Pettitt, Anthony and Friel, N. and Reeves, R. (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 (Statistical Methodology), 65 (1). pp. 235-246. ISSN 1369-7412

## Abstract

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.

Item Type: | Article |
---|---|

Journal or Publication Title: | Journal of the Royal Statistical Society: Series B (Statistical Methodology) |

Additional Information: | RAE_import_type : Journal article RAE_uoa_type : Statistics and Operational Research |

Subjects: | Q Science > QA Mathematics |

Departments: | Faculty of Science and Technology > Mathematics and Statistics |

ID Code: | 2433 |

Deposited By: | ep_importer |

Deposited On: | 31 Mar 2008 09:50 |

Refereed?: | Yes |

Published?: | Published |

Last Modified: | 08 Dec 2016 01:35 |

Identification Number: | |

URI: | http://eprints.lancs.ac.uk/id/eprint/2433 |

### Actions (login required)

View Item |