Consistent estimation of the accuracy of importance sampling using regenerative simulation

Importance sampling is a common technique traditionally used in cases where interest lies in estimation of characteristics of a density π(1)π(1), but samples are available from a different distribution π(0)π(0). It is important, however, to evaluate the accuracy of the estimate obtained using importance sampling. In cases where samples are obtained using Markov chain Monte Carlo methods, there does not seem to exist in the literature any consistent or easily computable estimate of the variance of the importance sampling estimator. In this paper we propose an estimator based on regenerative simulation that is consistent as well as easily computable.