Extensions of Fill's algorithm for perfect simulation
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 1999 · Volume 61 · Issue 4
Abstract
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.
Keywords
Auto-Poisson model, Conditionally specified model, Exact simulation, Gibbs sampler, Hard-core model, Markov chain Monte Carlo methods, Repulsive Markov random fields, Stochastic recursive sequences, Strauss process
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