Pettitt, Anthony and Reeves, R. (2004) Efficient recursions for general factorisable models. Biometrika, 91 (3). pp. 751-757. ISSN 1464-3510Full text not available from this repository.
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.
|Journal or Publication Title:||Biometrika|
|Additional Information:||RAE_import_type : Journal article RAE_uoa_type : Statistics and Operational Research|
|Uncontrolled Keywords:||Autologistic distribution ; Gibbs distribution ; Ising model ; Normalising constant ; Partition function ; Markov chain Monte Carlo.|
|Subjects:||Q Science > QA Mathematics|
|Departments:||Faculty of Science and Technology > Mathematics and Statistics|
|Deposited On:||31 Mar 2008 09:57|
|Last Modified:||30 Jan 2016 01:06|
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