摘要：We show how the mean of a monotone function (de ned 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 deter-
mined or not. Moreover, when a central limit theorem applies, we show how
con dence 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.
关键词：Asymptotic variance; Bayesian models; Burn-in; Ergodic average; Ising
model; Markov chain Monte Carlo; Mixture model; Monotonocity; Perfect simu-
lation; Random walk; Spatial models; Upper and lower dominating processes
