Implementation and application of the fundamental theorem of probability

Abstract

The "RIK" (Reasoning with Incomplete Knowledge) algorithm, a mathematical programming based algorithm for performing probabilistic inference on (possibly) incompletely specified systems of discrete events is reviewed and implemented. Developed by Myers, Freund, and Kaufman, it is a tractable reformulation of the computational approach implicit to the Fundamental Theorem of Probability as stated by De Finetti and extended by Lad, Dickey and Rahman. Enhancements to the original algorithm are presented and several applications of the algorithm to real-world systems including fault trees and belief networks are explored. The system is solved successfully for moderately large problems, providing practical information for system designers coping with uncertainty.