Partially collapsed Gibbs samplers: Theory and methods

David A. Van Dyk, Taeyoung Park

Research output: Contribution to journalArticle

121 Citations (Scopus)

Abstract

Ever-increasing computational power, along with ever-more sophisticated statistical computing techniques, is making it possible to fit ever-more complex statistical models. Among the more computationally intensive methods, the Gibbs sampler is popular because of its simplicity and power to effectively generate samples from a high-dimensional probability distribution. Despite its simple implementation and description, however, the Gibbs sampler is criticized for its sometimes slow convergence, especially when it is used to fit highly structured complex models. Here we present partially collapsed Gibbs sampling strategies that improve the convergence by capitalizing on a set of functionally incompatible conditional distributions. Such incompatibility generally is avoided in the construction of a Gibbs sampler, because the resulting convergence properties are not well understood. We introduce three basic tools (marginalization, permutation, and trimming) that allow us to transform a Gibbs sampler into a partially collapsed Gibbs sampler with known stationary distribution and faster convergence.

Original languageEnglish
Pages (from-to)790-796
Number of pages7
JournalJournal of the American Statistical Association
Volume103
Issue number482
DOIs
Publication statusPublished - 2008 Jun 1

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All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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