Looking at Markov samplers through cusum path plots: a simple diagnostic idea

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 e ectively 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 e ective tool for convergence diagnostics of a Markov sampler and for comparing di erent Markov samplers.