The Matrix Stick-Breaking Process: Flexible Bayes Meta Analysis

David B. Dunson, Ya Xue and Lawrence Carin

Biostatistics Branch, National Institute of Environmental Health Sciences, U.S. National Institutes of Health and Duke University

January, 2007

In analyzing data from multiple related studies, it is often of interest to borrow information across studies and to cluster similar studies. Although parametric hierarchical models are commonly used, a concern is sensitivity to the form chosen for the random effects distribution. A Dirichlet process (DP) prior can allow the distribution to be unknown, while clustering studies. However, the DP does not allow local clustering of studies with respect to a subset of the coefficients without making independence assumptions. Motivated by this problem, we propose a matrix stick-breaking process (MSBP) as a prior for a matrix of random probability measures. Theoretical properties of the MSBP are considered in detail, and methods are developed for posterior computation using MCMC. Using the MSBP as a prior for a matrix of study-specific regression coefficients, we demonstrate advantages over parametric modeling in simulated examples. The methods are further illustrated using a multinational uterotrophic bioassay study.

Keywords: Clustering; Dirichlet process; Hierarchical model; Mixture model; Nonparametric Bayes; Random effects.


The manuscript is available in PDF formats.