Increased robustness of Bayesian networks through probability intervals

Abstract 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 model-theoretic 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.