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

Record type: Article

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.

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Citation

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

More information

Published date: 1999
Keywords: bayesian analysis, contingency table, decomposable model, hierarchical log-linear model, graphical model, markov chain monte carlo, reversible jump
Organisations: Statistics

Identifiers

Local EPrints ID: 29957
URI: http://eprints.soton.ac.uk/id/eprint/29957
ISSN: 0006-3444
PURE UUID: 7b747003-c33d-433c-8fc4-4b87603fedc4

Catalogue record

Date deposited: 11 May 2007
Last modified: 17 Jul 2017 15:56

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Contributors

Author: P. Dellaportas
Author: J.J. Forster

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