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Activity Number: 542
Type: Invited
Date/Time: Wednesday, August 6, 2014 : 2:00 PM to 3:50 PM
Sponsor: Section on Statistical Computing
Abstract #310887 View Presentation
Title: Efficiency of Markov Chain Monte Carlo for Parametric Statistical Models
Author(s): Natesh S. Pillai and David Dunson and Dawn B. Woodard*+
Companies: Harvard and Duke University and Cornell University
Keywords: Monte Carlo ; Markov chain ; computation ; Bayesian
Abstract:

We analyze the efficiency of Markov chain Monte Carlo (MCMC) methods used in Bayesian computation. While convergence diagnosis is used to choose how long to run a Markov chain, it can be inaccurate and does not provide insight regarding how the efficiency scales with the number of parameters or other quantities of interest. We instead characterize the number of iterations of the Markov chain (the running time) sufficient to ensure that the approximate Bayes estimator obtained by MCMC preserves the property of asymptotic efficiency. We show that in many situations where the likelihood satisfies local asymptotic normality, the running time grows linearly in the number of observations n.


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