# BNR

## Seminar

### The matrix stick-breaking process: flexible Bayes meta analysis

Dunson, D (Duke)
Thursday 09 August 2007, 11:30-12:30

Seminar Room 1, Newton Institute

#### Abstract

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. Properties of the MSBP are considered, 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 applications to a multinational bioassay study and to borrowing of information in compressing signals.