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December 2012 Variable transformation to obtain geometric ergodicity in the random-walk Metropolis algorithm
Leif T. Johnson, Charles J. Geyer
Ann. Statist. 40(6): 3050-3076 (December 2012). DOI: 10.1214/12-AOS1048

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.

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Leif T. Johnson. Charles J. Geyer. "Variable transformation to obtain geometric ergodicity in the random-walk Metropolis algorithm." Ann. Statist. 40 (6) 3050 - 3076, December 2012. https://doi.org/10.1214/12-AOS1048

Information

Published: December 2012
First available in Project Euclid: 22 February 2013

zbMATH: 1302.46033
MathSciNet: MR3097969
Digital Object Identifier: 10.1214/12-AOS1048

Subjects:
Primary: 60J05 , 65C05
Secondary: 60J22

Keywords: change of variable , conjugate prior , drift condition , exponential family , Markov chain isomorphism , Markov chain Monte Carlo , Metropolis–Hastings–Green algorithm

Rights: Copyright © 2012 Institute of Mathematical Statistics

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Vol.40 • No. 6 • December 2012
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