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Influence Diagrams with Continuous Decision Variables and Non-Gaussian Uncertainties

Department of Economics and Business, Virginia Military Institute, Lexington, Virginia 24450
cobbbr{at}vmi.edu

The continuous decision MTE influence diagram (CDMTEID) uses mixtures of truncated exponentials (MTE) potentials to approximate probability density functions (pdfs) and utility functions, and develops a piecewise-linear decision rule for continuous decision variables. The operations for solving CDMTEIDs are defined, and the abilities of this model to identify nonmonotonic decision rules and accommodate discrete variables with continuous parents are demonstrated. The CDMTEID solution to a problem with a continuous decision variable and a non-Gaussian continuous chance variable is presented and compared to a benchmark solution and existing models. The CDMTEID improves the quality of the decision rule and the value of information, as compared to other methods for the example problem.

Key Words: continuous variables; decision rule; fusion algorithm; Gaussian; graphical models; influence diagrams; mixtures of truncated exponentials; probability; value of information
History: Received on April 9, 2007. Accepted on August 9, 2007.