</h2>
Define the Benford Law function using log base 10 and plot the predicted values.<br />
<pre class="prettyprint"><code class="language-r hljs ">benlaw <- <span class="hljs-keyword">function</span>(d) log10(<span class="hljs-number">1</span> + <span class="hljs-number">1</span> / d)
digits <- <span class="hljs-number">1</span>:<span class="hljs-number">9</span>
baseBarplot <- barplot(benlaw(digits), names.arg = digits, xlab = <span class="hljs-string">"First Digit"</span>,
ylim = c(<span class="hljs-number">0</span>, <span class="hljs-number">.35</span>))</code></pre>
<div class="separator" style="clear: both; text-align: center;">
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Remarks:<br />
<ul>
<li>That was easy!<a name='more'></a></li>
<li>Save the barplot output in an R object so the x-values of the bar centers can be used later in the line plots<a href="https://www.blogger.com/blogger.g?blogID=7342884208835933013#2" name="top2"><sup>2</sup></a></li>
<li>ylim extends the y-axis to 35% to accomodate the highest line value – eventually – below</li>
</ul>
Define a function that can pick out the first digit of the character respresentation of a number:<br />
<pre class="prettyprint"><code class="language-r hljs ">firstDigit <- <span class="hljs-keyword">function</span>(x) substr(gsub(<span class="hljs-string">'[0.]'</span>, <span class="hljs-string">''</span>, x), <span class="hljs-number">1</span>, <span class="hljs-number">1</span>)</code></pre>
Define a function that counts the absolute frequencies of each first digit (using “table”), calculates the relative frequencies (by dividing by “length”), and stores the results in a data.frame:<br />
<pre class="prettyprint"><code class="language-r hljs ">pctFirstDigit <- <span class="hljs-keyword">function</span>(x) data.frame(table(firstDigit(x)) / length(x))</code></pre>
Now generate 1000 random numbers between 0 and 100 (set.seed so your results won’t differ), calculate their first-digit frequencies, …<br />
<pre class="prettyprint"><code class="language-r hljs ">N <- <span class="hljs-number">1000</span>
set.seed(<span class="hljs-number">1234</span>)
x1 <- runif(N, <span class="hljs-number">0</span>, <span class="hljs-number">100</span>)
df1 <- pctFirstDigit(x1)
head(df1)</code></pre>
<pre class="prettyprint"><code class=" hljs vala"><span class="hljs-preprocessor">## Var1 Freq</span>
<span class="hljs-preprocessor">## 1 1 0.108</span>
<span class="hljs-preprocessor">## 2 2 0.112</span>
<span class="hljs-preprocessor">## 3 3 0.123</span>
<span class="hljs-preprocessor">## 4 4 0.097</span>
<span class="hljs-preprocessor">## 5 5 0.120</span>
<span class="hljs-preprocessor">## 6 6 0.110</span></code></pre>
… and plot the observations relative to Benford’s Law:<br />
<pre class="prettyprint"><code class=" hljs bash">lines(x = baseBarplot[,<span class="hljs-number">1</span>], y = df1<span class="hljs-variable">$Freq</span>, col = <span class="hljs-string">"red"</span>, lwd = <span class="hljs-number">4</span>,
<span class="hljs-built_in">type</span> = <span class="hljs-string">"b"</span>, pch = <span class="hljs-number">23</span>, cex = <span class="hljs-number">1.5</span>, bg = <span class="hljs-string">"red"</span>)</code></pre>
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Remarks:<br />
<ul>
<li>As Ms. Silverstein notes, not much agreement</li>
<li>Colors are assigned manually in base R</li>
<li>Base R’s <strong>lines</strong> function automatically adds lines to the previously generated plot</li>
<li>Base R allows for both points and lines to be generated in one call to <strong>lines</strong> via the option type = “b”</li>
<li><strong>lines</strong> arguments are set (e.g., point symbols are “diamonds” with pch = 23) to approximate Ms. Silverstein’s graphs</li>
</ul>
Now square each value and add their first-digit frequencies to the plot:<br />
<pre class="prettyprint"><code class=" hljs bash">df2 <- pctFirstDigit(x1^<span class="hljs-number">2</span>)
lines(x = baseBarplot[,<span class="hljs-number">1</span>], y = df2<span class="hljs-variable">$Freq</span>, col = <span class="hljs-string">"violet"</span>, lwd = <span class="hljs-number">4</span>,
<span class="hljs-built_in">type</span> = <span class="hljs-string">"b"</span>, pch = <span class="hljs-number">23</span>, cex = <span class="hljs-number">1.5</span>, bg = <span class="hljs-string">"violet"</span>)</code></pre>
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<br />
Notice the slight improvement in Benford-conformance.<br />
<br />
Next, simulate another 1000 values, divide the square of the first values by these numbers, and add their first-digit frequencies to the plot:<br />
<pre class="prettyprint"><code class=" hljs scss">x3 <- <span class="hljs-function">runif(N, <span class="hljs-number">0</span>, <span class="hljs-number">100</span>)</span>
df3 <- <span class="hljs-function">pctFirstDigit(x1^<span class="hljs-number">2</span> / x3)</span>
<span class="hljs-function">lines(x = baseBarplot[,<span class="hljs-number">1</span>], y = df3$Freq, col = <span class="hljs-string">"blue"</span>, lwd = <span class="hljs-number">4</span>,
type = <span class="hljs-string">"b"</span>, pch = <span class="hljs-number">23</span>, cex = <span class="hljs-number">1.5</span>, bg = <span class="hljs-string">"blue"</span>)</span></code></pre>
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<br />
Ms. Silverstein: “We’re getting closer!”<br />
<br />
Finally, simulate another set of values, multiply them by the result of the previous operation, and add those frequencies to the plot:<br />
<pre class="prettyprint"><code class=" hljs scss">x4 <- <span class="hljs-function">runif(N, <span class="hljs-number">0</span>, <span class="hljs-number">100</span>)</span>
df4 <- <span class="hljs-function">pctFirstDigit(x1^<span class="hljs-number">2</span> / x3 * x4)</span>
<span class="hljs-function">lines(x = baseBarplot[,<span class="hljs-number">1</span>], y = df4$Freq, col = <span class="hljs-string">"green"</span>, lwd = <span class="hljs-number">4</span>,
type = <span class="hljs-string">"b"</span>, pch = <span class="hljs-number">23</span>, cex = <span class="hljs-number">1.5</span>, bg = <span class="hljs-string">"green"</span>)</span></code></pre>
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Remarks:<br />
<ul>
<li>These plots agree somewhat with those in Ms. Silverstein’s video</li>
<li>Repeating the exercise with more simulated values (say, N = 100000) gives better results</li>
<li>A legend would be nice, but legends can be overly tedious in base R!</li>
</ul>
<h2 id="using-ggplot">
Using ggplot</h2>
In contrast to base R, <strong>ggplot</strong> relies on a data.frame as the source of data to plot, so store the ‘digits’ and Benford’s predictions in a data.frame, then bar-plot the values with “geom_bar”.<br />
<pre class="prettyprint"><code class="language-r hljs "><span class="hljs-keyword">library</span>(ggplot2)
df <- data.frame(x = digits, y = benlaw(digits))
ggBarplot <- ggplot(df, aes(x = factor(x), y = y)) + geom_bar(stat = <span class="hljs-string">"identity"</span>) +
xlab(<span class="hljs-string">"First Digit"</span>) + ylab(<span class="hljs-literal">NULL</span>)
print(ggBarplot)</code></pre>
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Remarks:<br />
<ul>
<li>Per typical <strong>ggplot2</strong> procedure, save the ggplot results in an R object, here named ‘ggBarplot’, for later use</li>
<li>“print” the saved object to see the plot</li>
<li>Use “factor(x)” so the bars are labeled on the x-axis with discrete values rather than with continuous values (the default when x is numeric)</li>
<li>Since there is only one observation per x value, there is nothing for geom_bar’s default summary statistic, count, to do, so set ‘stat’ equal to “identity” to avoid an error</li>
</ul>
As above, we can add curves corresponding to the actual first-digit frequency resulting from the four operations. One way is to successively add line and point “layers” for each of the four operations, saving each result in turn for display and for subsequent use. We demonstrate that for the first two curves only.<br />
<pre class="prettyprint"><code class="language-r hljs ">p1 <- ggBarplot +
geom_line(data = df1,
aes(x = Var1, y = Freq, group = <span class="hljs-number">1</span>),
colour = <span class="hljs-string">"red"</span>,
size = <span class="hljs-number">2</span>) +
geom_point(data = df1,
aes(x = Var1, y = Freq, group = <span class="hljs-number">1</span>),
colour = <span class="hljs-string">"red"</span>,
size = <span class="hljs-number">4</span>, pch = <span class="hljs-number">23</span>, bg = <span class="hljs-string">"red"</span>)
p2 <- p1 +
geom_line(data = df2,
aes(x = Var1, y = Freq, group = <span class="hljs-number">1</span>),
colour = <span class="hljs-string">"violet"</span>,
size = <span class="hljs-number">2</span>) +
geom_point(data = df2,
aes(x = Var1, y = Freq, group = <span class="hljs-number">1</span>),
colour = <span class="hljs-string">"violet"</span>,
size = <span class="hljs-number">4</span>, pch = <span class="hljs-number">23</span>, bg = <span class="hljs-string">"violet"</span>)
print(p2)</code></pre>
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Remarks:<br />
<ul>
<li>As with base graphics, manually set the colors of the curves</li>
<li>Base R’s names for the symbol style (<strong>pch</strong>) and symbol background color (<strong>bg</strong>) can be used for <strong>ggplot</strong> as well</li>
</ul>
However, this manual procedure does not take full advantage of the power of <strong>ggplot2</strong>! The more elegant <strong>ggplot</strong> approach is to store all observations in a single “long” data.frame – i.e., one row per digit and operation. Then let <strong>ggplot</strong> automatically assign colors according to which operation is being plotted. As an added bonus, <strong>ggplot</strong> builds a legend automatically. Here is one way to do that.<br />
<br />
First, bind the frequency columns of the four individual data.frames into one “wide” data.frame. Rename the columns so the eventual legend will be more informative.<br />
<pre class="prettyprint"><code class="language-r hljs ">DF <- cbind(df1, df2[<span class="hljs-number">2</span>], df3[<span class="hljs-number">2</span>], df4[<span class="hljs-number">2</span>])
names(DF) <- c("FirstDigit", "X1", "X1^2", "X1^2 / X3", "X1^2 / X3 * X4")
head(DF)</code></pre>
<pre class="prettyprint">## FirstDigit X1 X1^2 X1^2 / X3 X1^2 / X3 * X4
## 1 1 0.108 0.191 0.327 0.315
## 2 2 0.112 0.132 0.150 0.163
## 3 3 0.123 0.135 0.115 0.124
## 4 4 0.097 0.105 0.096 0.093
## 5 5 0.120 0.091 0.074 0.088
## 6 6 0.110 0.091 0.065 0.067</pre>
Next, use Hadley’s <strong>reshape2</strong> package to melt this “wide” data.frame into the “long” format <strong>ggplot</strong> thrives on.<br />
<pre class="prettyprint"><code class="language-r hljs "><span class="hljs-keyword">library</span>(reshape2)
mDF <- melt(DF, id = <span class="hljs-string">"FirstDigit"</span>, variable.name = <span class="hljs-string">"operation"</span>)
head(mDF)</code></pre>
<pre class="prettyprint"><code class=" hljs vala"><span class="hljs-preprocessor">## FirstDigit operation value</span>
<span class="hljs-preprocessor">## 1 1 X1 0.108</span>
<span class="hljs-preprocessor">## 2 2 X1 0.112</span>
<span class="hljs-preprocessor">## 3 3 X1 0.123</span>
<span class="hljs-preprocessor">## 4 4 X1 0.097</span>
<span class="hljs-preprocessor">## 5 5 X1 0.120</span>
<span class="hljs-preprocessor">## 6 6 X1 0.110</span></code></pre>
Now all the data can be plotted all at once.<br />
<pre class="prettyprint"><code class="language-r hljs ">P <- ggBarplot +
geom_line(data = mDF,
aes(x = FirstDigit, y = value, colour = operation, group = operation),
size = <span class="hljs-number">1.5</span>) +
geom_point(data = mDF,
aes(x = FirstDigit, y = value, colour = operation,
group = operation, bg = operation),
size = <span class="hljs-number">4</span>, pch = <span class="hljs-number">23</span>)
print(P)</code></pre>
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Remarks:<br />
<ul>
