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Modeling Probabilistic Networks of Discrete and Continuous Variables

By Enrique Castillo, José Manuel Gutiérrez and Ali S. Hadi

Abstract

In this paper we show how discrete and continuous variables can be combined using parametric conditional families of distributions and how the likelihood weighting method can be used for propagating uncertainty through the network in an efficient manner. To illustrate the method we use, as an example, the damage assessment of reinforced concrete structures of buildings and we formalize the steps to be followed when modeling probabilistic networks. We start with one set of conditional probabilities. Then, we examine this set for uniqueness, consistency, and parsimony. We also show that cycles can be removed because they lead to redundant probability information. This redundancy may cause inconsistency, hence the probabilities must be checked for consistency. This examination may require a reduction to an equivalent set instandard canonicalform from which one can always construct a Bayesian network, which is the most convenient model. We also perform a sensitivity analysis, which shows that the model is robust.Bayesian networks, compatibility, existence, simulation, uniqueness

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