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Activity Number:
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68
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Type:
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Topic Contributed
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Date/Time:
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Sunday, July 31, 2016 : 4:00 PM to 5:50 PM
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Sponsor:
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Section on Bayesian Statistical Science
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Abstract #318721
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Title:
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Analyzing MCMC Output
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Author(s):
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Dootika Vats* and James Flegal and Galin Jones
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Companies:
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University of Minnesota - Twin Cities and University of California at Riverside and University of Minnesota - Twin Cities
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Keywords:
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Markov chain Monte Carlo ;
Covariance matrix ;
multivariate
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Abstract:
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Markov chain Monte Carlo (MCMC) produces a correlated sample in order to estimate expectations with respect to a target distribution. A fundamental question is when should sampling stop so that we have good estimates of the desired quantities? The key to answering this question lies in assessing the Monte Carlo error through a multivariate Markov chain central limit theorem. However, the multivariate nature of this Monte Carlo error has been largely ignored in the MCMC literature. We provide conditions for consistently estimating the asymptotic covariance matrix via the multivariate batch means estimator. Based on this theoretical result we present a relative standard deviation fixed volume sequential stopping rule for terminating simulation. We show that this stopping rule is asymptotically equivalent to terminating when the effective sample size for the MCMC sample is above a desired threshold, giving an intuitive and theoretically justified approach to implementing the proposed method. The finite sample properties of the proposed method are then demonstrated in examples.
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Authors who are presenting talks have a * after their name.
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