<li><strong>size</strong> and <strong>pch</strong> are outside the <strong>aes</strong> call because they are the same for all curves</li>
<li><strong>bg</strong> is inside the <strong>aes</strong> call because the background colors differ by operation</li>
</ul>
<h2 id="conclusion">
Conclusion</h2>
<ul>
<li>The Kellogg student was correct</li>
<li>Base R’s graphics are more useful for quick, exploratory, “one-off” plots because the syntax is relatively straightforward</li>
<li><strong>gglot2</strong> is more useful for automated, elegant, presentation-level plots, but the learning curve is more steep</li>
</ul>
In a subsequent post I will summarize the steps that can turn Rmarkdown output into a blogger post.<br />
<div class="footnotes">
<hr />
<ol><span class="Apple-style-span" style="font-size: x-small;"> <a href="https://www.blogger.com/null" name="1"><b>1 </b></a>This topic has been previously explored at <a href="http://statistic-on-air.blogspot.com/2011/08/benfords-law-or-first-digit-law.html">http://statistic-on-air.blogspot.com/2011/08/benfords-law-or-first-digit-law.html</a><a href="https://www.blogger.com/blogger.g?blogID=7342884208835933013#top1"><sup>↩</sup></a> </span> <br />
<span class="Apple-style-span" style="font-size: x-small;"> <a href="https://www.blogger.com/null" name="2"><b>2 </b></a>Thanks to <a href="https://danganothererror.wordpress.com/2011/01/15/adding-lines-or-points-to-an-existing-barplot/">https://danganothererror.wordpress.com/2011/01/15/adding-lines-or-points-to-an-existing-barplot/</a><a href="https://www.blogger.com/blogger.g?blogID=7342884208835933013#top2"><sup>↩</sup></a> </span> <br />
</ol>
</div>
Murphy Danhttp://www.blogger.com/profile/02252526252924091700noreply@blogger.com0tag:blogger.com,1999:blog-7342884208835933013.post-18603505118512487202016-08-11T20:20:00.000-07:002016-08-11T20:20:12.126-07:00Forking, Cloning, and Pull Requests with Github DesktopThis is the best explanation I've found of how to collaborate on someone else's repository. Bonus! it's a video:<br />
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</div>
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<iframe width="320" height="266" class="YOUTUBE-iframe-video" data-thumbnail-src="https://i.ytimg.com/vi/XdhuWDdu-rk/0.jpg" src="https://www.youtube.com/embed/XdhuWDdu-rk?feature=player_embedded" frameborder="0" allowfullscreen></iframe></div>
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjXryr4dfsqTUHCUR9rICL8OElEIC3pSko3cx8W0ajprKxt7YgjtEpmVtB1xyHBIr3qppWzd7Vp13LK2f-GAFC4nI_79dA3nRi15TzQZ-7gtm5oQ0ndItfdkQJaoYpK7YggAsk1AxXEMeGi/s1600/Capture.PNG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><br /></a>Murphy Danhttp://www.blogger.com/profile/02252526252924091700noreply@blogger.com0tag:blogger.com,1999:blog-7342884208835933013.post-40308376651467846332016-07-31T22:19:00.000-07:002016-08-22T06:48:24.474-07:00A Diversified R in Insurance ConferenceI visited London this month for the first time in many years, having been honored to participate in the fourth annual <a href="http://www.cass.city.ac.uk/news-and-events/conferences/r-in-insurance2016" target="_blank">R in Insurance</a> conference held at the Cass Business School. Mired in the deep rooted polarity of the current American presidential election, this traveler was refreshed and uplifted by London's surprising and multi-faceted diversity. The conference <a href="http://www.magesblog.com/2016/05/r-in-insurance-2016-programme.html" target="_blank">program</a> organized by <a href="http://www.variopartners.com/p/markus-gesmann.html" target="_blank">Markus Gesmann</a> and <a href="https://www.researchgate.net/profile/Andreas_Tsanakas" target="_blank">Andreas Tsanakas</a> was similarly multi-faceted and equally enjoyable. See highlights in Markus' <a href="http://www.rininsurance.com/2016/07/notes-from-4th-r-in-insurance-conference.html" target="_blank">Notes from the Conference</a> and this amateur's images below.<br />
<br />
In addition to the conference, I had the pleasure of meeting up with old friends and making new ones.<br />
<br />
<a name='more'></a><br /><br />
For a creative way of securitizing portfolio risk, take a look at the work by <a href="http://www.variopartners.com/p/bryan-joseph.html" target="_blank">Bryan Joseph</a>, Gesmann, and colleagues at <a href="http://www.variopartners.com/p/about.html" target="_blank">Vario Partners</a>.<br />
<br />
Of course, I knew of <a href="https://people.math.ethz.ch/~wueth/" target="_blank">Dr. Mario Wüthrich</a>, the opening keynote speaker, by professional reputation, but had never had the pleasure until the morning of July 11. I will not forget Mario's sense of humor and easy way.<br />
<br />
I enjoyed an enthusiastic machine-learning breakfast discussion with Alex Marcuson (<a href="http://marcuson.co/" target="_blank">Marcuson Consulting</a>), Alan Chalk (see Alan's Casualty Actuarial Society machine learning paper <a href="http://www.casact.org/pubs/forum/16spforum/Chalk_McMurtrie.pdf" target="_blank">here</a>), Harpeet Kang (ProSight Specialty Insurance), and Markus.<br />
<br />
I am especially indebted to the generous hospitality of <a href="http://www.theactuary.com/archive/old-articles/part-4/kendra-felisky-joins-travelers-europe-in-cro-role/" target="_blank">Kendra Felisky</a> and her family in Kent. I experienced how a rugby club celebrates on Friday evenings and how to lose at ping pong in an English garden. I heard how ex-pats in Portugal perceive their post-Brexit future and watched bright young adults prepare for theirs. I learned a few cricket rules, walked a bit of local history, and downed a few pints. Many other wonderful memories are better held close!<br />
<br />
It was a special time to visit the UK -- Brexit, Wimbledon, a new prime minister, R in Insurance, miraculous weather, and, mostly, friends.<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://2.bp.blogspot.com/-lOKVvQpifMY/V51XXhohXcI/AAAAAAAALtY/bVom7_zttrIALnfm4U7x7Wh9EKGb9trigCKgB/s1600/20160711_091010.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="250" src="https://2.bp.blogspot.com/-lOKVvQpifMY/V51XXhohXcI/AAAAAAAALtY/bVom7_zttrIALnfm4U7x7Wh9EKGb9trigCKgB/s400/20160711_091010.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Dr. Wüthrich opens the conference</td></tr>
</tbody></table>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-dWXsTIuZuVQ/V51XXsC4BCI/AAAAAAAALuc/9NxDYcmxNxgSPN6Do7e2FXKWFBkQrZLPgCKgB/s1600/20160711_135940.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="286" src="https://1.bp.blogspot.com/-dWXsTIuZuVQ/V51XXsC4BCI/AAAAAAAALuc/9NxDYcmxNxgSPN6Do7e2FXKWFBkQrZLPgCKgB/s400/20160711_135940.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Marcela Granados discusses reserving under high inflation</td></tr>
</tbody></table>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-9fX8XnJ6uHhEjromdH_YEBB-r838Zn-wy3acBen2EbZNiCRh52e_eFHaEC7eVbBbIgd2vo-Qw1gEbz35ix9aLJz9XmXgRCggYjPEp0w27bBFfldH8-T8L376yuHtSCZan9gQZwjIEgTe/s1600/20160711_141454.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="236" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-9fX8XnJ6uHhEjromdH_YEBB-r838Zn-wy3acBen2EbZNiCRh52e_eFHaEC7eVbBbIgd2vo-Qw1gEbz35ix9aLJz9XmXgRCggYjPEp0w27bBFfldH8-T8L376yuHtSCZan9gQZwjIEgTe/s400/20160711_141454.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Jinsong Jheng presents an R package for life insurance SCR modeling</td></tr>
</tbody></table>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgWEqXJpCfgqU785wMMxqQ4qPKRq9vp90LinBbjUwylfUOZ5zEjNbvs1-gCBSJgseP_lD9-pvBwsa5GuefZVH6ucR7Uwg4zk3KM6eIJ1yJBCZHhj2BgLbz7AMnmhDa4m-738IPOdIuH5h-8/s1600/20160711_122316.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="175" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgWEqXJpCfgqU785wMMxqQ4qPKRq9vp90LinBbjUwylfUOZ5zEjNbvs1-gCBSJgseP_lD9-pvBwsa5GuefZVH6ucR7Uwg4zk3KM6eIJ1yJBCZHhj2BgLbz7AMnmhDa4m-738IPOdIuH5h-8/s400/20160711_122316.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Nicholas Baradel demonstrates how RPGM can help users build reserving models without extensive knowledge of R</td></tr>
</tbody></table>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjnMbM5CIDzlHROWU0vJazFHHh2ifsc0ieTRU3rBJ4dALcuTM05-geYGyKdt0cL7Bu90RKSZ1GEsIQu4Wpcso8IVOm4rnXty9_j6hCbrLNwnH7yz4XrDsPtzO4aYzVbpo3G8g9xDkFx8n9Z/s1600/20160711_121658.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="222" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjnMbM5CIDzlHROWU0vJazFHHh2ifsc0ieTRU3rBJ4dALcuTM05-geYGyKdt0cL7Bu90RKSZ1GEsIQu4Wpcso8IVOm4rnXty9_j6hCbrLNwnH7yz4XrDsPtzO4aYzVbpo3G8g9xDkFx8n9Z/s400/20160711_121658.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Mark Sellors presents a real-world R-as-a-service use case for a health insurer</td></tr>
</tbody></table>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEii2N3p9xjNmA529cuv8MgbLrWIUVBbgLM60bzwnfBsNgwngPffRly2CUNmQRBgkhi7s_YhhVf-Ne0saK5362Kr-IYybKIxEt2RRbXqVSXF9vNka-iSWprCdmWGyKjZptIPfW5tCretk9o5/s1600/IMG_0431.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEii2N3p9xjNmA529cuv8MgbLrWIUVBbgLM60bzwnfBsNgwngPffRly2CUNmQRBgkhi7s_YhhVf-Ne0saK5362Kr-IYybKIxEt2RRbXqVSXF9vNka-iSWprCdmWGyKjZptIPfW5tCretk9o5/s400/IMG_0431.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Moi (credit M. Gesmann)</td></tr>
</tbody></table>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiOfeHsy64wAyeDIc9tqbpK3kxKaux2Q6h2kvJPE99AOmd8QJs6ogQiSgtU7m8YodREZHYQ4jrcGJ6EEc6wP58prc_QqYl8QcHuC1sjq40xlY1hzYsF4OLY4v2Sp4iNYqsgVvDDqpi_h8gP/s1600/20160712_144030.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiOfeHsy64wAyeDIc9tqbpK3kxKaux2Q6h2kvJPE99AOmd8QJs6ogQiSgtU7m8YodREZHYQ4jrcGJ6EEc6wP58prc_QqYl8QcHuC1sjq40xlY1hzYsF4OLY4v2Sp4iNYqsgVvDDqpi_h8gP/s400/20160712_144030.jpg" width="266" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">The Lloyd's Building</td></tr>
</tbody></table>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhpXNOYYwZpoZpaotagUsn3kn0bxdsDEKmDUeneOJfOMDxfYH5YGzpMfA9p0fIuuL5dD7O4C1uCyX4x7MgD8aDBpZfAi2TabZWY2s8Oyr93z8eHY72ubuDmH05o92Ylbgu4lra-ktKzx8S_/s1600/20160713_145540.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="247" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhpXNOYYwZpoZpaotagUsn3kn0bxdsDEKmDUeneOJfOMDxfYH5YGzpMfA9p0fIuuL5dD7O4C1uCyX4x7MgD8aDBpZfAi2TabZWY2s8Oyr93z8eHY72ubuDmH05o92Ylbgu4lra-ktKzx8S_/s400/20160713_145540.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">John Harrison's H4 prize winning clock at the Royal Observatory (recommend <i>Longitude</i> by Dava Sobel)</td></tr>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://4.bp.blogspot.com/-Kei0OeJ9UXw/V51XXgv4UVI/AAAAAAAALsw/ueLu_DHkDRIt9lI4qs51xfZBKG97ijgYQCKgB/s1600/20160710_163104.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="148" src="https://4.bp.blogspot.com/-Kei0OeJ9UXw/V51XXgv4UVI/AAAAAAAALsw/ueLu_DHkDRIt9lI4qs51xfZBKG97ijgYQCKgB/s640/20160710_163104.jpg" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Andy Murray makes thousands of Brit's happy as they enjoy the big screen and sunshine at the foot of Tower Bridge</td></tr>
</tbody></table>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://2.bp.blogspot.com/-fp7HQRSOT20/V51XXsi9SmI/AAAAAAAAL3c/dJA1ID5jtTYdkbkba5rxkN-OodmsBWC1ACKgB/s1600/20160714_082836_001.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="218" src="https://2.bp.blogspot.com/-fp7HQRSOT20/V51XXsi9SmI/AAAAAAAAL3c/dJA1ID5jtTYdkbkba5rxkN-OodmsBWC1ACKgB/s400/20160714_082836_001.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">The resting place of Thomas Bayes, a few blocks from City University London</td></tr>
</tbody></table>
<br />Murphy Danhttp://www.blogger.com/profile/02252526252924091700noreply@blogger.com0tag:blogger.com,1999:blog-7342884208835933013.post-60680336919203210622016-04-01T15:05:00.000-07:002016-04-01T15:05:50.193-07:00R Tools for Visual Studio (RTVS) now available: good news for MS-only shopsMicrosoft informs in <a href="http://msdsug.microsoft.com/features/features-issue-2-february-2016/">Newsletter #2</a> that they are looking for people who are willing to evaluate an "early access trial" version of their Visual Studio IDE for R, called RTVS (for R Tools for Visual Studio).<br />
