Methodology for Bayesian graphical model determination for multinomial and multinormal data is introduced. The method is applicable to the complete class of graphical models, consisting of both decomposable and non-decomposable models. Model determination is performed by implementing an independence MCMC sampler. Moves in the model class are proposed by random deletion or addition of a single edge given the current graph. Conditional on a graphical model, the proposal distribution of the parameters is independent of their current values, and is obtained using existing results for hyper Markov distributions. The hyper Markov distributions utilized here are derived by marginalization from the posterior on the parameters of the model with complete graph under a reference prior. The introduced methodology is illustrated by means of several real data sets.

Key words: Bayesian model determination, Decomposable graphical models, Hyper Markov law, Independence MCMC sampler, Laplace approximation, Multinomial distribution, Multinormal distribution, Non-decomposable graphical models.

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Last update: 2000-02-15/CE