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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.