<br />
Based on the video, RTVS has the same four-window design as <a href="https://www.rstudio.com/">RStudio</a>, so there's not an immediate struggle with an unfamiliar layout. David Smith's <a href="http://blog.revolutionanalytics.com/2016/03/rtvs-preview.html">blog</a> lists some of RTVS's current shortcomings, such as automated package support, that may or may not be a problem for you. I looked for signs that VS might facilitate the integration of R with other languages – such as C# for a front-end and R for the back-end – but not a whiff.<br />
<br />
The greatest advantage of RTVS I can see is for IT shops that are comfortable<br />
<br />
<a name='more'></a>installing Microsoft products on company PC's but are not comfortable with non-MS, open-source programs like <a href="https://www.r-project.org/">R</a> or <a href="https://www.rstudio.com/">RStudio</a>.<br />
<br />
The greatest disadvantage of signing up for RTVS is the potential time dealing with bugs that first adopters can expect to uncover.<br />
<br />
Comments from willing RTVS first adopters are welcome below.Murphy Danhttp://www.blogger.com/profile/02252526252924091700noreply@blogger.com0tag:blogger.com,1999:blog-7342884208835933013.post-81431779447830724932016-03-24T19:51:00.001-07:002016-03-24T19:51:45.617-07:00Control totals of a data.frameWhen you are conducting a business analysis project with a data extract from the company's internal system, professional risk management suggests you make sure you are not missing any records or double counting any records. But you certainly don't want to look at every record. <i>Yikes!</i><br />
<br />
Auditors solve this predicament with <a href="http://www.encyclopedia.com/doc/1O11-batchcontrol.html">control totals</a>. When the sums of key fields and the numbers of records match known values, usually from some well-established "production report," it can be assumed your data "reconciles." *<br />
<br />
What does it mean to calculate "control totals" of a general data.frame? <br />
<a name='more'></a>For numeric columns it's obvious to use <span style="font-family: "courier new" , "courier" , monospace;"><b>sum</b></span>, the only question being what to do with missing values. For non-numeric columns, "sum" is not well-defined. You could say NA, but IMO it would be more informative to show <b>the number of non-NA values</b>.<br />
<br />
Hmm, maybe this has already been done before.<br />
<br />
A quick internet search for "summarise data.frame", "total data.frame" and variants led to hits with two shortcomings (see for example <a href="http://www.cookbook-r.com/Manipulating_data/Summarizing_data/">Cookbook for R</a>, <a href="http://www.inside-r.org/packages/cran/gdata/docs/nobs">gdata</a>, and <a href="https://cran.rstudio.com/web/packages/dplyr/vignettes/introduction.html">dplyr</a>):<br />
<ul>
<li>You can calculate <span style="font-family: "courier new" , "courier" , monospace;">sum</span>, or a version of <span style="font-family: "courier new" , "courier" , monospace;">count</span>, but not both</li>
<li>You must know the names of the columns in advance.</li>
</ul>
<div>
Something more "automatic" would apply to any data.frame without having to know column names or data types ahead of time. Something easy. How hard can that be??</div>
<br />
Here is my one-line function called <span style="font-family: "courier new" , "courier" , monospace;">controlTotals</span>:<br />
<div class="code">
controlTotals <- function(x, na.rm = FALSE)<br />
sapply(x, function(x) if (is.numeric(x)) sum(as.numeric(x), na.rm = na.rm) else isum(!is.na(x)))</div>
<br />
In typical business use cases, the most important fields to check <b>should not have missing values</b>, so <span style="font-family: "courier new" , "courier" , monospace;">na.rm=FALSE</span> by default. In that case NA's in a column are detected by<br />
<ul>
<li>numeric: NA returned</li>
<li>non-numeric: the number of non-NA values will be less than the number of rows.</li>
</ul>
If NA's in the data are acceptable, then set <span style="font-family: "courier new" , "courier" , monospace;">na.rm=TRUE</span> and the values returned will be<br />
<ul>
<li>numeric: the sum of all non-NA values (or NA if all are NA)</li>
<li>non-numeric: always the number of non-NA values.</li>
</ul>
Here is an example.<br />
<div class="code">
> extract <- data.frame(a = c(1:3), b = c(1, NA, 3),<br />
c = letters[1:3], d = c("high", NA, "low"))<br />
> controlTotals(extract)<br />
a b c d<br />
6 NA 3 2<br />
> controlTotals(extract, TRUE)<br />
a b c d<br />
6 4 3 2</div>
<br />
In the first, default case, column b's control total is NA and column d's control total is less than the number of records. Aha! there's something missing in both columns! Better check that out.<br />
<br />
<ul>
<li>R-technicality: In the definition of <span style="font-family: "courier new" , "courier" , monospace;">controlTotals</span> you may be wondering why <span style="font-family: "courier new" , "courier" , monospace;">as.numeric</span> is called after <span style="font-family: "courier new" , "courier" , monospace;">is.numeric</span> has already been established. That's because integer's are numeric, and summing integers can result in an overflow if the field contains large values, as when whole numbers are used for "record ID's." R recovers gracefully with only a warning in those situations, but error, recovery and warning are easily avoided with this extra step. BTW, this extra step was found in the code for <a href="https://cran.r-project.org/web/packages/gdata/index.html">gdata</a>'s <span style="font-family: "courier new" , "courier" , monospace;">nobs</span> method (kudos Gregory Warnes et. al.)</li>
</ul>
<br />
* P&C actuaries note: reconciliation is a professional concern not restricted to Schedule P<br />
<br />
<u>sessionInfo()</u><br />
<br />
<div style="border-width: 1px 1px 1px 20px; border: solid #5c7b90; height: 200px; overflow: auto; white-space: nowrap;">
R version 3.2.4 (2016-03-10)<br />
Platform: x86_64-w64-mingw32/x64 (64-bit)<br />
Running under: Windows >= 8 x64 (build 9200)<br />
<br />
locale:<br />
[1] LC_COLLATE=English_United States.1252 LC_CTYPE=English_United States.1252 <br />
[3] LC_MONETARY=English_United States.1252 LC_NUMERIC=C <br />
[5] LC_TIME=English_United States.1252 <br />
<br />
attached base packages:<br />
[1] stats graphics grDevices utils datasets methods base <br />
<br />
other attached packages:<br />
[1] roxygen2_4.1.1 devtools_1.8.0<br />
<br />
loaded via a namespace (and not attached):<br />
[1] magrittr_1.5 rversions_1.0.1 tools_3.2.3 curl_0.9 Rcpp_0.12.3 <br />
[6] memoise_0.2.1 xml2_0.1.1 stringi_1.0-1 git2r_0.10.1 stringr_1.0.0 <br />
[11] digest_0.6.9 <br />
<br /></div>
Murphy Danhttp://www.blogger.com/profile/02252526252924091700noreply@blogger.com0tag:blogger.com,1999:blog-7342884208835933013.post-75275121789761569872016-03-17T07:15:00.000-07:002016-03-17T07:15:09.079-07:00Google's New Search Algorithm Introduces BiasLarry Magid has a technology "article" on the local radio station. I always turn up the volume when Magid comes on. Today's spot tells how Google Search going forward may be biased for you personally based on your Google-stored relationships. This might be handy sometimes. For example, when looking for a restaurant you may want results skewed toward your friends' favorites. Google calls these "private results." For other searches, "private results" could hide or demote the actual results you'd hoped to find. On his website <a href="http://www.larrysworld.com/how-and-why-to-turn-off-googles-personalized-search-results/">Magid shows how to turn off</a> the privatizing feature after each search, as well as how to remove it for all searches via your Google settings.<br />
<br />
Magid mentions a third option: "Incognito" mode. In Incognito mode, it's as if you're not logged in to Google, in which case your bias-influencing relationships are (presumably!) not available. You can open a new Incognito window in Chrome via Ctrl-Shift-N. <a href="https://support.google.com/chrome/answer/95464">Here is the link</a> to Google's instructions on how to browse Incognito-ly on various devices.Murphy Danhttp://www.blogger.com/profile/02252526252924091700noreply@blogger.com0tag:blogger.com,1999:blog-7342884208835933013.post-68358742257820689462016-03-03T21:05:00.000-08:002016-03-07T16:26:04.238-08:00A horizontal scrolling code box in bloggerTo display code in a blog I like to use a "code box" because I think it presents a more "professional" look. But it's not that easy with blogger.<br />
<br />
By "code box" I mean a "window" with a monospaced font and vertical and horizontal scrolling bars as necessary. The internet search solutions I found almost worked, but not quite with blogger because the horizontal scroll bar wouldn't show up as expected. The vertical bar was there, but not the horizontal bar. Go figure.<br />
<br />
But if you are comfortable hitting the HTML button next to Compose, that's easily fixed.<br />
<br />
<a name='more'></a><br /><br />
First of all, vertical scroll bars aren't usually necessary with blogger because by default it stretches your window vertically as much as it takes. But that's exactly why you need scroll bars, because you don't want a long program to hijack the real estate of your blog. So you need to specify a height.<br />
<br />
Since I'm specifying the height, I might as well shrink the width too, a bit radically to more easily display the point. And let's start off with a default-ugly border so we can more easily see the window.<br />
<br />
Here is a some HTML that should repeat a Mother Goose rhyme in a monospace-fonted window with as-necessary scroll bars:<br />
<br />
<div style="border: solid; height: 1in; width: 50%; font-family:courier; overflow: auto;"><br />
Peter Piper picked a peck of pickled peppers.<br />
Peter Piper picked a peck of pickled peppers.<br />
Peter Piper picked a peck of pickled peppers.<br />
Peter Piper picked a peck of pickled peppers.<br />
Peter Piper picked a peck of pickled peppers.<br />
Peter Piper picked a peck of pickled peppers.<br />
</div><br />
<br />
And here is what the window looks like. See the problem?<br />
<br />
<div style="border: solid; font-family: "courier"; height: 1in; overflow: auto; width: 50%;">
Peter Piper picked a peck of pickled peppers.<br />
Peter Piper picked a peck of pickled peppers.<br />
Peter Piper picked a peck of pickled peppers.<br />
Peter Piper picked a peck of pickled peppers.<br />
Peter Piper picked a peck of pickled peppers.<br />
Peter Piper picked a peck of pickled peppers.</div>
<br />
The lines wrap when they should have stayed extended, and a horizontal scroll bar should have shown up because I said, quite clearly, "overflow: auto;". So how do I get horizontal scrolling with blogger?<br />
<br />
Here's the trick: add "white-space:nowrap;" Wow. Didn't see that coming.<br />
<br />
Here is the code box's final opening opening div:<br />
<br />
<div style="border: solid; height: 1in; width: 50%; font-family:courier; overflow: auto; white-space:nowrap;"><br />
<br />
and here is the resulting window:<br />
<br />
<div style="border: solid; font-family: "courier"; height: 1in; overflow: auto; white-space: nowrap; width: 50%;">
Peter Piper picked a peck of pickled peppers.<br />
Peter Piper picked a peck of pickled peppers.<br />
Peter Piper picked a peck of pickled peppers.<br />
Peter Piper picked a peck of pickled peppers.<br />
Peter Piper picked a peck of pickled peppers.<br />
Peter Piper picked a peck of pickled peppers.</div>
<br />
Works for me.<br />
∎Murphy Danhttp://www.blogger.com/profile/02252526252924091700noreply@blogger.com3tag:blogger.com,1999:blog-7342884208835933013.post-69022048078203898392016-02-25T22:23:00.000-08:002016-03-07T16:27:30.621-08:00The making of a shiny mauc: chapter 2This continues last week's post <a href="http://trinostics.blogspot.com/2016/02/the-making-of-shiny-mauc.html" target="_blank">The making of a shiny mauc</a>, based on Greg McNulty's <a href="http://opensourcesoftware.casact.org/blogs:2" target="_blank">mauc</a> blog. It utilizes the <a href="https://www.rstudio.com/home/" target="_blank">RStudio </a>interface to R, Desktop version.<br />
