{"id":292,"date":"2015-03-02T17:51:10","date_gmt":"2015-03-02T23:51:10","guid":{"rendered":"http:\/\/harrysurden.com\/wordpress\/?p=292"},"modified":"2015-05-04T15:49:11","modified_gmt":"2015-05-04T21:49:11","slug":"probability-tree-diagrams-in-r","status":"publish","type":"post","link":"https:\/\/www.harrysurden.com\/wordpress\/archives\/292","title":{"rendered":"Probability Tree Diagrams in R"},"content":{"rendered":"

As part of a\u00a0Problem Solving Course<\/a>\u00a0that I teach, I have\u00a0several sessions\u00a0on probability theory. Given that attorneys must frequently make decisions in environments of\u00a0uncertainty, probability\u00a0can be a useful skill for law students to learn.<\/p>

Conditional probability<\/a>, and Bayes’ Theorem<\/a>, are important sub-topics that I focus upon. \u00a0In teaching my\u00a0students about Conditional Probability<\/a>, it is often helpful\u00a0to create a Conditional Probability Tree<\/em> diagram\u00a0like the one pictured below (sometimes called a probability tree). \u00a0I’ll explain in a future post why such a diagram\/graph\u00a0is a useful visualization for learners.<\/p>

(See also this Javascript Conditional Probability Tree Diagram webpage that I created in that I describe<\/a> in a different\u00a0post.)<\/p>\n

Conditional Probability\u00a0Tree\u00a0Diagram<\/strong><\/h2>

\"Conditioal<\/a><\/p>\n

No Probability Tree Diagrams in R ?<\/h2>

Like many others, I use the popular free, and open-source\u00a0R statistical programming language<\/a>.\u00a0 R is one of the top computing platforms in which to perform machine learning and other statistical tasks (along with Python<\/a> – another favorite of mine). \u00a0To program in R, I use the excellent R-Studio application<\/a> which makes the experience\u00a0much better.<\/p>

Given the relationship between R and statistics, I was somewhat surprised that I was unable to find any easily accessible R code or functions to create visually appealing Conditional Probability Tree diagrams\u00a0like the one above.<\/p>

Thus, I put together some basic R code below for visualizing conditional probability trees, using the\u00a0Rgraphviz<\/a> R package. \u00a0You must install the Rgraphviz package before using the R code below. If you know of other ways to create visually appealing conditional probability tree in R that I may have missed in my search, please let me know.<\/p>

I thought I’d release the\u00a0code below to others in case it is useful.<\/p>

(Caveat: \u00a0This is rough code, and has not been thoroughly tested, and is just meant as a starting example to help make your own probability tree diagrams – so no guarantees).<\/p>

(You can also look at this\u00a0other\u00a0post about\u00a0creating a\u00a0Probability Tree Diagram Using Javascript and D3<\/a>\u00a0if R is not your preferred platform.)<\/p>\n

