Increased robustness of Bayesian networks through probability intervals

We present an extension of Bayesian networks to probability intervals, aiming at a more realistic and flexible modeling of applications with uncertain and imprecise knowledge. Within the logical framework of causal programs we provide a modeltheoretic foundation for a formal treatment of consistency and of logical consequences. A set of local inference rules is developed, which is proved to be sound and--in the absence of loops--also to be complete; i.e., tightest probability bounds can be computed incrementally by bounds propagation. These inference rules can be evaluated very efficiently in linear time and space. An important feature of this approach is that sensitivity analyses can be carried out systematically, unveiling portions of the network that are prone to chaotic behavior. Such investigations can be employed for improving network design towards more robust and reliable decision analysis. © 1997 Elsevier Science Inc. K E Y W O R D S : Bayesian network, probability interval, logical inference, precise probabilistic conclusion, efficient bounds propagation, sensitivity analysis, robust decision analysis Address correspondence to Ulrich Giintzer, Wilhelm-Schickard-lnstitut, Unversitiit Tiibingen, Sand 13, D-72076 Tiibingen, Germany. E-mail." guentzer@informatik, uni tuebingen, de. Received February 1, 1995; accepted September 1, 1996. International Journal of Approximate Reasoning 1997; 17:37-76 © 1997 Elsevier Science Inc. 0888-613X/97/$17.00 655 Avenue of the Americas, New York, NY 10010 PII S0888-613X(96)00138-7 38 H. Th6ne, U. Giintzer, and W. Kicl31ing