Bayesian Joint Estimation of Binomial Proportions

Testing the hypothesis H that k > 1 binomial parameters are equal and jointly estimating these parameters are related problems. A Bayesian argument can simultaneously answer these inference questions: to test the hypothesis H the posterior probability = (H | x) of H given the experimental data x can be used; to estimate each binomial parameter, their Bayesian estimates under H and its complement H are combined, with weights and 1 -, respectively.