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In this paper, we discuss the Bayesian sequential learning on probabilities from incomplete data in decomposable graphical models. We give exact formulas of the posterior distribution, and the posterior mean and the posterior second moment based on a hyper Dirichlet prior distribution and an incomplete observation. The posterior distribution is usually a mixture hyper Dirichlet distribution when there exist incomplete data. In order to approximate the mixture posterior, we choose a single hyper Dirichlet distribution which has the same mean and the same average variance sum as those of the exact posterior.

BAYESIAN SEQUENTIAL LEARNING FROM INCOMPLETE DATA ON DECOMPOSABLE GRAPHICAL MODELS