Multivariate output analysis for Markov chain Monte Carlo

Dootika Vats, James M Flegal and Galin L Jones

Biometrika, 2019, vol. 106, issue 2, 321-337

Abstract: SUMMARYMarkov chain Monte Carlo produces a correlated sample which may be used for estimating 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. The multivariate nature of this Monte Carlo error has been largely ignored in the literature. We present a multivariate framework for terminating a simulation in Markov chain Monte Carlo. We define a multivariate effective sample size, the estimation of which requires strongly consistent estimators of the covariance matrix in the Markov chain central limit theorem, a property we show for the multivariate batch means estimator. We then provide a lower bound on the number of minimum effective samples required for a desired level of precision. This lower bound does not depend on the underlying stochastic process and can be calculated a priori. This result is obtained by drawing a connection between terminating simulation via effective sample size and terminating simulation using a relative standard deviation fixed-volume sequential stopping rule, which we demonstrate is an asymptotically valid procedure. The finite-sample properties of the proposed method are demonstrated in a variety of examples.

Keywords: Covariance matrix estimation; Effective sample size; Markov chain Monte Carlo; Multivariate analysis (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (16)

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