Proceedings of the 34th conference on Winter simulation: exploring new frontiers
Bayesian methods for discrete event simulation
WSC '04 Proceedings of the 36th conference on Winter simulation
D-vine EDA: a new estimation of distribution algorithm based on regular vines
Proceedings of the 12th annual conference on Genetic and evolutionary computation
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High dimensional probabilistic models are often formulated as belief nets (BN's), that is, as directed acyclic graphs with nodes representing random variables and arcs representing "influence". BN's are conditionalized on incoming information to support probabilistic inference in expert system applications. For continuous random variables, an adequate theory of BN's exists only for the joint normal distribution. In general, an arbitrary correlation matrix is not compatible with arbitrary marginals, and conditionalization is quite intractable. Transforming to normals is unable to reproduce exactly a specified rank correlation matrix. We show that a continuous belief net can be represented as a regular vine, where an arc from node i to j is associated with a (conditional) rank correlation between i and j. Using the elliptical copula and the partial correlation transformation properties, it is very easy to conditionalize the distribution on the value of any node, and hence update the BN.