Efficient recursions for general factorisable models

Reeves, Robert W. & Pettitt, Anthony N. (2004) Efficient recursions for general factorisable models. Biometrika, 91(3), pp. 751-757.

View at publisher


Let n S-valued categorical variables be jointly distributed according to a distribution known only up to an unknown normalising constant. For an unnormalised joint likelihood expressible as a product of factors, we give an algebraic recursion which can be used for computing the normalising constant and other summations. A saving in computation is achieved when each factor contains a lagged subset of the components combining in the joint distribution, with maximum computational efficiency as the subsets attain their minimum size. If each subset contains at most r+1 of the n components in the joint distribution, we term this a lag-r model, whose normalising constant can be computed using a forward recursion in O(Sr+1) computations, as opposed to O(Sn) for the direct computation. We show how a lag-r model represents a Markov random field and allows a neighbourhood structure to be related to the unnormalised joint likelihood. We illustrate the method by showing how the normalising constant of the Ising or autologistic model can be computed.

Impact and interest:

29 citations in Scopus
26 citations in Web of Science®
Search Google Scholar™

Citation counts are sourced monthly from Scopus and Web of Science® citation databases.

These databases contain citations from different subsets of available publications and different time periods and thus the citation count from each is usually different. Some works are not in either database and no count is displayed. Scopus includes citations from articles published in 1996 onwards, and Web of Science® generally from 1980 onwards.

Citations counts from the Google Scholar™ indexing service can be viewed at the linked Google Scholar™ search.

Full-text downloads:

246 since deposited on 17 Oct 2007
11 in the past twelve months

Full-text downloads displays the total number of times this work’s files (e.g., a PDF) have been downloaded from QUT ePrints as well as the number of downloads in the previous 365 days. The count includes downloads for all files if a work has more than one.

ID Code: 10211
Item Type: Journal Article
Refereed: Yes
DOI: 10.1093/biomet/91.3.751
ISSN: 0006-3444
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Copyright Owner: Copyright 2004 Oxford University Press
Copyright Statement: This is an electronic version of an article published in Reeves, Robert W. and Pettitt, Tony N. (2004) Efficient recursions for general factorisable models . Biometrika 91(3):pp. 751-757.
Deposited On: 17 Oct 2007 00:00
Last Modified: 29 Feb 2012 13:09

Export: EndNote | Dublin Core | BibTeX

Repository Staff Only: item control page