A Partition Model for Bayesian Multiple Comparisons

• Activity Number: 271
• Type: Contributed
• Date/Time: Tuesday, August 9, 2005 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Jie Yang*+ and Peter McCullagh
• Companies: The University of Chicago and The University of Chicago
• Keywords: Allowance for selection ; Ewens partition process ; Multiple comparisons ; Multivariate t distribution ; Residual configuration statistic ; Self-similar partition

Abstract

We illustrate how a partition model may be used to judge equivalence or nonequivalence of varieties in a conventional experiment where multiple testing might be used for a similar purpose. A clustering of n objects, such as varieties, is a partition of those objects into disjoint nonempty sets called blocks or equivalence classes. To each partition E of {1,..., n}, there corresponds a subspace X(E) of $R^n$ consisting of vectors that are constant on blocks. In fact, X(E) is the linear span of the binary matrix E, so the dimension is the rank of E or the number of blocks in the partition. We construct an exchangeable, real-valued process such that for each $n\ge 1$ and for each partition E of {1,..., n}, the subspace X(E) has positive probability. The process is a Gaussian mixture such that $Y_i \sim N(0, 1)$. When this process is used as a prior in a Gaussian model, inferences are obtained in the form of a posterior distribution on partitions. Inference for variety contrasts from the partition model also is given.