General Methods for Monitoring Convergence of Iterative Simulations |
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| Authors: | Stephen P. Brooks Andrew Gelman |
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| Affiliation: | 1. Department of Mathematics , University of Bristol, University Walk , Bristol , BS8 1TW , England;2. Department of Statistics , Columbia University , New York , NY , 10027 , USA |
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| Abstract: | 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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| Keywords: | Convergence diagnosis Inference Markov chain Monte Carlo |
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