## Contour plots on R

In one of the homework problems, you are asked to do a Bayesian sensitivity analysis for a posterior probability with respect to the prior. Specifically, suppose we are interested in learning about a proportion and we wish to compute the posterior probability . We observe the data (25 successes, 40 failures) and we want to know the sensitivity of the posterior probability with respect to the prior mean and the prior precision parameter where and are the beta shape parameters.

It is easy to construct a contour plot to illustrate this sensitivity analysis on R.

1. First we set up a grid of values of and :

eta = seq(.1, .9, by=.1) K = c(1, 2, 8, 16, 32)

2. Next we write a short function that computes the posterior probability as a function of and .

myfun=function(eta, K) 1 - pbeta(.5, K*eta+ 25, K*(1-eta) + 40)

3. We now use the outer function to compute this probability on all combinations of and — the result is a matrix where the rows correspond to and the columns to .

PROB = outer(eta, K, myfun)

4. Last, we use the contour function with inputs the two vectors and the matrix of probabilities. We can specify which levels to draw on the contour graph.

contour(eta, K, PROB, levels=c(0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 0.95), xlab="eta", ylab="K", main="P(theta > 0.5)")