Importance Sampling with Multiple Proposals: New Advances and Comparison

• Activity Number: 661
• Type: Contributed
• Date/Time: Thursday, August 4, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Wentao Li*+ and Zhiqiang Tan and Rong Chen
• Companies: Rutgers University and Rutgers University and Rutgers University
• Keywords: Importance sampling ; Stratified sampling ; Mixture Distribution ; Variance Reduction

Abstract

Abstract Importance sampling is a common method of reducing variance for estimating numerical integration. Various methods have been proposed using samples from multiple proposal distributions including Hesterberg's stratified importance sampling estimator, Owen and Zhou's regression estimator and Tan's maximum likelihood estimator. For the problem of efficiently allocating samples to different proposals, it is common to apply a pilot study to select the mixture proportions before the actual estimation. For such a two-stage procedure, most of the discussions are in empirical sense. Here we investigate the theoretical properties of applying the two-stage procedure in various methods. Using numerical study, it is shown that these two-stage estimators can perform much better than the estimators with naive choice of mixture proportions. Furthermore, while Owen and Zhou's regression estimator and Tan's MLE are designed for estimating normalizing constant, we extend their usage to estimate expectation and apply the two-stage procedure for this extension.