Bayesian Analysis

Ergodic averages for monotone functions using upper and lower dominating processes

Kerrie Mengersen and Jesper M{\o}ller

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We show how the mean of a monotone function (defined on a state space equipped with a partial ordering) can be estimated, using ergodic averages calculated from upper and lower dominating processes of a stationary irreducible Markov chain. In particular, we do not need to simulate the stationary Markov chain and we eliminate the problem of whether an appropriate burn-in is determined or not. Moreover, when a central limit theorem applies, we show how confidence intervals for the mean can be estimated by bounding the asymptotic variance of the ergodic average based on the equilibrium chain. Our methods are studied in detail for three models using Markov chain Monte Carlo methods and we also discuss various types of other models for which our methods apply.

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Bayesian Anal. Volume 2, Number 4 (2007), 761-781.

First available in Project Euclid: 22 June 2012

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Asymptotic variance Bayesian models Burn-in Ergodic average Ising model Markov chain Monte Carlo Mixture model Monotonocity Perfect simulation Random walk Spatial models Upper and lower dominating processes


M{\o}ller, Jesper; Mengersen, Kerrie. Ergodic averages for monotone functions using upper and lower dominating processes. Bayesian Anal. 2 (2007), no. 4, 761--781. doi:10.1214/07-BA231.

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