Open Access
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


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.


Download Citation

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.


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

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

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

Vol.40 • No. 6 • December 2012
Back to Top