Facilitating the Gibbs sampler: The Gibbs stopper and the Griddy–Gibbs sampler

Christian Ritter, Martin A. Tanner

Research output: Contribution to journalArticlepeer-review

231 Scopus citations

Abstract

The article briefly reviews the history, literature, and form of the Gibbs sampler. An importance sampling device is proposed for converting the output of the Gibbs sampler to a sample from the exact posterior. This Gibbs stopper technique is also useful for assessing convergence of the Gibbs sampler for moderate sized problems. Also presented is an approach for implementing the Gibbs sampler in nonconjugate situations. The basic idea is to approximate the true cdf of each conditional distribution by a piecewise linear function and then sample from the approximation. Questions relating to the number of nodes in the approximation, gap size between successive nodes, and the treatment of unbounded intervals for a given conditional are discussed. The methodology is illustrated using a genetic linkage model, a nonlinear regression model, and the Cox model.

Original languageEnglish (US)
Pages (from-to)861-868
Number of pages8
JournalJournal of the American Statistical Association
Volume87
Issue number419
DOIs
StatePublished - Sep 1992

Keywords

  • Bayesian statistics
  • Cox regression
  • Monte Carlo methods
  • Nonlinear regression

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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