Analysis of a Nonreversible Markov Chain Sampler

Persi Diaconis, Dept. of Statistics and Dept. of Mathematics, Stanford University
Susan Holmes, Dept. of Statistics, Stanford University and Unité de Biométrie, INRA-Montpellier
Radford M. Neal, Dept. of Statistics and Dept. of Computer Science, University of Toronto

We analyse the convergence to stationarity of a simple non-reversible Markov chain that serves as a model for several non-reversible Markov chain sampling methods that are used in practice. Our theoretical and numerical results show that non-reversibility can indeed lead to improvements over the diffusive behavior of simple Markov chain sampling schemes. The analysis uses both probabilistic techniques and an explicit diagonalisation.

Annals of Applied Probability, vol. 10, pp. 726-752 (2000).

Associated reference: This is a revised version of the following technical report:
Diaconis, P., Holmes, S., and Neal, R. M. (1997) ``Analysis of a non-reversible Markov chain sampler'', Technical Report BU-1385-M, Biometrics Unit, Cornell University, 26 pages: abstract, postscript, pdf.