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Efficient calculation of the normalizing constant of the autologistic and related models on the cylinder and lattice

Author

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  • A. N. Pettitt
  • N. Friel
  • R. Reeves

Abstract

Summary. Motivated by the autologistic model for the analysis of spatial binary data on the two‐dimensional lattice, we develop efficient computational methods for calculating the normalizing constant for models for discrete data defined on the cylinder and lattice. Because the normalizing constant is generally unknown analytically, statisticians have developed various ad hoc methods to overcome this difficulty. Our aim is to provide computationally and statistically efficient methods for calculating the normalizing constant so that efficient likelihood‐based statistical methods are then available for inference. We extend the so‐called transition method to find a feasible computational method of obtaining the normalizing constant for the cylinder boundary condition. To extend the result to the free‐boundary condition on the lattice we use an efficient path sampling Markov chain Monte Carlo scheme. The methods are generally applicable to association patterns other than spatial, such as clustered binary data, and to variables taking three or more values described by, for example, Potts models.

Suggested Citation

  • A. N. Pettitt & N. Friel & R. Reeves, 2003. "Efficient calculation of the normalizing constant of the autologistic and related models on the cylinder and lattice," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 235-246, February.
    • Handle: RePEc:bla:jorssb:v:65:y:2003:i:1:p:235-246
    DOI: 10.1111/1467-9868.00383
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    References listed on IDEAS

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    1. Evans, Michael & Swartz, Timothy, 2000. "Approximating Integrals via Monte Carlo and Deterministic Methods," OUP Catalogue, Oxford University Press, number 9780198502784.
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    1. Daniel A Griffith, 2004. "A Spatial Filtering Specification for the Autologistic Model," Environment and Planning A, , vol. 36(10), pages 1791-1811, October.
    2. Jin, Ick Hoon & Liang, Faming, 2014. "Use of SAMC for Bayesian analysis of statistical models with intractable normalizing constants," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 402-416.
    3. Cécile Hardouin & Xavier Guyon, 2014. "Recursions on the marginals and exact computation of the normalizing constant for Gibbs processes," Computational Statistics, Springer, vol. 29(6), pages 1637-1650, December.
    4. Magnussen, Steen & Reeves, Rob, 2008. "A method for bias-reduction of sample-based MLE of the autologistic model," Computational Statistics & Data Analysis, Elsevier, vol. 53(1), pages 103-111, September.
    5. Dormann, Carsten F., 2007. "Assessing the validity of autologistic regression," Ecological Modelling, Elsevier, vol. 207(2), pages 234-242.

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