<br />
Recall, the goal is to make an online shiny app that will run Greg's code using his data, all supplied in his <a href="http://opensourcesoftware.casact.org/blogs:2" target="_blank">post</a>. Today we will address what modifications are necessary to show his first plot (below) on a web page. In a subsequent post we will see how to display all Greg's plots. After that we will see how <br />
<a name='more'></a>to upload the app to an online server so anyone can run it in a browser, even if you don't have R.<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj8-i1C-R4ZWgT6akmvD1Urp2zGUvftRpLTdATgDlRonOZebGuXwPQJv7STiQSr8IkmyUoaByYVaR6Vv45cTlp7_c9-_xdGAg6_CuH1fVisFa1vatlU6dUVDijJ3H2gu1JqMkvSZ7qcH8Sf/s1600/McNulty+Plot+1.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="179" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj8-i1C-R4ZWgT6akmvD1Urp2zGUvftRpLTdATgDlRonOZebGuXwPQJv7STiQSr8IkmyUoaByYVaR6Vv45cTlp7_c9-_xdGAg6_CuH1fVisFa1vatlU6dUVDijJ3H2gu1JqMkvSZ7qcH8Sf/s200/McNulty+Plot+1.JPG" width="200" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">mauc's first plot: let's name this baby <span style="color: blue; font-family: "arial" , "helvetica" , sans-serif;"><i>copula_data_plot</i></span></td></tr>
</tbody></table>
<br />
A shiny app essentially consists of two files<br />
<ul>
<li><b>ui.r</b>: defines the user-interface (UI), i.e., the "look" of the web page</li>
<li><b>server.r</b>: the set of instructions that "services" the UI, i.e, takes input from the user (there is none in Greg's paper) and generates the output. In our case, all servicing instructions are contained in Greg's R script, "R code CAS blog v2.R".</li>
</ul>
As long as those two files are contained in your working directory, and are well-formed, RStudio will be able to create your shiny app.<br />
<br />
In step 1 we see how to define a UI that displays a plot named "copula_data_plot" (indeed, any ol' plot named "copula_data_plot"). In step 2 we see where to insert Greg's code and where to add two new lines so that the <i style="color: blue; font-family: Arial, Helvetica, sans-serif;">copula_data_plot</i> above is served up specifically.<br />
<br />
<div>
<span style="font-family: "verdana" , sans-serif;"><b>Step 1: ui.r - contains and defines the function 'shinyUI'</b></span></div>
<br />
Like a painter, we first envision what objects we are going to place on our canvas and where. This is called the "layout." Since our "painting" will be of a single plot, our layout can be very simple. What do we put into <span style="font-family: "courier new" , "courier" , monospace;">shinyUI</span> so as to define a simple, one plot layout?<br />
<br />
The shiny <a href="http://shiny.rstudio.com/articles/layout-guide.html" target="_blank">Application layout guide</a> discusses some of the basic layouts. Let's use the first one there, the Sidebar Layout, which happens to display a plot in the Main Area. We currently have no inputs to receive from the Sidebar, so we will adopt the "# Inputs excluded for brevity" technique (from the second Sidebar Layout example on that page). Here is our <b>ui.r</b> file:<br />
<br />
<div class="code">
shinyUI(fluidPage(<br />
titlePanel("Shiny mauc: Version 1"),<br />
sidebarLayout(<br />
sidebarPanel(<br />
# Inputs excluded for brevity<br />
),<br />
mainPanel(<br />
plotOutput("copula_data_plot")<br />
)<br />
)<br />
))</div>
<br />
All this says is that our "canvas" consists of an (empty) area on the left called the sidebarPanel and an area to its right called the mainPanel. The only thing in the mainPanel will be the output of a plot. In fact, that plot must be named "copula_data_plot" or it won't show. Put another way, whenever ui.r comes across a plot named "copula_data_plot", then no matter what that plot looks like, it will display that plot right there in the mainPanel. Oh, and there's a title at the top.<br />
<br />
<div>
<span style="font-family: "verdana" , sans-serif;"><b>Step 2: server.r -</b></span><b style="font-family: verdana, sans-serif;"> contains and defines the function 'shinyServer'</b></div>
<br />
The point of most shiny apps is to "react to" user input, so in the shiny <a href="http://shiny.rstudio.com/tutorial/lesson4/" target="_blank">tutorial</a> and elsewhere you will see lots of talk about your shiny app being "reactive." Beh... not every app has to be "reactive." Ours certainly won't be -- it's simply going to take Greg's input data and display <i style="color: blue; font-family: Arial, Helvetica, sans-serif;">copula_data_plot</i>. We're not going to make any changes whatsoever. Not change the input data, not fit a different distribution to the ALAE, not choose a different copula than the Gumbel .. Nada! There will be nothing "going on" to which server.r must react.<br />
<br />
Therefore, per Step 2 of the <a href="http://shiny.rstudio.com/tutorial/lesson4/" target="_blank">shiny tutorial</a>, when we "Provide R code to build the object" all we have to do is insert the entirety of Greg's script, "R code CAS blog v2.R", into server.r and that's it! ... Well, and add two small lines of code. But then, really, that's it! ☺<br />
<br />
First, we start off with an almost-blank server.r file that looks like this:<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjomDWENpqTRbDhJ9ZSz8z4lAPkqQMGKZTrHktmjBl1xDPN7d3TL2shanVJvRunmUT4TfO7zByW9gcH6TcdBQdAMTSD7L_MbLrejQh8Ci2tACYNO5gh5fCs7xLIPyju53cRJaAqx5uJo8ih/s1600/Blank+Server+with+copy+and+paste+here.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="95" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjomDWENpqTRbDhJ9ZSz8z4lAPkqQMGKZTrHktmjBl1xDPN7d3TL2shanVJvRunmUT4TfO7zByW9gcH6TcdBQdAMTSD7L_MbLrejQh8Ci2tACYNO5gh5fCs7xLIPyju53cRJaAqx5uJo8ih/s400/Blank+Server+with+copy+and+paste+here.JPG" width="400" /></a></div>
Open the "R code CAS blog v2.R" file, select all, copy to the clipboard, highlight the contents of line 2 above, and paste the clipboard contents into that spot.<br />
<br />
Next, from Greg's blog you will see that his first plot consists of these two lines<br />
<div class="separator" style="clear: both; text-align: center;">
</div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgpESPhVUHb9-AAc-ilLsbCbePd4tVMd2y5rSfTWUCj8san0TLLLhJKCkj7dE1JK8f1_QwyoSaHQojsQH2SCmfdTeqoPvvO9xIsZ8t4hSdManZTi4FJI9XBvBpo5lz785fo6DQW3v-bs6XO/s1600/Original+Plot+1+commands.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="70" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgpESPhVUHb9-AAc-ilLsbCbePd4tVMd2y5rSfTWUCj8san0TLLLhJKCkj7dE1JK8f1_QwyoSaHQojsQH2SCmfdTeqoPvvO9xIsZ8t4hSdManZTi4FJI9XBvBpo5lz785fo6DQW3v-bs6XO/s400/Original+Plot+1+commands.JPG" width="400" /></a></div>
which send their output to R's graphics device. "Painting onto a canvas" and "rendering onto a web page" mean the same thing, so to "render" <i style="color: blue; font-family: Arial, Helvetica, sans-serif;">copula_data_plot</i> onto the mainPanel, we wrap those two lines within the shiny <span style="font-family: "courier new" , "courier" , monospace;">renderPlot</span> function. As soon as that function's result is assigned to an <b>output</b> object named (in R-speak, "<b>$</b>") <i style="color: blue; font-family: Arial, Helvetica, sans-serif;">copula_data_plot</i><br />
<br />
<div class="code">
output$copula_data_plot <- renderPlot({Gregs's 2 lines go here})</div>
<br />
ui.r will see it and recognize it as the plot to display in the mainPanel.<br />
<br />
So place the two new lines you see below around Greg's code:<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgO5YS0zWHMEh0LLPGXQTDneZcR9V-g4FrOpypa_tdooeMXi_MfaW_137bYZcxjbk9xO1DONlVXv12GeaW6ITRFIMBDGcB2Z8E_LjtGt5waU9ujjuL_UrzMdeV_IMUegJl3ZkDRh6aNGotB/s1600/output+to+renderPlot.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="56" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgO5YS0zWHMEh0LLPGXQTDneZcR9V-g4FrOpypa_tdooeMXi_MfaW_137bYZcxjbk9xO1DONlVXv12GeaW6ITRFIMBDGcB2Z8E_LjtGt5waU9ujjuL_UrzMdeV_IMUegJl3ZkDRh6aNGotB/s400/output+to+renderPlot.JPG" width="400" /></a></div>
save the server.r file, hit the "Run App" button<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjtPDTU8dhTDlcr4LBi_TAhD86RlkMa4e2yS9FsqOFP9iSCD6uk-tMGTHc8lEzb-LsL3vEblXV1QfDQ5ssooBzmRxX-rNBoYAcWuTs-orC0gzEXIM6X12lISCjtD7ZDRxRIUxuhUO5kNUz4/s1600/RunAppButton.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjtPDTU8dhTDlcr4LBi_TAhD86RlkMa4e2yS9FsqOFP9iSCD6uk-tMGTHc8lEzb-LsL3vEblXV1QfDQ5ssooBzmRxX-rNBoYAcWuTs-orC0gzEXIM6X12lISCjtD7ZDRxRIUxuhUO5kNUz4/s1600/RunAppButton.JPG" /></a></div>
and you will eventually see <i style="color: blue; font-family: Arial, Helvetica, sans-serif;">copula_data_plot</i><br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi9CJJR0mls9Mem6cVhr7-rLqSD1CnAByECjNeR5cTOraAbT6WbCuaLI4GAG2huu59IpYCqYNmSfZHtdZkUhpGhFvXR9N2tKOiQwPReIifrE7h8wy0c3Oz-dsiP9Nf0CDIin_Z2p_zMXOkT/s1600/Version+1+output.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="231" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi9CJJR0mls9Mem6cVhr7-rLqSD1CnAByECjNeR5cTOraAbT6WbCuaLI4GAG2huu59IpYCqYNmSfZHtdZkUhpGhFvXR9N2tKOiQwPReIifrE7h8wy0c3Oz-dsiP9Nf0CDIin_Z2p_zMXOkT/s400/Version+1+output.JPG" width="400" /></a></div>
<br />
Notes:<br />
<ol>
<li>Close that browser window to return to RStudio, or in RStudio hit escape.</li>
<li>The UI's title panel is at the top, the empty sidebar panel is to the left, the main panel is to the right, and the only thing there is a plot.</li>
<li>This app turns out to be "reactive" after all, in the sense that if you resize the window the objects magically reposition themselves. Thank you, Shiny!!</li>
<li>The program's remaining plots can be found in RStudio's plot window, printed output can be found in RStudio's console window, and the output csv files can be found in your working directory (<span style="font-family: "courier new" , "courier" , monospace;">getwd()</span>). All those things happen because you are running the desktop version of the app through RStudio. What happens when you run the online version of the app through a browser? Stay tuned and let's see!</li>
</ol>
<br />
That's it for this week. Next week we will see how to display <u>all</u> Greg's plots with our shiny mauc.<br />
<br />
<u>sessionInfo()</u><br />
<div style="height: 200px; overflow: auto;">
> sessionInfo()<br />
R version 3.2.3 (2015-12-10)<br />
Platform: x86_64-w64-mingw32/x64 (64-bit)<br />
Running under: Windows >= 8 x64 (build 9200)<br />
<br />
Or when on my mac:<br />
Platform: x86_64-apple-darwin13.4.0 (64-bit)<br />
Running under: OS X 10.10.5 (Yosemite)<br />
<br />
<br />
locale:<br />
[1] LC_COLLATE=English_United States.1252 LC_CTYPE=English_United States.1252 <br />
[3] LC_MONETARY=English_United States.1252 LC_NUMERIC=C <br />
[5] LC_TIME=English_United States.1252 <br />
<br />
Or when on my mac<br />
locale:<br />
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8 <br />
<br />
attached base packages:<br />
[1] stats4 stats graphics grDevices utils datasets methods base <br />
<br />
other attached packages:<br />
[1] distr_2.5.3 SweaveListingUtils_0.6.2 sfsmisc_1.0-29 <br />
[4] startupmsg_0.9 copula_0.999-14 actuar_1.1-10 <br />
[7] shiny_0.12.1 <br />
<br />
loaded via a namespace (and not attached):<br />
[1] Rcpp_0.12.3 rstudioapi_0.5 ADGofTest_0.3 xtable_1.7-4 <br />
[5] pspline_1.0-17 lattice_0.20-33 R6_2.0.1 tools_3.2.3 <br />
[9] grid_3.2.3 htmltools_0.2.6 digest_0.6.9 Matrix_1.2-3 <br />
[13] mime_0.3 gsl_1.9-10.1 stabledist_0.7-0 jsonlite_0.9.16 <br />
[17] mvtnorm_1.0-4 httpuv_1.3.2 rstudio_0.98.1103</div>
Murphy Danhttp://www.blogger.com/profile/02252526252924091700noreply@blogger.com0tag:blogger.com,1999:blog-7342884208835933013.post-74418040367062190052016-02-17T16:55:00.004-08:002016-03-07T16:28:40.664-08:00The making of a shiny mauc<div dir="ltr">
