Management Science
Valuation-based systems for Bayesian decision analysis
Operations Research
Moment methods for decision analysis
Management Science
Lagrange interpolation on Chebyshev points of two variables
Journal of Approximation Theory
Decision Analysis by Augmented Probability Simulation
Management Science
Mixtures of Truncated Exponentials in Hybrid Bayesian Networks
ECSQARU '01 Proceedings of the 6th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Sampling Methods for Action Selection in Influence Diagrams
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
Axioms for probability and belief-function proagation
UAI '88 Proceedings of the Fourth Annual Conference on Uncertainty in Artificial Intelligence
Representing and Solving Decision Problems with Limited Information
Management Science
Decision Analysis
Arc reversals in hybrid Bayesian networks with deterministic variables
International Journal of Approximate Reasoning
A forward-backward Monte Carlo method for solving influence diagrams
International Journal of Approximate Reasoning
Inference in hybrid Bayesian networks using mixtures of polynomials
International Journal of Approximate Reasoning
International Journal of Approximate Reasoning
Quantile-Parameterized Distributions
Decision Analysis
Nonuniform dynamic discretization in hybrid networks
UAI'97 Proceedings of the Thirteenth conference on Uncertainty in artificial intelligence
Mixtures of Gaussians and minimum relative entropy techniques for modeling continuous uncertainties
UAI'93 Proceedings of the Ninth international 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
Two issues in using mixtures of polynomials for inference in hybrid Bayesian networks
International Journal of Approximate Reasoning
Factor graphs and the sum-product algorithm
IEEE Transactions on Information Theory
Two issues in using mixtures of polynomials for inference in hybrid Bayesian networks
International Journal of Approximate Reasoning
From the Editors---Games and Decisions in Reliability and Risk
Decision Analysis
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We describe a framework and an algorithm for approximately solving a class of hybrid influence diagrams (IDs) containing discrete and continuous chance variables, discrete and continuous decision variables, and deterministic conditional distributions for chance variables. A conditional distribution for a chance variable is said to be deterministic if its variances, for each state of its parents, are all zeroes. The solution algorithm is an extension of Shenoy's fusion algorithm for discrete influence diagrams. To mitigate the integration and optimization problems associated with solving hybrid IDs, we propose using mixture of polynomials approximations of conditional probability density and utility functions and piecewise linear approximations of nonlinear deterministic conditional distributions for continuous chance variables. The class of hybrid IDs that can be solved by our framework are those that do not involve divisions. The framework and algorithm are illustrated by solving two small examples of hybrid IDs.