Suppose that we have a situation in which the Bayes test that rejects H0 when Pr(H0 true x) 0 is the same as the level 0 test of H0 for all 0 (Example 9 8 5 has this property, but so do many other situations ) Prove that the p value equals the posterior probability that H0 is true ...

We shall argue indirectly Suppose that there is x ...

Suppose that we have a situation in which the Bayes test that rejects H0 when Pr(H0 true

Question:

Suppose that we have a situation in which the Bayes test that rejects H0 when Pr(H0 true |x) ≤ α0 is the same as the level α0 test of H0 for all α0. (Example 9.8.5 has this property, but so do many other situations.) Prove that the p-value equals the posterior probability that H0 is true.