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On Exact Simulation of Markov Random Fields Using Coupling from the Past

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  • Olle Haggstrom
  • Karin Nelander

Abstract

A general framework for exact simulation of Markov random fields using the Propp–Wilson coupling from the past approach is proposed. Our emphasis is on situations lacking the monotonicity properties that have been exploited in previous studies. A critical aspect is the convergence time of the algorithm; this we study both theoretically and experimentically. Our main theoretical result in this direction says, roughly, that if interactions are sufficiently weak, then the expected running time of a carefully designed implementation is O(N log N), where N is the number of interacting components of the system. Computer experiments are carried out for random q‐colourings and for the Widom–Rowlinson lattice gas model.

Suggested Citation

  • Olle Haggstrom & Karin Nelander, 1999. "On Exact Simulation of Markov Random Fields Using Coupling from the Past," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(3), pages 395-411, September.
    • Handle: RePEc:bla:scjsta:v:26:y:1999:i:3:p:395-411
    DOI: 10.1111/1467-9469.00156
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