Markov chain Monte Carlo model determination for hierarchical and graphical log-linear models

Dellaportas, P. and Forster, J.J. (1999) Markov chain Monte Carlo model determination for hierarchical and graphical log-linear models. Biometrika, 86, (3), 615-633. (doi:10.1093/biomet/86.3.615).


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We use reversible jump Markov chain Monte Carlo methods (Green, 1995) to develop strategies for calculating posterior probabilities of hierarchical, graphical or decomposable log-linear models for high-dimensional contingency tables. Even for tables of moderate size, these sets of models may be very large. The choice of suitable prior distributions for model parameters is also discussed in detail, and two examples are presented. For the first example, a three-way table, the model probabilities calculated using our reversible jump approach are compared with model probabilities calculated exactly or by using an alternative approximation. The second example is a six-way contingency table for which exact methods are infeasible, because of the large number of possible models. We identify the most probable hierarchical, graphical and decomposable models, and compare the results with alternatives approaches.

Item Type: Article
Digital Object Identifier (DOI): doi:10.1093/biomet/86.3.615
ISSNs: 0006-3444 (print)
Related URLs:
Keywords: bayesian analysis, contingency table, decomposable model, hierarchical log-linear model, graphical model, markov chain monte carlo, reversible jump
Subjects: Q Science > QA Mathematics
H Social Sciences > HA Statistics
Divisions : University Structure - Pre August 2011 > School of Mathematics > Statistics
ePrint ID: 29957
Accepted Date and Publication Date:
Date Deposited: 11 May 2007
Last Modified: 31 Mar 2016 11:56

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