Coupling from the past: A user's guide

The Markov chain Monte Carlo method is a general technique for obtaining samples from a probability distribution. In earlier work, we showed that for many applications one can modify the Markov chain Monte Carlo method so as to remove all bias in the output resulting from the biased choice of an initial state for the chain; we have called this method Coupling From The Past (CFTP). Here we describe this method in a fashion that should make our ideas accessible to researchers from diverse areas. Our expository strategy is to avoid proofs and focus on sample applications.

[1]  R. M. Loynes,et al.  The stability of a queue with non-independent inter-arrival and service times , 1962, Mathematical Proceedings of the Cambridge Philosophical Society.

[2]  Parag A. Pathak,et al.  Massachusetts Institute of Technology , 1964, Nature.

[3]  V. Anantharam,et al.  A proof of the Markov chain tree theorem , 1989 .

[4]  Andrei Z. Broder,et al.  Generating random spanning trees , 1989, 30th Annual Symposium on Foundations of Computer Science.

[5]  Philip Heidelberger,et al.  Bias Properties of Budget Constrained Simulations , 1990, Oper. Res..

[6]  David Aldous,et al.  The Random Walk Construction of Uniform Spanning Trees and Uniform Labelled Trees , 1990, SIAM J. Discret. Math..

[7]  Peter W. Glynn,et al.  Stationarity detection in the initial transient problem , 1992, TOMC.

[8]  A. A. Borovkov,et al.  STOCHASTICALLY RECURSIVE SEQUENCES AND THEIR GENERALIZATIONS , 1992 .

[9]  Dana Randall,et al.  Markov chain algorithms for planar lattice structures , 1995, Proceedings of IEEE 36th Annual Foundations of Computer Science.

[10]  E. Denardo,et al.  Exact Mixing in an Unknown Markov Chain , 1995 .

[11]  D. Aldous On Simulating a Markov Chain Stationary Distribution when Transition Probabilities are Unknown , 1995 .

[12]  N. Madras,et al.  Factoring graphs to bound mixing rates , 1996, Proceedings of 37th Conference on Foundations of Computer Science.

[13]  David Bruce Wilson,et al.  Exact sampling with coupled Markov chains and applications to statistical mechanics , 1996, Random Struct. Algorithms.

[14]  Olle Häggström,et al.  Characterisation results and Markov chain Monte Carlo algorithms including exact simulation for some , 1996 .

[15]  Eric Vigoda,et al.  Approximately counting up to four (extended abstract) , 1997, STOC '97.

[16]  James Allen Fill,et al.  An interruptible algorithm for perfect sampling via Markov chains , 1997, STOC '97.

[17]  R. Tweedie,et al.  Perfect simulation and backward coupling , 1998 .

[18]  Dana Randall,et al.  Analyzing Glauber Dynamics by Comparison of Markov Chains , 1998, LATIN.

[19]  David Bruce Wilson,et al.  How to Get a Perfectly Random Sample from a Generic Markov Chain and Generate a Random Spanning Tree of a Directed Graph , 1998, J. Algorithms.

[20]  Wilfrid S. Kendall,et al.  Perfect Simulation for the Area-Interaction Point Process , 1998 .

[21]  P. Green,et al.  Exact Sampling from a Continuous State Space , 1998 .