Partition-Weighted Monte Carlo Estimation

Abstract

Although various efficient and sophisticated Markov chain Monte Carlo sampling methods have been developed during the last decade, the sample mean is still a dominant in computing Bayesian posterior quantities. The sample mean is simple, but may not be efficient. The weighted sample mean is a natural generalization of the sample mean. In this regard, a new weighted sample mean is proposed by partitioning the support of posterior distribution, so that the same weight is assigned to observations that belong to the same subset in the partition. A novel application of this new weighted sample mean in computing ratios of normalizing constants and necessary theory are provided. Illustrative examples are given to demonstrate the methodology.