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Biometrika 2009 96(2):249-262; doi:10.1093/biomet/asp021
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© 2009 Biometrika Trust

Article

Nonparametric Bayes local partition models for random effects

David B. Dunson

Department of Statistical Science, Box 90251, Duke University, Durham, North Carolina 27708, U.S.A. dunson{at}stat.duke.edu

Received for publication 1 February 2008. Revision received 1 November 2008.
  Abstract

This paper focuses on the problem of choosing a prior for an unknown random effects distribution within a Bayesian hierarchical model. The goal is to obtain a sparse representation by allowing a combination of global and local borrowing of information. A local partition process prior is proposed, which induces dependent local clustering. Subjects can be clustered together for a subset of their parameters, and one learns about similarities between subjects increasingly as parameters are added. Some basic properties are described, including simple two-parameter expressions for marginal and conditional clustering probabilities. A slice sampler is developed which bypasses the need to approximate the countably infinite random measure in performing posterior computation. The methods are illustrated using simulation examples, and an application to hormone trajectory data.

Key Words: Dirichlet process • Functional data • Local shrinkage • Meta-analysis • Multi-task learning • Partition model • Slice sampling • Stick-breaking


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