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Markov Chain Monte Carlo Algorithms: Theory and Practice

In: Monte Carlo and Quasi-Monte Carlo Methods 2008

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  • Jeffrey S. Rosenthal

    (University of Toronto, Department of Statistics)

Abstract

We describe the importance and widespread use of Markov chain Monte Carlo (MCMC) algorithms, with an emphasis on the ways in which theoretical analysis can help with their practical implementation. In particular, we discuss how to achieve rigorous quantitative bounds on convergence to stationarity using the coupling method together with drift and minorisation conditions. We also discuss recent advances in the field of adaptive MCMC, where the computer iteratively selects from among many different MCMC algorithms. Such adaptive MCMC algorithms may fail to converge if implemented naively, but they will converge correctly if certain conditions such as Diminishing Adaptation are satisfied.

Suggested Citation

  • Jeffrey S. Rosenthal, 2009. "Markov Chain Monte Carlo Algorithms: Theory and Practice," Springer Books, in: Pierre L' Ecuyer & Art B. Owen (ed.), Monte Carlo and Quasi-Monte Carlo Methods 2008, pages 157-169, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-04107-5_9
    DOI: 10.1007/978-3-642-04107-5_9
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