December 1, 1998Journal of Computational and Graphical Statistics6,158 citations
General Methods for Monitoring Convergence of Iterative Simulations
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Key Points
- This work aims to improve monitoring of convergence in iterative simulations through variance comparisons.
- Generalized Gelman and Rubin method for comparing variances between and within multiple chains.
- Development of convergence-monitoring summaries tailored for simulation purposes.
- Recommended tests for mixing derived from individual sequences and their mixtures.
- Introduction of a battery of tests ensuring robust convergence assessment.
- Establishment of methods for assessing multivariate convergence for multiple parameters.
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.
Cite This Study
Brooks et al. (1998) studied this question.