Variable transformation to obtain geometric ergodicity in the random-walk Metropolis algorithm

Leif T. Johnson, Charles J. Geyer

Research output: Contribution to journalArticle

12 Scopus citations

Abstract

A random-walk Metropolis sampler is geometrically ergodic if its equilibrium density is super-exponentially light and satisfies a curvature condition [Stochastic Process. Appl. 85 (2000) 341-361]. Many applications, including Bayesian analysis with conjugate priors of logistic and Poisson regression and of log-linear models for categorical data result in posterior distributions that are not super-exponentially light. We show how to apply the change-of variable formula for diffeomorphisms to obtain new densities that do satisfy the conditions for geometric ergodicity. Sampling the new variable and mapping the results back to the old gives a geometrically ergodic sampler for the original variable. This method of obtaining geometric ergodicity has very wide applicability.

Original languageEnglish (US)
Pages (from-to)3050-3076
Number of pages27
JournalAnnals of Statistics
Volume40
Issue number6
DOIs
StatePublished - Dec 1 2012

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Keywords

  • Change of variable
  • Conjugate prior
  • Drift condition
  • Exponential family
  • Markov chain Monte Carlo
  • Markov chain isomorphism
  • Metropolis-Hastings-Green algorithm

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