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Journal Article

General Methods for Monitoring Convergence of Iterative Simulations

Stephen P. Brooks and Andrew Gelman
Journal of Computational and Graphical Statistics
Vol. 7, No. 4 (Dec., 1998), pp. 434-455
DOI: 10.2307/1390675
Stable URL: http://www.jstor.org/stable/1390675
Page Count: 22
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General Methods for Monitoring Convergence of Iterative Simulations
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Abstract

We generalize the method proposed by Gelman and Rubin (1992a) for monitoring the convergence of iterative simulations by comparing between and within variances of multiple chains, in order to obtain a family of tests for convergence. We review methods of inference from simulations in order to develop convergence-monitoring summaries that are relevant for the purposes for which the simulations are used. We recommend applying a battery of tests for mixing based on the comparison of inferences from individual sequences and from the mixture of sequences. Finally, we discuss multivariate analogues, for assessing convergence of several parameters simultaneously.

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