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The matrix stick-breaking process: flexible Bayes meta analysis

Thursday 9th August 2007 - 11:30 to 12:30
INI Seminar Room 1

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.

Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons