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Extensions of Fill's algorithm for perfect simulation
Author(s) -
Møller J.,
Schladitz K.
Publication year - 1999
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/1467-9868.00213
Subject(s) - monotone polygon , algorithm , markov chain , poisson distribution , lattice (music) , neighbourhood (mathematics) , mathematics , coding (social sciences) , state space , computer science , discrete mathematics , theoretical computer science , mathematical analysis , statistics , physics , geometry , acoustics
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.