When an excess of loss (XOL) reinsurance pricing actuary has only indemnity to work with, how can s/he reflect allocated loss adjustment expense (ALAE) in final cost projections? Such is the situation addressed by Greg McNulty in his blog <a href="http://opensourcesoftware.casact.org/blogs:2" target="_blank">Modeling ALAE Using Copulas</a> (MAUC). According to McNulty, the classical approach — loading the indemnity value of each claim with an average ALAE/indemnity ratio — rests on "two very strong implicit assumptions"<span style="font-family: inherit;">:</span> 1) ALAE and indemnity are "scaled copies" of each other and 2) ALAE and indemnity are "100% correlated." When those assumptions are questionable McNulty suggests an alternative approach.<br />
<a name='more'></a><br />
<br />
From a different dataset of (indemnity, ALAE) pairs, McNulty fits a marginal distribution to the ALAE and a copula distribution to the joint pairs. He then marries the original indemnity to the fitted ALAE using the presiding copula. The result is a bivariate distribution of indemnity and ALAE which<br />
<br />
<ul>
<li>maintains the shape of the original indemnity, </li>
<li>reflects its expected interaction with ALAE throughout their combined domain, and </li>
<li>can be used to simulate risk-adjusted pricing for XOL layers of interest and under the two standard treatments of ALAE. </li>
</ul>
McNulty's paper presents a solid actuarial solution to this reinsurance pricing dilemma. ... But wait! There's more!</div>
<div dir="ltr">
<b><br /></b>
<b>McNulty provides the supporting R code to implement all his algorithms and reproduce all his results!</b> With this paper Greg takes his place in the evolution of Reproducible Research (see <a href="https://en.wikipedia.org/wiki/Reproducibility#Reproducible_research" target="_blank">1</a> and <a href="https://www.coursera.org/learn/reproducible-research" target="_blank">2</a> and even <a href="http://www.cbsnews.com/news/deception-at-duke-fraud-in-cancer-care/" target="_blank">3</a>) within the research arm of <a href="http://www.casact.org/" target="_blank">my professional organization</a>.<br />
<br />
A more thorough discussion of the actuarial content of McNulty's paper is not the purpose of this blog. This blog will be much more geeky! Over the coming weeks we will walk through the steps that will turn McNulty's code into an online <a href="http://shiny.rstudio.com/" target="_blank">shiny</a> app. Once online, his code can be run by virtually anyone. No need to install R or any of the required packages. All that's needed is a browser. That way, non-R-conversant actuaries will be able to reproduce McNulty's results, hopefully leading to a deeper appreciation of his concepts. An enhanced version of the app that could run the calculations on your own data would probably lead to an even deeper appreciation, but let's not get ahead of ourselves!<br />
<br />
For the purpose of this exercise Greg has generously granted his permission for his code to be shared online in a <a href="https://github.com/" target="_blank">github</a> public repository (anyone can view the site and all its content). You can find the MAUC repository <a href="https://github.com/chiefmurph/MAUC" target="_blank">here</a>.<br />
<br />
Cheers to you, Greg, for providing this solution and software, and to the <a href="http://www.casact.org/" target="_blank">Casualty Actuarial Society</a> and its <a href="http://opensourcesoftware.casact.org/" target="_blank">Open-SourceSoftware Committee</a> for supporting his work.<br />
<br />
<br />
<br />
<br /></div>
Murphy Danhttp://www.blogger.com/profile/02252526252924091700noreply@blogger.com0tag:blogger.com,1999:blog-7342884208835933013.post-85521076478702327562015-10-21T18:02:00.001-07:002015-11-23T12:42:23.128-08:00Water Damage at Cal!Dag Lohmann gave an exhaustive (not "-ing"!) <a href="http://www.meetup.com/r-enthusiasts/events/223626822/" target="_blank">presentation</a> on <a href="http://www.katrisk.com/" target="_blank">Katrisk</a> modeling of water damage at The Berkeley R Language Beginner Study Group last night in <a href="http://berkeleyheritage.com/berkeley_landmarks/northgate_hall.html" target="_blank">The Ark</a>. A bit beyond "beginner", Dag! :-) Thanks for the snips of your shiny. Nice graphs.Murphy Danhttp://www.blogger.com/profile/02252526252924091700noreply@blogger.com0tag:blogger.com,1999:blog-7342884208835933013.post-771392442484237852014-10-19T20:06:00.000-07:002016-03-07T16:29:36.580-08:00pasteFromExcelSuppose you have a triangle in Excel that you would like to analyze in R. In Excel, select the cells comprising the triangle <em>including the labels identifying accident year and age</em> and copy to the clipboard.<br />
<img alt="smalltri.png" src="https://raw.githubusercontent.com/trinostics/excelRio/master/Rmd/Smalltri.PNG" title="" /><br />
<br />
<a name='more'></a>Back in R, load the <a href="https://github.com/trinostics/excelRio">excelRio package</a> and run the function that pastes content from the clipboard. Be sure to tell the function that your data has a “header” for the column names (development ages) and a “rowheader” for the row names (accident years).<br />
<pre class="prettyprint"><code class="language-{r} hljs r"><span class="hljs-keyword">library</span>(excelRio)
tri <- pasteFromExcel(header = <span class="hljs-literal">TRUE</span>, rowheader = <span class="hljs-literal">TRUE</span>)
tri
<span class="hljs-number">12</span> <span class="hljs-number">24</span> <span class="hljs-number">36</span> <span class="hljs-number">48</span> <span class="hljs-number">60</span>
<span class="hljs-number">2010</span> <span class="hljs-number">1000</span> <span class="hljs-number">1200</span> <span class="hljs-number">1320</span> <span class="hljs-number">1386</span> <span class="hljs-number">1414</span>
<span class="hljs-number">2011</span> <span class="hljs-number">1200</span> <span class="hljs-number">1452</span> <span class="hljs-number">1568</span> <span class="hljs-number">1631</span> <span class="hljs-literal">NA</span>
<span class="hljs-number">2012</span> <span class="hljs-number">800</span> <span class="hljs-number">1040</span> <span class="hljs-number">1113</span> <span class="hljs-literal">NA</span> <span class="hljs-literal">NA</span>
<span class="hljs-number">2013</span> <span class="hljs-number">1100</span> <span class="hljs-number">1320</span> <span class="hljs-literal">NA</span> <span class="hljs-literal">NA</span> <span class="hljs-literal">NA</span>
<span class="hljs-number">2014</span> <span class="hljs-number">850</span> <span class="hljs-literal">NA</span> <span class="hljs-literal">NA</span> <span class="hljs-literal">NA</span> <span class="hljs-literal">NA</span></code></pre>
<strong>excelRio</strong> has special handling to strip out the dollar signs and commas when appropriate. <strong>excelRio</strong>’s interpretation of “appropriate” is, if after stripping out the dollar signs and commas the column of results can be successfully converted to <strong>numeric</strong>, then that’s what will happen. Without special handling, this would not normally happen, as below when the first two character elements lose numeric value.<br />
<pre class="prettyprint"><code class="language-{r} hljs vbnet"><span class="hljs-keyword">as</span>.numeric(c(<span class="hljs-string">"$1,000"</span>, <span class="hljs-string">"1,200"</span>, <span class="hljs-string">"800"</span>))
[<span class="hljs-number">1</span>] NA NA <span class="hljs-number">800</span>
Warning message:
NAs introduced <span class="hljs-keyword">by</span> coercion </code></pre>
The argument that controls this special handling is <strong>convertFormattedNumbers</strong> and can be turned off, as in the code below. Note that I also set <strong>stringsAsFactors = FALSE</strong> because my installation of <strong>R</strong> has the default value TRUE for that global option.<br />
<pre class="prettyprint"><code class="language-{r} hljs r">tri <- pasteFromExcel(header = <span class="hljs-literal">TRUE</span>, rowheader = <span class="hljs-literal">TRUE</span>,
convertFormattedNumbers = <span class="hljs-literal">FALSE</span>,
stringsAsFactors = <span class="hljs-literal">FALSE</span>)
tri
<span class="hljs-number">12</span> <span class="hljs-number">24</span> <span class="hljs-number">36</span> <span class="hljs-number">48</span> <span class="hljs-number">60</span>
<span class="hljs-number">2010</span> <span class="hljs-string">" $1,000 "</span> <span class="hljs-string">" $1,200 "</span> <span class="hljs-string">" $1,320 "</span> <span class="hljs-string">" $1,386 "</span> <span class="hljs-string">" $1,414 "</span>
<span class="hljs-number">2011</span> <span class="hljs-string">" 1,200 "</span> <span class="hljs-string">" 1,452 "</span> <span class="hljs-string">" 1,568 "</span> <span class="hljs-string">" 1,631 "</span> <span class="hljs-literal">NA</span>
<span class="hljs-number">2012</span> <span class="hljs-string">" 800 "</span> <span class="hljs-string">" 1,040 "</span> <span class="hljs-string">" 1,113 "</span> <span class="hljs-literal">NA</span> <span class="hljs-literal">NA</span>
<span class="hljs-number">2013</span> <span class="hljs-string">" 1,100 "</span> <span class="hljs-string">" 1,320 "</span> <span class="hljs-literal">NA</span> <span class="hljs-literal">NA</span> <span class="hljs-literal">NA</span>
<span class="hljs-number">2014</span> <span class="hljs-string">" 850 "</span> <span class="hljs-literal">NA</span> <span class="hljs-literal">NA</span> <span class="hljs-literal">NA</span> <span class="hljs-literal">NA</span>
mode(tri)
[<span class="hljs-number">1</span>] <span class="hljs-string">"character"</span>
class(tri)
[<span class="hljs-number">1</span>] <span class="hljs-string">"matrix"</span></code></pre>
The <em>class</em> of the above raises a subtle point about the value of the result from <strong>pasteFromExcel</strong>. <br />
Data in Excel is often comprised of columns of data of many different types: numeric, character, and dates, to name a few. By default, therefore, <strong>pasteFromExcel</strong> will create a data.frame, an <strong>R</strong> object that allows differently typed columns. But when all the columns of data are “compatible,” <strong>pasteFromExcel</strong> will return a matrix object of the common “type” (or “mode”) by default, if possible, under the assumption that a matrix object would be “intuitively expected.” The argument that controls that option is <strong>simplify</strong>. By calling the function with <strong>simplify = FALSE</strong>, a data.frame will always be returned.<br />
For more information about <strong>pasteFromExcel</strong> and its various optional arguments, see<br />
<pre class="prettyprint"><code class=" hljs ">?pasteFromExcel</code></pre>
Finally, Dear Reader, I leave you with a warning and a request for assistance! :)<br />
<h3 id="warning">
<em>Warning!</em></h3>
Formatted numbers in Excel are stripped of their “adornments” via a <a href="http://en.wikipedia.org/wiki/Regular_expression">regular expression</a> I found on the internet <a href="http://stackoverflow.com/questions/354044/what-is-the-best-u-s-currency-regex">here</a>. <strong>This expression will not work outside the U.S.</strong> <br />
I repeat: <br />
<strong><em>Warning! excelRio’s special currency handling will only work with dollar signs, with periods as decimal separator, and with commas separating triples.</em></strong> I apologize. :( <br />
(For the curious, <strong>excelRio</strong> stores its current regex pattern for currency in the variable <strong>currencypattern</strong> on line 38 in the file <strong>excelRio.r</strong> in the R folder of the package on github. )<br />
<h3 id="request-for-assistance-1">
<em>Request for Assistance!</em></h3>
If anyone is interested in suggesting a currency pattern for their location I would really appreciate the collaboration — woohoo!! You can reach me at danielmarkmurphy at gmail. Thank you sincerely in advance.<br />
Dan <br />
<hr />
created (mostly) with RMarkdown in RStudioMurphy Danhttp://www.blogger.com/profile/02252526252924091700noreply@blogger.com0tag:blogger.com,1999:blog-7342884208835933013.post-74191139436355618102014-10-06T10:58:00.001-07:002014-10-06T10:58:11.130-07:00AIM Matters<div class="separator" style="clear: both; text-align: center;">
