Convergence Analysis of MCMC

Adrian Barbu and Song-Chun Zhu
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Adrian Barbu: Florida State University, Department of Statistics
Song-Chun Zhu: University of California, Los Angeles, Departments of Statistics and Computer Science

Chapter 7 in Monte Carlo Methods, 2020, pp 189-209 from Springer

Abstract: Abstract One of the major issues that many practitioners run into when using MCMC is the slow convergence rate. While many MCMC methods have been shown to converge to the target distribution, the entire convergence largely depends upon the magnitude of the second largest eigenvalue of the transition matrix λ slem. For this reason there are many bounds on the convergence rate of νKn based on this quantity. In this chapter some of the most useful of these bounds are derived and implemented. These bounds are studied through the application of randomly shuffling a deck of cards. Additionally, in order to speed up the convergence process, the concepts of trade map, bottleneck, and conductance are explained. Finally, the topics of path coupling and exact sampling are covered and an application of these methods to the Ising model is included.

Date: 2020
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DOI: 10.1007/978-981-13-2971-5_7

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