Estimating standard errors for importance sampling estimators with multiple Markov chains

摘要: The naive importance sampling estimator, based on samples from a single density, can be numerically unstable. Instead, we consider generalized estimators where more than one probability distribution are combined. We study this problem in the Markov chain Monte Carlo context, independent replaced with samples. If chains converge to their respective target distributions at polynomial rate, then under two finite moment conditions, show central limit theorem holds for estimators. Further, develop an easy implement method calculate valid asymptotic standard errors batch means. also provide means estimator calculating asymptotically of Geyer(1994) reverse logistic estimator. illustrate using Bayesian variable selection procedure linear regression. In particular, is used perform empirical Bayes and obtain high-dimensional setting current methods not applicable.