Warp Bridge Sampling: The Next Generation

• Activity Number: 309
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Computing
• Author(s): Lazhi Wang*+ and Xiao-Li Meng
• Companies: Harvard University and Harvard University
• Keywords: Monte Carlo Methods ; Bridge Sampling ; Transformations ; Warp Bridge Sampling

Abstract

Warp bridge sampling (Meng and Schilling, 2002, JCGS) aims to dramatically reduce Monte Carlo errors in applying bridge sampling (Meng and Wong, 1996,  Statistica Sinica) for estimating normalizing constants, an common problem in statistics and scientific studies. The idea of warp bridge sampling relies on the fact that we can warp two densities into having substantial overlaps without altering the normalizing constants. Since the Monte Carlo errors of bridge sampling are controlled by the amount of distributional overlaps, warp bridge sampling can be substantially more accurate than the original bridge sampling without unduly increasing the computational load. In this talk we will first review the warp I, II and III transformations introduced in Meng and Schilling (2002). We then introduce a class of stochastic transformation that is capable of transforming a multimodal distribution into a unimodal one. We present preliminary theoretical and empirical results to demonstrate the great potential of this new class of wrap transformations, as well as open problems that need to be solved before they can be applied effectively and routinely. (This is join work with Xiao-Li Meng.)