Exercise

Independent beta priors

What if you assume that one's beliefs about the relief probabilities pS and pN are independent?

A beta curve with shape parameters 4.91 and 3.38 is used to represent one's opinion about pS, and the same \(beta(4.91, 3.38)\) curve is used as a prior for pN.

1000 values of (pS, pN) are simulated from this prior distribution and displayed in the figure on the right.

Instructions

100 XP

Simulate 1000 draws from the beta prior on pS, and 1000 draws from the beta prior on pN.
For each pair of proportions, compute the difference d_NS = pN - pS.
Construct a histogram of the prior on the difference in proportions d_NS.
Find the prior probability that d_NS is greater than 0.
Find a 90% probability interval for d_NS based on the prior.