Comment: extracting more diagnostic information from a single run using the cusum path plot [1 citations — 0 self]
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Abstract:
Markov chain Monte Carlo (MCMC) methods accessible to more statisticians, especially applied statisticians. I am glad to see that different algorithms are reviewed in a unified way and many examples are given. Although the article gives general recommendations as to which algorithms and sampling scans to choose, there is not much discussion on the empirical monitoring of convergence of the Markov chains. Since the convergence issue is very critical to the success of MCMC methods, and something close to my heart, I will make this issue my topic here. In particular, using the prostate cancer example in the Besag et al paper and the Ising model example in Gelman and Rubin (1992a), I illustrate that the cusum path plot in Yu and Mykland (1994) can effectively bring out the local mixing property of the Markov chain. It had been believed by many MCMC researchers (including this author) that information solely from a single run of a Markov chain can be misleading since, for example, it can get trapped at a local mode of the target density. Consequently, additional information beyond that from a single run has been introduced to the convergence diagnostics. Gelman and Rubin (1992b) proposed a multiple chain approach in the MCMC context, followed by Liu, Liu, and Rubin (1992) and Roberts (1992). Yu (1994) introduced additional information to a single run by taking advantage of the unnormalized target density. In the context of Gibbs samplers, Ritter and Tanner (1992) and Cui,
