Abstract

In this paper, we propose to monitor a Markov chain sampler using the cusum path plot of a chosen 1-dimensional summary statistic. We argue that the cusum path plot can bring out, more effectively than the sequential plot, those aspects of a Markov sampler which tell the user how quickly or slowly the sampler is moving around in its sample space, in the direction of the summary statistic. The proposal is then illustrated in four examples which represent situations where the cusum path plot works well and not well. Moreover, a rigorous analysis is given for one of the examples. We conclude that the cusum path plot is an effective tool for convergence diagnostics of a Markov sampler and for comparing different Markov samplers. KEY WORDS: Convergence diagnostic; Cusum path plot, Markov sampler; Mixing; Sequential plot; Summary statistic. Research supported in part by ARO Grant DAAL03-91-G-007. y Research supported in part by NSF Grant DMS-9305601. 1 Introduction As Markov chain Mon...

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