Seminars

General Departmental Seminar Series

A New Sampler for Dirichlet Process Mixture Models with an Application to Gene Expression Data

David Dahl, Ph.D. candidate, Department of Statistics, UW-Madison

Friday, April 4, 2003, 12 p.m.

6225 Medical Sciences Center (CSSC), 1300 University Avenue

ABSTRACT

Conjugate Dirichlet Process (DP) mixture models are a popular Bayesian approach to identifying latent classes which explain dependencies among observations. These models are typically fit using the Gibbs sampler which, due to its incremental nature, is prone to being trapped in local models. At the other extreme, a split-merge sampler proposes drastic updates which are rarely accepted. Both samplers can lead to slow mixing in the underlying Markov chain. This paper introduces the Grab sampler, a new sampler which generalizes the Gibbs sampler and is related to sequential importance sampling. The Grab sampler provides for non-incremental updates and can be tuned to a chosen acceptance rate.

The second part of this paper proposes a new conjugate DP mixture model for gene expression data from DNA microarrays. While existing methods typically focus on finding differential expression between two treatment conditions, this model simultaneously estimates expression levels for an arbitrary number of treatment conditions. Probabilities for over- and under-expression between pairs of treatment combinations are readily computed as well as probabilities for more complicated contrasts involving many treatments.

The proposed model is applied to data from a microarray experiment. The model is fit using existing samplers and the new Grab sampler. Model interpretability is discussed and sampler performance is evaluated.

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