Analysis of a Non-Reversible Markov Chain Sampler

Persi Diaconis, Maths and ORIE, Cornell University and Dept. of Mathematics, Harvard University
Susan Holmes, Biometrics Unit, Cornell 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.

Technical Report BU-1385-M, Biometrics Unit, Cornell University, 26 pages: postscript, pdf.

Associated reference: A revised version of this technical report has been published as the following paper:
Diaconis, P., Holmes, S., and Neal, R. M. (2000) ``Analysis of a nonreversible Markov chain sampler'', Annals of Applied Probability, vol. 10, pp. 726-752: abstract.