</div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhhBfv-KYQAgAyPLseOelSKBN9uD0bmbnwK_PO0nf5AecpUaaZsf8gU6Pl28-KE7HY4cjbkKKClt67b7WFikPBpDizcOZnkxEvpsNyXKtxjVDHDTDecjfIXecsDswqKYHkyL-nodRrU8z1-/s1600/Strawberry.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhhBfv-KYQAgAyPLseOelSKBN9uD0bmbnwK_PO0nf5AecpUaaZsf8gU6Pl28-KE7HY4cjbkKKClt67b7WFikPBpDizcOZnkxEvpsNyXKtxjVDHDTDecjfIXecsDswqKYHkyL-nodRrU8z1-/s1600/Strawberry.JPG" /></a></div>
Props to my college roommate, Brian Conrey, who this summer celebrated the 20 year anniversary of the American Institute of Mathematics (<a href="http://aimath.org/">AIM</a>), a math "think tank" in Palo Alto, California. With the help of math enthusiast John Fry and a supportive board, AIM has discovered creative ways to generate mathematics research at all levels. For example, Math Teachers' Circles (MTCs) bring together middle school teachers and professional mathematicians around the country to work on interesting problems that help bolster the classroom skills of our early math instructors. AIM originated the SQuaREs program, an inventive way to gather researchers into concentrated week-long workshops, a fertile model that non-math disciplines could look to emulate. <i>Science Nation</i> recently highlighted AIM's partnership with <a href="http://www.driscolls.com/">Driscoll's</a> (Watsonville CA) and other berry growers that modeled various water and land management techniques for balancing aquifer levels (<a href="http://www.nsf.gov/news/special_reports/science_nation/strawberryfields.jsp">"Strawberry fields forever - with some help from mathematicians!”</a>).<br />
<br />
This week the <a href="http://frysopengolf.com/">Frys.com Open</a> golf tournament takes place at the Silverado Resort and Spa in Napa, California. Besides volunteering as Shotlink operators, AIM supporters will also be manning a booth. Come on by to learn more and meet some nice mathematicians!Murphy Danhttp://www.blogger.com/profile/02252526252924091700noreply@blogger.com0tag:blogger.com,1999:blog-7342884208835933013.post-16460127362560064102014-10-05T11:22:00.000-07:002014-10-05T11:22:57.619-07:00Implementing CLFM with the ChainLadder PackageOne of the requirements of the popular stochastic reserving method known as the Mack Method (see for example <a href="http://www.actuaries.org/LIBRARY/ASTIN/vol23no2/213.pdf" target="_blank">Dr. Mack's original paper</a>, <a href="http://www.casact.org/pubs/proceed/proceed94/94154.pdf" target="_blank">Murphy's original paper</a>, <a href="http://casualtyactuarialsociety.com/library/00pcas/barnett.pdf" target="_blank">Barnett & Zehnwirth</a>, and others) is that the actuary select one of the "standard" averages, such as the simple or volume-weighted averages of the observed link ratios. If an actuary's selection differs from one of those then -- strictly speaking -- the results of the papers above do not apply.<br />
<a name='more'></a> A <a href="http://www.variancejournal.org/issues/06-02/143.pdf" target="_blank">recent paper</a> in the journal <i><a href="http://www.variancejournal.org/" target="_blank">Variance</a></i> demonstrated the existence of a broader family of Chain-Ladder Factor Models (CLFM) to which, under certain conditions, many more selected factors conform. If those conditions are satisfied, the selected factor may be considered the "best linear unbiased estimate" (<a href="http://en.wikipedia.org/wiki/Gauss%E2%80%93Markov_theorem" target="_blank">BLUE</a>) of a member of the family, and uncertainty estimates of the chain-ladder central estimates are <u>directly applicable</u>. This post will demonstrate how the ChainLadder package implements CLFM for estimating chain-ladder method uncertainty when link ratios are "selected." (Note: the CLFM's psi function is not yet fully implemented in ChainLadder.)<br />
<br />
<div style="background-color: white; color: #333333; font-family: 'Helvetica Neue Light', HelveticaNeue-Light, 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px; margin: 0px; outline: none; padding: 0px;">
<div style="margin: 0px; padding: 0px;">
As with a previous post, our example will consider data from the Institute and Faculty of Actuaries <a href="https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&ved=0CDgQFjAB&url=http%3A%2F%2Fwww.actuaries.org.uk%2Fsystem%2Ffiles%2Fdocuments%2Fpdf%2Fcrm1-G.pdf&ei=ixqoUdbsE-GligKrh4GIAg&usg=AFQjCNHoPFjt14eGxB-LaQqSAeZlUWBYKA&sig2=XoDwqEK5Qv1N2Zjn-atXdw&bvm=bv.47244034,d.cGE" style="-webkit-transition: color 0.3s; color: #009eb8; display: inline; outline: none; text-decoration: none; transition: color 0.3s;"><i>Claims Reserving Manual</i>, Section F, "Case Estimates & the Projection of Incurred Claims"</a>, p. 9:</div>
</div>
<div style="background-color: white; color: #333333; font-family: 'Helvetica Neue Light', HelveticaNeue-Light, 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px; margin: 0px; outline: none; padding: 0px;">
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<br /></div>
</div>
<div style="background-color: white; font-family: 'Helvetica Neue Light', HelveticaNeue-Light, 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px; margin: 0px; outline: none; padding: 0px;">
<div style="margin: 0px; padding: 0px;">
<span style="font-family: 'Courier New', Courier, monospace;"><span style="color: red;">> ReportedLossTriangle <- matrix(c(</span></span></div>
</div>
<div style="background-color: white; font-family: 'Helvetica Neue Light', HelveticaNeue-Light, 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px; margin: 0px; outline: none; padding: 0px;">
<div style="margin: 0px; padding: 0px;">
<span style="font-family: 'Courier New', Courier, monospace;"><span style="color: red;"> 2777, 3264, 3452, 3594, 3719, 3717,</span></span></div>
</div>
<div style="background-color: white; font-family: 'Helvetica Neue Light', HelveticaNeue-Light, 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px; margin: 0px; outline: none; padding: 0px;">
<div style="margin: 0px; padding: 0px;">
<span style="font-family: 'Courier New', Courier, monospace;"><span style="color: red;"> 3252, 3804, 3973, 4231, 4319, NA,</span></span></div>
</div>
<div style="background-color: white; font-family: 'Helvetica Neue Light', HelveticaNeue-Light, 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px; margin: 0px; outline: none; padding: 0px;">
<div style="margin: 0px; padding: 0px;">
<span style="font-family: 'Courier New', Courier, monospace;"><span style="color: red;"> 3725, 4404, 4779, 4946, NA, NA,</span></span></div>
</div>
<div style="background-color: white; font-family: 'Helvetica Neue Light', HelveticaNeue-Light, 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px; margin: 0px; outline: none; padding: 0px;">
<div style="margin: 0px; padding: 0px;">
<span style="font-family: 'Courier New', Courier, monospace;"><span style="color: red;"> 4521, 5422, 5676, NA, NA, NA,</span></span></div>
</div>
<div style="background-color: white; font-family: 'Helvetica Neue Light', HelveticaNeue-Light, 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 14px; line-height: 19px; margin: 0px; outline: none; padding: 0px;">
<div style="margin: 0px; padding: 0px;">
<span style="font-family: 'Courier New', Courier, monospace;"><span style="color: red;"> 5369, 6142, NA, NA, NA, NA,</span></span></div>
</div>
<span style="color: red; font-family: 'Courier New', Courier, monospace;"> 5818, NA, NA, NA, NA, NA), nrow = 6, byrow = TRUE)</span><br />
<div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 2.52pt; text-indent: 0in; unicode-bidi: embed; word-break: normal;">
<span style="color: red; font-family: Courier New, Courier, monospace;"><span style="color: red; font-family: "Courier New"; font-size: 10.5pt; language: en-US; mso-ascii-font-family: "Courier New"; mso-bidi-font-family: "Courier New"; mso-fareast-font-family: +mn-ea; mso-fareast-theme-font: minor-fareast; mso-font-kerning: 12.0pt; mso-style-textfill-fill-alpha: 100.0%; mso-style-textfill-fill-color: red; mso-style-textfill-type: solid;">>
library(</span><span style="color: red; font-family: "Courier New"; font-size: 10.5pt; language: en-US; mso-ascii-font-family: "Courier New"; mso-bidi-font-family: "Courier New"; mso-fareast-font-family: +mn-ea; mso-fareast-theme-font: minor-fareast; mso-font-kerning: 12.0pt; mso-style-textfill-fill-alpha: 100.0%; mso-style-textfill-fill-color: red; mso-style-textfill-type: solid;">ChainLadder</span><span style="color: red; font-family: "Courier New"; font-size: 10.5pt; language: en-US; mso-ascii-font-family: "Courier New"; mso-bidi-font-family: "Courier New"; mso-fareast-font-family: +mn-ea; mso-fareast-theme-font: minor-fareast; mso-font-kerning: 12.0pt; mso-style-textfill-fill-alpha: 100.0%; mso-style-textfill-fill-color: red; mso-style-textfill-type: solid;">)</span></span></div>
<br />
The observed link ratios, along with the simple and volume-weighted averages, are<br />
<span style="color: red; font-family: Courier New, Courier, monospace;">> ata(ReportedLossTriangle)</span><br />
<span style="color: blue; font-family: Courier New, Courier, monospace;"> Age</span><br />
<span style="color: blue; font-family: Courier New, Courier, monospace;">Accident Year 12-24 24-36 36-48 48-60 60-72</span><br />
<span style="color: blue; font-family: Courier New, Courier, monospace;"> 2007 1.175 1.058 1.041 1.035 0.999</span><br />
<span style="color: blue; font-family: Courier New, Courier, monospace;"> 2008 1.170 1.044 1.065 1.021 NA</span><br />
<span style="color: blue; font-family: Courier New, Courier, monospace;"> 2009 1.182 1.085 1.035 NA NA</span><br />
<span style="color: blue; font-family: Courier New, Courier, monospace;"> 2010 1.199 1.047 NA NA NA</span><br />
<span style="color: blue; font-family: Courier New, Courier, monospace;"> 2011 1.144 NA NA NA NA</span><br />
<span style="color: blue; font-family: Courier New, Courier, monospace;"> smpl 1.174 1.059 1.047 1.028 0.999</span><br />
<span style="color: blue; font-family: Courier New, Courier, monospace;"> vwtd 1.173 1.058 1.046 1.027 0.999</span><br />
<div>
<br />
Suppose we made the following selections:</div>
<div>
<span style="color: red; font-family: Courier New, Courier, monospace;">> selected <- c(1.175, 1.059, 1.045, 1.03, .999)</span></div>
<div>
Then we can find each link ratio's "consistent" member of the CLFM family (i.e., the model whose expected value equals the selected factor) with the 'CLFMdelta' function</div>
<div>
<div>
<span style="color: red; font-family: Courier New, Courier, monospace;">> CLFMdelta(ReportedLossTriangle, selected)</span></div>
<div>
<span style="color: blue; font-family: Courier New, Courier, monospace;">12 24 36 48 60 </span></div>
<div>
<span style="color: blue; font-family: Courier New, Courier, monospace;"> 3 2 -1 6 1 </span></div>
<div>
<span style="color: blue; font-family: Courier New, Courier, monospace;">attr(,"foundSolution")</span></div>
<div>
<span style="color: blue; font-family: Courier New, Courier, monospace;">[1] TRUE TRUE TRUE TRUE TRUE</span></div>
</div>
<div>
<b><br /></b></div>
<div>
<b>Some background</b>: Each member of the CLFM family is distinguished by the exponent of the beginning value of loss that impacts the variance of the age-to-age projection. The exponent need not be an integer. The fact that the attribute "<span style="font-family: Courier New, Courier, monospace;">foundSolution</span>" is all TRUE indicates that a member was successfully found for each element of "<span style="font-family: Courier New, Courier, monospace;">selected</span>" relative to the <span style="font-family: 'Courier New', Courier, monospace;">ReportedLossTriangle</span>. A "solution" is not guaranteed. For example, CLFMdelta cannot find a solution for a 24-36 selection of 1.06. Refer to the <a href="http://www.variancejournal.org/issues/06-02/143.pdf" target="_blank">paper</a> for the necessary conditions.</div>
<div>
<br /></div>
<div>
To continue, save the "solution" (i.e., the index to the CLFM member model) in an R variable:</div>
