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Activity Number: 235
Type: Topic Contributed
Date/Time: Monday, August 1, 2016 : 2:00 PM to 3:50 PM
Sponsor: Section on Bayesian Statistical Science
Abstract #320454 View Presentation
Title: Approximations of Markov Chains and Bayesian Inference
Author(s): James Johndrow* and Jonathan Mattingly and Sayan Mukherjee and David Dunson
Companies: Duke University and Duke University and Duke University and Duke University
Keywords: Bayesian ; approximate MCMC ; computation ; perturbations of Markov chains ; big data ; scalable

The Markov Chain Monte Carlo method is the dominant paradigm for posterior computation in Bayesian analysis. It has long been common to control computation time by making approximations to the Markov transition kernel. Comparatively little attention has been paid to convergence and estimation error in these approximating Markov Chains. We propose a framework for assessing when to use approximations in MCMC algorithms, and how much error in the transition kernel should be tolerated to obtain optimal estimation performance with respect to a specified discrepancy measure and computational budget. The results require only ergodicity of the exact kernel and control of the kernel approximation accuracy. The theoretical framework is applied to approximations based on random subsets of data, low-rank approximations of Gaussian processes, and a novel approximating Markov chain for discrete mixture models.

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