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Assessing Convergence of the Markov Chain Monte Carlo Algorithms: A Review MCMC

Sinharay, Sandip
Publication Year:
Report Number:
ETS Research Report
Document Type:
Page Count:
Subject/Key Words:
Convergence Diagnostics, Bayesian Analysis, Algorithms, Markov Chain Monte Carlo (MCMC)


Markov Chain Monte Carlo (MCMC) algorithms are in wide use for fitting complicated statistical models in psychometrics in situations where the traditional estimation techniques are very difficult to apply. One of the stumbling blocks in using an MCMC algorithm is determining the convergence of the algorithm. Because the convergence is not that of a scalar quantity to a point, but that of a distribution to another distribution, the issue remains an enigma to many users of MCMC, especially those without a sound knowledge of mathematical statistics. This report is an attempt to provide psychometricians using the MCMC algorithms a better understanding of the concept of convergence of the algorithms and an improved knowledge about the diagnostics tools to assess convergence of the MCMC algorithms.

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