<div>
<span style="color: red; font-family: Courier New, Courier, monospace;">> delta <- CLFMdelta(ReportedLossTriangle, selected)</span></div>
<div>
<br />
Now call the MackChainLadder function with the method's "alpha" parameter equal to 2 - delta. (<b>Aside</b>: The CLFM paper formulates the exponent a-la <a href="http://www.casact.org/pubs/proceed/proceed94/94154.pdf" target="_blank">Murphy</a> and <a href="http://casualtyactuarialsociety.com/library/00pcas/barnett.pdf" target="_blank">Barnett&Zehnwirth</a>; ChainLadder uses Mack's formulation. "CLFMalpha" would have been a more appropriate name relative to the CLFM paper, but ChainLadder's choice of notation had already been made.)</div>
<div>
<div>
<span style="color: red; font-family: Courier New, Courier, monospace;">> MackChainLadder(ReportedLossTriangle, alpha = 2 - delta, est.sigma = "Mack", mse.method = "Independence")</span></div>
<div>
<span style="color: blue; font-family: Courier New, Courier, monospace;">MackChainLadder(Triangle = ReportedLossTriangle, alpha = 2 - </span></div>
<div>
<span style="color: blue; font-family: Courier New, Courier, monospace;"> delta, est.sigma = "Mack", mse.method = "Independence")</span></div>
<div>
<span style="color: blue; font-family: Courier New, Courier, monospace;"><br /></span></div>
<div>
<span style="color: blue; font-family: Courier New, Courier, monospace;"> Latest Dev.To.Date Ultimate IBNR Mack.S.E CV(IBNR)</span></div>
<div>
<span style="color: blue; font-family: Courier New, Courier, monospace;">2007 3,717 1.000 3,717 0.00 0.00e+00 NaN</span></div>
<div>
<span style="color: blue; font-family: Courier New, Courier, monospace;">2008 4,319 1.001 4,317 -2.32 9.06e-21 -3.90e-21</span></div>
<div>
<span style="color: blue; font-family: Courier New, Courier, monospace;">2009 4,946 0.971 5,092 145.61 8.33e+01 5.72e-01</span></div>
<div>
<span style="color: blue; font-family: Courier New, Courier, monospace;">2010 5,676 0.930 6,106 429.87 1.59e+02 3.70e-01</span></div>
<div>
<span style="color: blue; font-family: Courier New, Courier, monospace;">2011 6,142 0.878 6,994 851.72 2.59e+02 3.05e-01</span></div>
<div>
<span style="color: blue; font-family: Courier New, Courier, monospace;">2012 5,818 0.747 7,784 1,966.45 3.64e+02 1.85e-01</span></div>
<div>
<span style="color: blue; font-family: Courier New, Courier, monospace;"><br /></span></div>
<div>
<span style="color: blue; font-family: Courier New, Courier, monospace;"> Totals</span></div>
<div>
<span style="color: blue; font-family: Courier New, Courier, monospace;">Latest: 30,618.00</span></div>
<div>
<span style="color: blue; font-family: Courier New, Courier, monospace;">Dev: 0.90</span></div>
<div>
<span style="color: blue; font-family: Courier New, Courier, monospace;">Ultimate: 34,009.32</span></div>
<div>
<span style="color: blue; font-family: Courier New, Courier, monospace;">IBNR: 3,391.32</span></div>
<div>
<span style="color: blue; font-family: Courier New, Courier, monospace;">Mack S.E.: 532.88</span></div>
<div>
<span style="color: blue; font-family: Courier New, Courier, monospace;">CV(IBNR): 0.16</span></div>
</div>
<div>
<br /></div>
<div>
In this case, the central estimates for Ultimate Loss and IBNR will be exactly equal to what the actuary would produce under the deterministic Chain-Ladder Method with those selected factors. Furthermore, the total standard error, 532.88, is immediately applicable to the total estimates of Ultimate and IBNR.</div>
<div>
<br /></div>
<div>
<b>Caveats:</b></div>
<div>
<ol>
<li>Of course, the standard error does not account for model error. Residuals should be analyzed for potential model misspecification. </li>
<li>The "psi function" of the CLFM approach has not yet been implemented in ChainLadder. This is a future enhancement currently being considered by the package developers. Contributors are welcome!</li>
</ol>
<div>
- dmm</div>
</div>
<br />
------------------------------------------------<br />
<br />
<a href="https://code.google.com/p/chainladder/" style="-webkit-animation: 0ms !important; -webkit-transition: none !important; color: #009eb8; display: inline; outline: none; text-decoration: none; transition: none !important;">ChainLadder</a> is a package for the <a href="http://cran.r-project.org/" style="-webkit-animation: 0ms !important; -webkit-transition: none !important; color: #009eb8; display: inline; outline: none; text-decoration: none; transition: none !important;">R</a> statistical environment that contains various functions for performing loss reserving for Property/Casualty/General Insurance.Murphy Danhttp://www.blogger.com/profile/02252526252924091700noreply@blogger.com0tag:blogger.com,1999:blog-7342884208835933013.post-51451091280582972102013-08-28T22:24:00.000-07:002014-10-05T11:25:14.166-07:00IBNR with the Bornhuetter-Ferguson Method using the R ChainLadder package<div class="article-content entry-content" itemprop="articleBody" style="-webkit-animation: 0ms !important; -webkit-transition: none !important; clear: both; color: #333333; font-family: 'Helvetica Neue Light', HelveticaNeue-Light, 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 14px; line-height: 1.4; margin: 10px auto 5px; outline: none; padding: 0px; text-align: justify; transition: none !important;">
This is the third of a trilogy of posts demonstrating how to implement three basic deterministic Property&Casualty/General/Non-Life insurance actuarial techniques using the <a href="https://code.google.com/p/chainladder/" target="_blank">ChainLadder</a> package in <a href="http://www.r-project.org/" target="_blank">R</a>.<br />
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In simplest form, the <a href="http://www.casact.org/pubs/proceed/proceed73/73161.pdf" target="_blank">Bornhuetter-Ferguson ("BF") Method</a> estimates IBNR for an accident/policy/underwriting/origin year (tranch of exposure) as the product of an <i>a-priori</i> estimate of ultimate loss for that exposure and an estimate of the percent of that ultimate loss unknown/unreported/undeveloped at the time:<br />
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IBNR = <i>a-priori</i>EstimatedUltimateLoss * PercentUnreported</div>
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Then a BF estimate of ultimate loss is the sum of reported loss known at the time plus IBNR:<br />
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EstimatedUltimateLoss = ReportedLoss + IBNR</div>
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<i>A-priori</i> estimates of ultimate loss may originate from widespread sources. We will demonstrate with the Loss Ratio Method (see <a href="http://trinostics.blogspot.com/2013/06/ibnr-with-loss-ratio-method-using.html" target="_blank">previous post</a>). Estimates of unreported percents are commonly borne from a loss development analysis of a reported loss triangle (see <a href="http://trinostics.blogspot.com/2013/06/ibnr-with-chain-ladder-method-using-r.html" target="_blank">previous post</a>), demonstrated here.<br />
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For an example we will use data from the Institute and Faculty of Actuaries <i style="-webkit-animation: 0 !important; -webkit-transition: none !important; transition: none !important;">Claims Reserving Manual</i>, Sections F & G (see previous posts at links above for online sources). The R statements below following the carat (">") may be copied and pasted into an R session.<br />
<ul>
<li>First, <i>a-priori </i>EstimatedUltimateLoss</li>
</ul>
<span style="color: blue; font-family: 'Courier New', Courier, monospace; line-height: 1.4;">> Premium = c(4486, 5024, 5680, 6590, 7482, 8502)</span><br />
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<span style="color: blue; font-family: 'Courier New', Courier, monospace; line-height: 1.4;">> ELR = .83 </span><br />
<span style="color: blue; font-family: 'Courier New', Courier, monospace; line-height: 1.4;">> aprioriEstimatedUltimateLoss = Premium * ELR</span><br />
<ul>
<li>Next, PercentUnreported</li>
<ul>
<li>The reported loss triangle</li>
</ul>
</ul>
<span style="color: blue; font-family: 'Courier New', Courier, monospace;">> ReportedLossTriangle = matrix(c(</span><br />
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<span style="color: blue; font-family: Courier New, Courier, monospace;"> 2777, 3264, 3452, 3594, 3719, 3717,</span></div>
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<span style="color: blue; font-family: Courier New, Courier, monospace;"> 3252, 3804, 3973, 4231, 4319, NA,</span></div>
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<span style="color: blue; font-family: Courier New, Courier, monospace;"> 3725, 4404, 4779, 4946, NA, NA,</span></div>
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<span style="color: blue; font-family: Courier New, Courier, monospace;"> 4521, 5422, 5676, NA, NA, NA,</span></div>
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<span style="color: blue; font-family: Courier New, Courier, monospace;"> 5369, 6142, NA, NA, NA, NA,</span></div>
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<span style="color: blue; font-family: Courier New, Courier, monospace;"> 5818, NA, NA, NA, NA, NA), nrow = 6, byrow = TRUE)</span></div>
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<ul><ul>
<li>Fire up ChainLadder. Select the volume weighted average age-to-age factors. Append a unity tail under the assumption that the first year is already at ultimate. Cumulate (multiplicatively) in appropriate order. Pause to inspect the cumulative development factors.</li>
</ul>
</ul>
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<span style="color: blue; font-family: 'Courier New', Courier, monospace;">> library(ChainLadder)</span><br />
<span style="color: blue; font-family: 'Courier New', Courier, monospace;">> selected = attr(ata(ReportedLossTriangle), "vwtd")</span><br />
<span style="color: blue;"><span style="font-family: 'Courier New', Courier, monospace;">> selected = </span><span style="font-family: 'Courier New', Courier, monospace;">c(</span><span style="font-family: 'Courier New', Courier, monospace;">selected, 1.000)</span></span><br />
<span style="color: blue;"><span style="font-family: 'Courier New', Courier, monospace;">> CDF = cumprod(rev(selected</span><span style="font-family: 'Courier New', Courier, monospace;">))</span></span><br />
<span style="color: blue; font-family: Courier New, Courier, monospace;">> round(CDF, 3)</span><br />
<span style="font-family: Courier New, Courier, monospace;">[1] 1.000 0.999 1.027 1.074 1.137 1.333</span><br />
<ul></ul>
<ul><ul>
<li>Notice how reversing the order of the age-to-age (ATA) factors before cumulating enables the tail factor to line up with the first, most mature year and the last factor to line up with the last, least mature year. Also, the last observed ATA is less than 1.000 -- as is the second CDF -- so we should expect to see (slightly) negative IBNR for the second-most-mature accident year.</li>
<li>Now calculate the unreported percents using the familiar formula</li>
</ul>
</ul>
<span style="color: blue; font-family: 'Courier New', Courier, monospace;">> PercentUnreported = 1 - 1 / CDF</span><br />
<ul>
<li>IBNR</li>
</ul>
<span style="color: blue; font-family: 'Courier New', Courier, monospace;">> IBNR = aprioriEstimatedUltimateLoss * PercentUnreported</span><br />
<span style="color: blue; font-family: 'Courier New', Courier, monospace;">> round(IBNR)</span><br />
<span style="font-family: 'Courier New', Courier, monospace;">[1] 0 -2 122 379 749 1764</span><br />
<ul>
<li>For the value of reported loss known at the time we can use ChainLadder's <span style="font-family: Courier New, Courier, monospace;">getLatestCumulative</span> function</li>
</ul>
<span style="color: blue;"><span style="font-family: 'Courier New', Courier, monospace;">></span><span style="font-family: 'Courier New', Courier, monospace;"> </span><span style="font-family: Courier New, Courier, monospace;">ReportedLoss = getLatestCumulative(ReportedLossTriangle)</span></span><br />
<ul>
<li>Finally</li>
</ul>
