© 1999 by Biometrika Trust
Markov chain Monte Carlo model determination for hierarchical and graphical log-linear models
A1 Department of Statistics, Athens University of Economics and Business, 76 Patission Street, Athens 10434, Greece E-mail: petros@aueb.gr A2 Department of Mathematics, University of Southampton, Highfield, Southampton SO17 1BJ, UK E-mail: jjf@maths.soton.ac.uk
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.
Key Words: Bayesian analysis; Contingency table; Decomposable model; Hierarchical log-linear model; Graphical model; Markov chain Monte Carlo; Reversible jump
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