Operations Research
Probabilistic inference and influence diagrams
Operations Research
Management Science
Distributions in the physical and engineering sciences
Distributions in the physical and engineering sciences
Stable local computation with conditional Gaussian distributions
Statistics and Computing
Axioms for probability and belief-function proagation
UAI '88 Proceedings of the Fourth Annual Conference on Uncertainty in Artificial Intelligence
Operations for inference in continuous Bayesian networks with linear deterministic variables
International Journal of Approximate Reasoning
Nonuniform dynamic discretization in hybrid networks
UAI'97 Proceedings of the Thirteenth conference on Uncertainty in artificial intelligence
Nonlinear deterministic relationships in bayesian networks
ECSQARU'05 Proceedings of the 8th European conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Variations over the message computation algorithm of lazy propagation
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Inference in Hybrid Bayesian Networks with Deterministic Variables
ECSQARU '09 Proceedings of the 10th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Inference in hybrid Bayesian networks using mixtures of polynomials
International Journal of Approximate Reasoning
International Journal of Approximate Reasoning
Answering queries in hybrid Bayesian networks using importance sampling
Decision Support Systems
Ordering arc-reversal operations when eliminating variables in lazy AR propagation
International Journal of Approximate Reasoning
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This article discusses arc reversals in hybrid Bayesian networks with deterministic variables. Hybrid Bayesian networks contain a mix of discrete and continuous chance variables. In a Bayesian network representation, a continuous chance variable is said to be deterministic if its conditional distributions have zero variances. Arc reversals are used in making inferences in hybrid Bayesian networks and influence diagrams. We describe a framework consisting of potentials and some operations on potentials that allows us to describe arc reversals between all possible kinds of pairs of variables. We describe a new type of conditional distribution function, called partially deterministic, if some of the conditional distributions have zero variances and some have positive variances, and show how it can arise from arc reversals.