<span style="color: blue;"><span style="font-family: 'Courier New', Courier, monospace;">></span><span style="font-family: 'Courier New', Courier, monospace;"> </span><span style="font-family: Courier New, Courier, monospace;">EstimatedUltimateLoss = ReportedLoss + IBNR</span></span><br />
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</span> It is possible to program the steps above into an R function. Is there a ChainLadder volunteer? Contributors welcome! Contact Markus Gesmann or one of the other authors found <a href="http://cran.r-project.org/web/packages/ChainLadder/">here</a> or under "Members" <a href="https://code.google.com/p/chainladder/">here</a>.<br />
<br />
-dmm<br />
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<a href="https://code.google.com/p/chainladder/" style="-webkit-animation: 0ms !important; -webkit-transition: none !important; color: #009eb8; display: inline; outline: none; text-decoration: none; transition: none !important;">ChainLadder</a>, a package for the <a href="http://www.r-project.org/" style="-webkit-animation: 0ms !important; -webkit-transition: none !important; color: #009eb8; display: inline; outline: none; text-decoration: none; transition: none !important;">R</a> statistical environment primarily targeted toward stochastic reserving actuaries, contains many helper functions to implement deterministic methods as well.</div>
Murphy Danhttp://www.blogger.com/profile/02252526252924091700noreply@blogger.com1tag:blogger.com,1999:blog-7342884208835933013.post-70192509480788557272013-06-22T06:13:00.001-07:002014-10-05T11:21:34.608-07:00IBNR with the Loss Ratio Method using the ChainLadder package<div class="article-content entry-content" itemprop="articleBody" style="-webkit-animation: 0ms !important; -webkit-transition: none !important; clear: both; color: #333333; font-family: 'Helvetica Neue Light', HelveticaNeue-Light, 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 14px; line-height: 1.4; margin: 10px auto 5px; outline: none; padding: 0px; text-align: justify; transition: none !important;">
<a href="https://code.google.com/p/chainladder/" style="-webkit-animation: 0ms !important; -webkit-transition: none !important; color: #009eb8; display: inline; outline: none; text-decoration: none; transition: none !important;">ChainLadder</a> is a package for the <a href="http://cran.r-project.org/" style="-webkit-animation: 0ms !important; -webkit-transition: none !important; color: #009eb8; display: inline; outline: none; text-decoration: none; transition: none !important;">R</a> statistical environment that contains various functions for performing loss reserving for Property/Casualty/General Insurance. Mostly, the package's functions are intended to implement sophisticated stochastic models, but many simpler, deterministic methods are relatively easy to perform using helper functions in the package. This post will demonstrate how to calculate <a href="http://en.wikipedia.org/wiki/Incurred_but_not_reported" style="-webkit-animation: 0ms !important; -webkit-transition: none !important; color: #009eb8; display: inline; outline: none; text-decoration: none; transition: none !important;">IBNR </a>with the Loss Ratio Method.<br />
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In simplest terms, the Loss Ratio Method estimates ultimate loss as the product of premium and an expected loss ratio (ELR):<br />
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EstimatedUltimateLoss = Premium * ELR</div>
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Then, IBNR is the difference between estimated ultimate loss and loss known to date (referred to here as "reported loss"):<br />
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IBNR = EstimatedUltimateLoss - ReportedLoss</div>
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For an example we will look at the data in the Institute and Faculty of Actuaries <a href="https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&ved=0CDgQFjAB&url=http%3A%2F%2Fwww.actuaries.org.uk%2Fsystem%2Ffiles%2Fdocuments%2Fpdf%2Fcrm1-G.pdf&ei=ixqoUdbsE-GligKrh4GIAg&usg=AFQjCNHoPFjt14eGxB-LaQqSAeZlUWBYKA&sig2=XoDwqEK5Qv1N2Zjn-atXdw&bvm=bv.47244034,d.cGE" style="-webkit-animation: 0ms !important; -webkit-transition: none !important; color: #009eb8; display: inline; outline: none; text-decoration: none; transition: none !important;"><i style="-webkit-animation: 0 !important; -webkit-transition: none !important; transition: none !important;">Claims Reserving Manual</i>, Section G, "Methods Using Loss Ratio & Loss Ratio Projections"</a>, p. 4.<br />
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<span style="color: blue; font-family: Courier New, Courier, monospace; line-height: 1.4;">> ReportedLoss <- c(3483, 3844, 3977, 3880, 3261, 1889) </span><span style="color: blue; font-family: 'Courier New', Courier, monospace; line-height: 1.4;"># the "current diagonal"</span><br />
<span style="color: blue; font-family: 'Courier New', Courier, monospace; line-height: 1.4;">> Premium <- c(4486, 5024, 5680, 6590, 7482, 8502)</span><br />
<span style="color: blue; font-family: 'Courier New', Courier, monospace; line-height: 1.4;">> ELR <- .83 </span><br />
<span style="color: blue; font-family: 'Courier New', Courier, monospace; line-height: 1.4;">> EstimatedUltimateLoss <- Premium * ELR</span><br />
<span style="color: blue; font-family: 'Courier New', Courier, monospace; line-height: 1.4;">> IBNR <- EstimatedUltimateLoss - ReportedLoss</span><br />
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<span style="color: #333333; font-family: Helvetica Neue Light, HelveticaNeue-Light, Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 1.4;">Voila. Simple and succinct in R.</span><br />
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<span style="color: #333333; font-family: Helvetica Neue Light, HelveticaNeue-Light, Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 1.4;"><b>Note:</b> the Claims Reserving Manual gives premium ("aP" in the manual) in reverse accident year order (most recent year first, oldest accident year last), but we enter the accident year premium and loss data in chronological order (oldest accident year first).</span><br />
<br style="-webkit-animation: 0 !important; -webkit-transition: none !important; transition: none !important;" />
<span style="color: #333333; font-family: Helvetica Neue Light, HelveticaNeue-Light, Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 1.4;">In the example above we expect the same loss ratio for every year, so ELR is a scalar and R knows to replicate that value for every element in the Premium vector before performing the multiplication. If we think 83% is expected for the most recent accident year but is expected to be 2 points less per year before that, we could store that pattern in an ELR </span><u style="color: #333333; font-family: 'Helvetica Neue Light', HelveticaNeue-Light, 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 14px; line-height: 1.4;">vector</u><span style="color: #333333; font-family: Helvetica Neue Light, HelveticaNeue-Light, Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 1.4;">:</span><br />
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<span style="color: blue; font-family: 'Courier New', Courier, monospace; font-size: 14px; line-height: 1.4;">> ELR <- </span><span style="color: blue; font-family: Courier New, Courier, monospace;"><span style="font-size: 14px; line-height: 19px;">.83 + (-5:0) * .02</span></span><br />
<br style="-webkit-animation: 0 !important; -webkit-transition: none !important; transition: none !important;" />
<span style="color: #333333; font-family: Helvetica Neue Light, HelveticaNeue-Light, Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 1.4;">and the remaining two calculations still hold.</span><br />
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<span style="color: #333333; font-family: Helvetica Neue Light, HelveticaNeue-Light, Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 1.4;">For a final complication, if we were provided a </span><u style="color: #333333; font-family: 'Helvetica Neue Light', HelveticaNeue-Light, 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 14px; line-height: 1.4;">triangle</u><span style="color: #333333; font-family: Helvetica Neue Light, HelveticaNeue-Light, Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 1.4;"> of reported losses, ChainLadder has a helper function to pull off the most recent diagonal automatically. Again, from the </span><i style="color: #333333; font-family: 'Helvetica Neue Light', HelveticaNeue-Light, 'Helvetica Neue', Helvetica, Arial, sans-serif; font-size: 14px; line-height: 1.4;">Claims Reserving Manual</i><br />
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<span style="color: blue; font-family: 'Courier New', Courier, monospace; font-size: 14px; line-height: 1.4;">> ReportedLossTriangle <- matrix(c(</span><br />
<span style="color: blue; font-family: 'Courier New', Courier, monospace; font-size: 14px; line-height: 1.4;"> 1001, 1855, 2423, 2988, 3335, 3483,</span><br />
<span style="color: blue; font-family: 'Courier New', Courier, monospace; font-size: 14px; line-height: 1.4;"> 1113, 2103, 2774, 3422, 3844, NA,</span><br />
<span style="color: blue; font-family: 'Courier New', Courier, monospace; font-size: 14px; line-height: 1.4;"> 1265, 2433, 3233, 3977, NA, NA,</span><br />
<span style="color: blue; font-family: 'Courier New', Courier, monospace; font-size: 14px; line-height: 1.4;"> 1490, 2873, 3880, NA, NA, NA,</span><br />
<span style="color: blue; font-family: 'Courier New', Courier, monospace; font-size: 14px; line-height: 1.4;"> 1725, 3261, NA, NA, NA, NA,</span><br />
<span style="color: blue; font-family: 'Courier New', Courier, monospace; font-size: 14px; line-height: 1.4;"> 1889, NA, NA, NA, NA, NA), nrow = 6, byrow = TRUE)</span><br />
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<span style="color: #333333; font-family: Helvetica Neue Light, HelveticaNeue-Light, Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 1.4;">Note: Use NA's for future values that truly are "not available" yet. The shape of the matrix (6x6) is completely specified by "nrow=6" because 36 values are given. Finally, R stores data in column format and expects data to be entered accordingly, so byrow=TRUE is required here because the data is entered in more readable, row-wise order.</span><br />
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<span style="color: #333333; font-family: Helvetica Neue Light, HelveticaNeue-Light, Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 1.4;">Then</span><br />
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<span style="color: blue; font-family: 'Courier New', Courier, monospace; font-size: 14px; line-height: 1.4;">> library(ChainLadder) # nothing above required the package</span><br />
<span style="color: blue; font-family: 'Courier New', Courier, monospace; font-size: 14px; line-height: 1.4;">> ReportedLoss <- getLatestCumulative(ReportedLossTriangle)</span><br />
<br style="-webkit-animation: 0 !important; -webkit-transition: none !important; transition: none !important;" />
<span style="color: #333333; font-family: Helvetica Neue Light, HelveticaNeue-Light, Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 1.4;">yields the original values above and the remaining calculations work without change. </span><br />
<br style="-webkit-animation: 0 !important; -webkit-transition: none !important; transition: none !important;" />
<span style="color: #333333; font-family: Helvetica Neue Light, HelveticaNeue-Light, Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 1.4;">This is the first post demonstrating how to carry out deterministic reserving methods with the ChainLadder package in R.</span><br />
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<span style="color: #333333; font-family: Helvetica Neue Light, HelveticaNeue-Light, Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 14px; line-height: 1.4;">-dmm</span></div>
Murphy Danhttp://www.blogger.com/profile/02252526252924091700noreply@blogger.com0