Home > R work > Contour plots on R

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 P(\theta > 0.5).  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 \eta = a/(a+b) and the prior precision parameter K = a + b where a and b 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 \eta and K:

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 P(\theta > 0.5) as a function of  \eta and K.

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  \eta and K — the result is a matrix where the rows correspond to \eta and the columns to K.

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)")


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