Bayesian Multiple Comparisons Using Dirichlet Process Priors

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Abstract
We consider the problem of multiple comparisons from a Bayesian viewpoint. The family of Dirichlet process priors is applied in the form of baseline prior/likelihood combinations to obtain posterior probabilities for various hypotheses of equality among population means. The baseline prior/likelihood combinations considered here are beta/binomial and normal/inverted gamma with equal variances on treatment means. The prior probabilities of the hypotheses depend directly on the concentration parameter of the Dirichlet process prior. Finding posterior distributions is analytically intractable; we use Gibbs sampling. The posterior probabilities of hypotheses of interest are easily obtained as a by-product in evaluating the marginal posterior distributions of the parameters. The proposed procedure is compared to Duncan's multiple range test and shown to be more powerful under certain alternative hypotheses.

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