creating a probability tree using draw in open ofic

As part of a Problem Solving Course that I teach, I have several sessions on probability theory. Given that attorneys must frequently make decisions in environments of uncertainty, probability can be a useful skill for law students to learn.

Conditional probability, and Bayes' Theorem, are important sub-topics that I focus upon.  In teaching my students about Conditional Probability, it is often helpful to create a Conditional Probability Tree diagram like the one pictured below (sometimes called a probability tree).  I'll explain in a future post why such a diagram/graph is a useful visualization for learners.

(See also this Javascript Conditional Probability Tree Diagram webpage that I created in that I describe in a different post.)

Conditional Probability Tree Diagram

No Probability Tree Diagrams in R ?

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

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 like the one above.

Thus, I put together some basic R code below for visualizing conditional probability trees, using the Rgraphviz R package.  You 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.

I thought I'd release the code below to others in case it is useful.

(Caveat:  This 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).

(You can also look at this other post about creating a Probability Tree Diagram Using Javascript and D3 if R is not your preferred platform.)

R Code to Create a Visual Conditional Probability Tree

            # R Conditional Probability Tree Diagram  # The Rgraphviz graphing package must be installed to do this require("Rgraphviz")  # Change the three variables below to match your actual values # These are the values that you can change for your own probability tree # From these three values, other probabilities (e.g. prob(b)) will be calculated   # Probability of a a<-.01  # Probability (b | a) bGivena<-.99  # Probability (b | ¬a) bGivenNota<-.10  ###################### Everything below here will be calculated  # Calculate the rest of the values based upon the 3 variables above notbGivena<-1-bGivena notA<-1-a notbGivenNota<-1-bGivenNota  #Joint Probabilities of a and B, a and notb, nota and b, nota and notb aANDb<-a*bGivena aANDnotb<-a*notbGivena notaANDb <- notA*bGivenNota notaANDnotb <- notA*notbGivenNota  # Probability of B b<- aANDb + notaANDb notB <- 1-b  # Bayes theorum - probabiliyt of A | B # (a | b) = Prob (a AND b) / prob (b) aGivenb <- aANDb / b  # These are the labels of the nodes on the graph # To signify "Not A" - we use A' or A prime   node1<-"P" node2<-"A" node3<-"A'" node4<-"A&B" node5<-"A&B'" node6<-"A'&B" node7<-"A'&B'" nodeNames<-c(node1,node2,node3,node4, node5,node6, node7)  rEG <- new("graphNEL", nodes=nodeNames, edgemode="directed") #Erase any existing plots dev.off()  # Draw the "lines" or "branches" of the probability Tree rEG <- addEdge(nodeNames[1], nodeNames[2], rEG, 1) rEG <- addEdge(nodeNames[1], nodeNames[3], rEG, 1) rEG <- addEdge(nodeNames[2], nodeNames[4], rEG, 1) rEG <- addEdge(nodeNames[2], nodeNames[5], rEG, 1) rEG <- addEdge(nodeNames[3], nodeNames[6], rEG, 1) rEG <- addEdge(nodeNames[3], nodeNames[7], rEG, 10)  eAttrs <- list()  q<-edgeNames(rEG)  # Add the probability values to the the branch lines  eAttrs$label <- c(toString(a),toString(notA),  toString(bGivena), toString(notbGivena),  toString(bGivenNota), toString(notbGivenNota)) names(eAttrs$label) <- c(q[1],q[2], q[3], q[4], q[5], q[6]) edgeAttrs<-eAttrs  # Set the color, etc, of the tree attributes<-list(node=list(label="foo", fillcolor="lightgreen", fontsize="15"),  edge=list(color="red"),graph=list(rankdir="LR"))  #Plot the probability tree using Rgraphvis plot(rEG, edgeAttrs=eAttrs, attrs=attributes) nodes(rEG) edges(rEG)  #Add the probability values to the leaves of A&B, A&B', A'&B, A'&B' text(500,420,aANDb, cex=.8)  text(500,280,aANDnotb,cex=.8)  text(500,160,notaANDb,cex=.8)  text(500,30,notaANDnotb,cex=.8)  text(340,440,"(B | A)",cex=.8)  text(340,230,"(B | A')",cex=.8)  #Write a table in the lower left of the probablites of A and B text(80,50,paste("P(A):",a),cex=.9, col="darkgreen") text(80,20,paste("P(A'):",notA),cex=.9, col="darkgreen")  text(160,50,paste("P(B):",round(b,digits=2)),cex=.9) text(160,20,paste("P(B'):",round(notB, 2)),cex=.9)  text(80,420,paste("P(A|B): ",round(aGivenb,digits=2)),cex=.9,col="blue")        

Another Probability Tree Example in Light Blue with (¬ sign)

Harry Surden

Harry Surden is an Associate Professor of Law at the University of Colorado Law School. His scholarship centers upon intellectual property law with a substantive focus on patents and copyright, information privacy law, legal informatics and legal automation, and the application of computer technology within the legal system. His Twitter is : @Harry Surden

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