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Centre for Mathematical Physics and Stochastics
Department of Mathematical Sciences, University of Aarhus

Funded by The Danish National Research Foundation

MPS-RR 1998-3
May 1998

Extensions of Fill's algorithm for perfect simulation


Jesper Møller

Katja Schladitz


Fill's algorithm for perfect simulation for attractive finite state space models, unbiased for user impatience, is presented in terms of stochastic recursive sequences and extended in two ways. Repulsive discrete Markov random fields with two coding sets like the auto-Poisson distribution on a lattice with 4-neighbourhood can be treated as monotone systems if a particular partial ordering and quasi-maximal and quasi-minimal states are used. Fill's algorithm then applies directly. Combining Fill's rejection sampling with sandwiching leads to a version of the algorithm, which works for general discrete conditionally specified repulsive models. Extensions to other types of models are briefly discussed.

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This paper has now been published in J. R. Stat. Soc. Ser. B Stat. Methodol. 61 (1999), no. 4, 955--969