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Symbolic propagation in discrete and continuous Bayesian networks
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| Organization: | Department of Applied Mathematics and Computational Science |
| Department: | University of Cantabria |
| Organization: | University of Cantabria |
| Department: | Department of Applied Mathematics and Computational Science |
| Organization: | Cornell University |
| Department: | Department of Statistics |
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| Mathematics with Vision: Proceedings of the First International Mathematica Symposium |
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The paper presents a method for symbolic propagation of uncertainty in Bayesian discrete and continuous (normal) networks, using Mathematica. For the normal Bayesian networks we derive a method which allows the joint distribution of non-evidence nodes given the evidence to be calculated in an incremental form. An example of uncertainty propagation in a clique tree is used to illustrate all the steps and the corresponding code in the Mathematica programming language is given. The analysis of some examples sheds some light on the characterization of the algebraic structure of probabilities. For the discrete case, the marginal probabilities of nodes are shown to be rational functions of the parameters. For the normal case, it is shown that the mean and variance of conditional probabilities are also rational functions of the parameters.
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