R Code to Create a Visual Conditional Probability Tree<\/strong><\/h3>\n
\r\n\r\n# R Conditional Probability Tree Diagram\r\n\r\n# The Rgraphviz graphing package must be installed to do this\r\nrequire("Rgraphviz")\r\n\r\n# Change the three variables below to match your actual values\r\n# These are the values that you can change for your own probability tree\r\n# From these three values, other probabilities (e.g. prob(b)) will be calculated \r\n\r\n# Probability of a\r\na<-.01\r\n\r\n# Probability (b | a)\r\nbGivena<-.99\r\n\r\n# Probability (b | \u00aca)\r\nbGivenNota<-.10\r\n\r\n###################### Everything below here will be calculated\r\n\r\n# Calculate the rest of the values based upon the 3 variables above\r\nnotbGivena<-1-bGivena\r\nnotA<-1-a\r\nnotbGivenNota<-1-bGivenNota\r\n\r\n#Joint Probabilities of a and B, a and notb, nota and b, nota and notb\r\naANDb<-a*bGivena\r\naANDnotb<-a*notbGivena\r\nnotaANDb <- notA*bGivenNota\r\nnotaANDnotb <- notA*notbGivenNota\r\n\r\n# Probability of B\r\nb<- aANDb + notaANDb\r\nnotB <- 1-b\r\n\r\n# Bayes theorum - probabiliyt of A | B\r\n# (a | b) = Prob (a AND b) \/ prob (b)\r\naGivenb <- aANDb \/ b\r\n\r\n# These are the labels of the nodes on the graph\r\n# To signify "Not A" - we use A' or A prime \r\n\r\nnode1<-"P"\r\nnode2<-"A"\r\nnode3<-"A'"\r\nnode4<-"A&B"\r\nnode5<-"A&B'"\r\nnode6<-"A'&B"\r\nnode7<-"A'&B'"\r\nnodeNames<-c(node1,node2,node3,node4, node5,node6, node7)\r\n\r\nrEG <- new("graphNEL", nodes=nodeNames, edgemode="directed")\r\n#Erase any existing plots\r\ndev.off()\r\n\r\n# Draw the "lines" or "branches" of the probability Tree\r\nrEG <- addEdge(nodeNames[1], nodeNames[2], rEG, 1)\r\nrEG <- addEdge(nodeNames[1], nodeNames[3], rEG, 1)\r\nrEG <- addEdge(nodeNames[2], nodeNames[4], rEG, 1)\r\nrEG <- addEdge(nodeNames[2], nodeNames[5], rEG, 1)\r\nrEG <- addEdge(nodeNames[3], nodeNames[6], rEG, 1)\r\nrEG <- addEdge(nodeNames[3], nodeNames[7], rEG, 10)\r\n\r\neAttrs <- list()\r\n\r\nq<-edgeNames(rEG)\r\n\r\n# Add the probability values to the the branch lines\r\n\r\neAttrs$label <- c(toString(a),toString(notA),\r\n toString(bGivena), toString(notbGivena),\r\n toString(bGivenNota), toString(notbGivenNota))\r\nnames(eAttrs$label) <- c(q[1],q[2], q[3], q[4], q[5], q[6])\r\nedgeAttrs<-eAttrs\r\n\r\n# Set the color, etc, of the tree\r\nattributes<-list(node=list(label="foo", fillcolor="lightgreen", fontsize="15"),\r\n edge=list(color="red"),graph=list(rankdir="LR"))\r\n\r\n#Plot the probability tree using Rgraphvis\r\nplot(rEG, edgeAttrs=eAttrs, attrs=attributes)\r\nnodes(rEG)\r\nedges(rEG)\r\n\r\n#Add the probability values to the leaves of A&B, A&B', A'&B, A'&B'\r\ntext(500,420,aANDb, cex=.8)\r\n\r\ntext(500,280,aANDnotb,cex=.8)\r\n\r\ntext(500,160,notaANDb,cex=.8)\r\n\r\ntext(500,30,notaANDnotb,cex=.8)\r\n\r\ntext(340,440,"(B | A)",cex=.8)\r\n\r\ntext(340,230,"(B | A')",cex=.8)\r\n\r\n#Write a table in the lower left of the probablites of A and B\r\ntext(80,50,paste("P(A):",a),cex=.9, col="darkgreen")\r\ntext(80,20,paste("P(A'):",notA),cex=.9, col="darkgreen")\r\n\r\ntext(160,50,paste("P(B):",round(b,digits=2)),cex=.9)\r\ntext(160,20,paste("P(B'):",round(notB, 2)),cex=.9)\r\n\r\ntext(80,420,paste("P(A|B): ",round(aGivenb,digits=2)),cex=.9,col="blue")\r\n\r\n<\/pre>\n
Another Probability Tree Example in Light Blue with (\u00ac sign)<\/strong><\/h3>
 <\/p>
\"Rplot02\"<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"
As part of a\u00a0Problem Solving Course\u00a0that I teach, I have\u00a0several sessions\u00a0on probability theory. Given that attorneys must frequently make decisions in environments of\u00a0uncertainty, probability\u00a0can be a useful skill for law students to learn.Conditional probability, and Bayes’ Theorem, are important sub-topics that I focus upon. \u00a0In teaching my\u00a0students about Conditional Probability, it is often helpful\u00a0to create […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[11],"tags":[],"_links":{"self":[{"href":"https:\/\/www.harrysurden.com\/wordpress\/wp-json\/wp\/v2\/posts\/292"}],"collection":[{"href":"https:\/\/www.harrysurden.com\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.harrysurden.com\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.harrysurden.com\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.harrysurden.com\/wordpress\/wp-json\/wp\/v2\/comments?post=292"}],"version-history":[{"count":10,"href":"https:\/\/www.harrysurden.com\/wordpress\/wp-json\/wp\/v2\/posts\/292\/revisions"}],"predecessor-version":[{"id":349,"href":"https:\/\/www.harrysurden.com\/wordpress\/wp-json\/wp\/v2\/posts\/292\/revisions\/349"}],"wp:attachment":[{"href":"https:\/\/www.harrysurden.com\/wordpress\/wp-json\/wp\/v2\/media?parent=292"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.harrysurden.com\/wordpress\/wp-json\/wp\/v2\/categories?post=292"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.harrysurden.com\/wordpress\/wp-json\/wp\/v2\/tags?post=292"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}