VARIABLE TRANSFORMATION TO OBTAIN GEOMETRIC ERGODICITY IN THE RANDOM-WALK METROPOLIS ALGORITHM

• 成果类型: Article
• 署名作者: Johnson, Leif T.; Geyer, Charles J.
• 署名单位: Alphabet Inc.; Google Incorporated; University of Minnesota System; University of Minnesota Twin Cities
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/12-AOS1048
• 发表日期: 2012
• 页码: 3050-3076
• 关键词: CENTRAL-LIMIT-THEOREM; chain monte-carlo; exploring posterior distributions; random effects model; markov-chain; GIBBS SAMPLER; hierarchical-models; convergence-rates; estimators; hastings

摘要

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.