Bayesian multiple comparisons of simply ordered means using priors with a point mass

Abstract

Comparison of k treatment means under the simple-order assumption ( μ 1 ≤ μ 2 ≤ ⋯ ≤ μ k ) is considered. Under an order restriction, isotonic estimates and global tests of homogeneity have been known for several decades. Recently, some multiple-comparison techniques have been proposed, but none has become the standard. In this article, we develop multiple-comparison and clustering techniques for simply ordered means using a Bayesian hierarchical model. We parameterize each individual mean in terms of the difference between the preceding mean and itself. Estimates for such difference parameters are obtained using the MCMC method. Pairwise comparisons and determination of the most probable ordered clustering are based on the posterior probabilities of the difference parameters being zero. Numerical examples are given.