Properties of Sensitivity Analysis of Bayesian Belief Networks

Authors:
Veerle M. H. Coupé;Linda C. van der Gaag
Affiliations:
Center for Clinical Decision Sciences, Erasmus University Rotterdam, P.O. Box 1738, 3000 DR Rotterdam, The Netherlands coupe@mgz.fgg.eur.nl;Utrecht University, Department of Computer Science, P.O. Box 80.089, 3508 TB Utrecht, The Netherlands linda@cs.uu.nl
Venue:
Annals of Mathematics and Artificial Intelligence
Year:
2002

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Abstract

The assessments for the various conditional probabilities of a Bayesian belief network inevitably are inaccurate, influencing the reliability of its output. By subjecting the network to a isensitivity analysis with respect to its conditional probabilities, the reliability of its output can be investigated. Unfortunately, straightforward sensitivity analysis of a belief network is highly time-consuming. In this paper, we show that by qualitative considerations several analyses can be identified as being uninformative as the conditional probabilities under study cannot affect the output. In addition, we show that the analyses that are informative comply with simple mathematical functions. More specifically, we show that a belief network's output can be expressed as a quotient of two functions that are linear in a conditional probability under study. These properties allow for considerably reducing the computational burden of sensitivity analysis of Bayesian belief networks.