BAYESIAN MULTIPLE COMPARISONS USING DIRICHLET PROCESS PRIORS

We consider the problem of multiple comparisons from a Bayesian viewpo int. The family of Dirichlet process priors is applied in the form of baseline prior/likelihood combinations to obtain posterior probabiliti es for various hypotheses of equality among population means. The base line prior/likelihood combinations considered here are beta/binomial a nd normal/inverted gamma with equal variances on treatment means. The prior probabilities of the hypotheses depend directly on the concentra tion parameter of the Dirichlet process prior. Finding posterior distr ibutions is analytically intractable; we use Gibbs sampling. The poste rior probabilities of hypotheses of interest are easily obtained as a by-product in evaluating the marginal posterior distributions of the p arameters. The proposed procedure is compared to Duncan's multiple ran ge test and shown to be mon powerful under certain alternative hypothe ses.