stephens999
commented
10 years ago The answers are "Yes, I believe so" and "Yes, the 0.23 definitely corresponds to the posterior probability, not the posterior odds. Recall also that the posterior probability is equal to the (conditional) frequentist error probability (remember the two are the same under repeated sampling of the parameter from the prior and the data from p(x|theta))"
Is the 0.289 alpha(p) Berger proposes in the first column, second page of the article as both the frequentist error probability and the default posterior is only true if the prior odds are, as stated,1. Otherwise, B(alpha) = 0.409 would need to be multiplied a different prior odds ratio and then the posterior would be obtained by solving Post.Odds=PriorOdds/(1-PriorOdds). Also, the 0.23 minimum mentioned for a p value of 0.05 would correspond to the posterior probability, not the posterior odds, correct? I think I incorrectly wrote in my notes that this was the posterior odds, but upon rereading it seems like this is the probability of the theta=0 given the data. Thanks very much.