An Adaptive Exchange Algorithm for Sampling from Distribution with Doubly Intractable Normalizing Constants

• Activity Number: 427
• Type: Contributed
• Date/Time: Tuesday, August 2, 2016 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Computing
• Author(s): Ick Hoon Jin* and Faming Liang and Qifan Song and Jun S. Liu
• Companies: University of Notre Dame and University of Florida and Purdue University and Harvard
• Keywords: Exchange Algorithm ; Doubly-Intractable Normalizing Constant ; Stochastic Approximation Monte Carlo ; Autologistic Model

Abstract

Sampling from the posterior distribution for a model whose normalizing constant is intractable is a long-standing problem in statistical research. We propose a new algorithm, the so-called adaptive exchange (AEX) algorithm, to tackle this problem. The new algorithm can be viewed as a MCMC extension of the exchange algorithm, which generates auxiliary variables via an importance sampling procedure from a Markov chain running in parallel. The convergence of the algorithm is established under mild conditions. Compared to the exchange algorithm, the new algorithm removes the requirement that the auxiliary variables must be drawn using a perfect sampler, and thus can be applied to many models for which the perfect sampler is not available or very expensive. Compared to the approximate exchange algorithms, such as the double MH sampler, the new algorithm overcomes their theoretical flaw on convergence. The new algorithm is tested on spatial autologistic models, and the numerical results indicate its validity and efficiency.