Abstract
We illustrate how the recursive algorithm of Reeves Pettitt (2004) for general factorizable models can be extended to allow exact sampling, maximization of distributions and computation of marginal distributions. All of the methods we describe apply to discrete-valued Markov random fields with nearest neighbour integrations defined on regular lattices; in particular we illustrate that exact inference can be performed for hidden autologistic models defined on moderately sized lattices. In this context we offer an extension of this methodology which allows approximate inference to be carried out for larger lattices without resorting to simulation techniques such as Markov chain Monte Carlo. In particular our work offers the basis for an automatic inference machine for such models.
Original language | English (US) |
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Pages (from-to) | 661-672 |
Number of pages | 12 |
Journal | Biometrika |
Volume | 94 |
Issue number | 3 |
DOIs | |
State | Published - 2007 |
Externally published | Yes |
Keywords
- Autologistic distribution
- Exact sampling
- Hidden Markov random field
- Ising model
- Normalizing constant
ASJC Scopus subject areas
- Statistics and Probability
- General Mathematics
- Agricultural and Biological Sciences (miscellaneous)
- General Agricultural and Biological Sciences
- Statistics, Probability and Uncertainty
- Applied Mathematics