Bayesian Belief Networks have been largely overlooked by Expert Systems practitioners on the grounds that they do not correspond to the human inference mechanism. In this paper, we introduce an explanation mechanism designed to generate intuitive yet probabilistically sound explanations of inferences drawn by a Bayesian Belief Network. In particular, our mechanism accounts for the results obtained due to changes in the causal and the evidential support of a node.

The generalized fault diagram, a data structure for failure analysis based on the influence diagram, is defined. Unlike the fault tree, this structure allows for dependence among the basic events and replicated logical elements. A heuristic procedure is developed for efficient processing of these structures.

This paper examines the relationship between Shafer's belief functions and convex sets of probability distributions. Kyburg's (1986) result showed that belief function models form a subset of the class of closed convex probability distributions. This paper emphasizes the importance of Kyburg's result by looking at simple examples involving Bernoulli trials. Furthermore, it is shown that many convex sets of probability distributions generate the same belief function in the sense that they support the same lower and upper values. This has implications for a decision theoretic extension. Dempster's rule of combination is also compared with Bayes' rule of conditioning.

This paper describes a heuristic Bayesian method for computing probability distributions from experimental data, based upon the multivariate normal form of the influence diagram. An example illustrates its use in medical technology assessment. This approach facilitates the integration of results from different studies, and permits a medical expert to make proper assessments without considerable statistical training.

The fundamental elements of evidential reasoning problems are described, followed by a discussion of the structure of various types of problems. Bayesian inference networks and state space formalism are used as the tool for problem representation. A human-oriented decision making cycle for solving evidential reasoning problems is described and illustrated for a military situation assessment problem. The implementation of this cycle may serve as the basis for an expert system shell for evidential reasoning; i.e. a situation assessment processor.

We start by defining an approach to non-monotonic probabilistic reasoning in terms of non-monotonic categorical (true-false) reasoning. We identify a type of non-monotonic probabilistic reasoning, akin to default inheritance, that is commonly found in practice, especially in "evidential" and "Bayesian" reasoning. We formulate this in terms of the Maximization of Conditional Independence (MCI), and identify a variety of applications for this sort of default. We propose a formalization using Pointwise Circumscription. We compare MCI to Maximum Entropy, another kind of non-monotonic principle, and conclude by raising a number of open questions

Cutset conditioning and clique-tree propagation are two popular methods for performing exact probabilistic inference in Bayesian belief networks. Cutset conditioning is based on decomposition of a subset of network nodes, whereas clique-tree propagation depends on aggregation of nodes. We describe a means to combine cutset conditioning and clique- tree propagation in an approach called aggregation after decomposition (AD). We discuss the application of the AD method in the Pathfinder system, a medical expert system that offers assistance with diagnosis in hematopathology.

Two different approaches to dealing with probabilistic knowledge are examined -models and inductive inference. Examples of the first are: influence diagrams [1], Bayesian networks [2], log-linear models [3, 4]. Examples of the second are: games-against nature [5, 6] varieties of maximum-entropy methods [7, 8, 9], and the author's min-score induction [10]. In the modeling approach, the basic issue is manageability, with respect to data elicitation and computation. Thus, it is assumed that the pertinent set of users in some sense knows the relevant probabilities, and the problem is to format that knowledge in a way that is convenient to input and store and that allows computation of the answers to current questions in an expeditious fashion. The basic issue for the inductive approach appears at first sight to be very different. In this approach it is presumed that the relevant probabilities are only partially known, and the problem is to extend that incomplete information in a reasonable way to answer current questions. Clearly, this approach requires that some form of induction be invoked. Of course, manageability is an important additional concern. Despite their seeming differences, the two approaches have a fair amount in common, especially with respect to the structural framework they employ. Roughly speaking, this framework involves identifying clusters of variables which strongly interact, establishing marginal probability distributions on the clusters, and extending the subdistributions to a more complete distribution, usually via a product formalism. The product extension is justified on the modeling approach in terms of assumed conditional independence; in the inductive approach the product form arises from an inductive rule.

In previous work (Fertig and Breese, 1989; Fertig and Breese, 1990) we defined a mechanism for performing probabilistic reasoning in influence diagrams using interval rather than point-valued probabilities. In this paper we extend these procedures to incorporate decision nodes and interval-valued value functions in the diagram. We derive the procedures for chance node removal (calculating expected value) and decision node removal (optimization) in influence diagrams where lower bounds on probabilities are stored at each chance node and interval bounds are stored on the value function associated with the diagram's value node. The output of the algorithm are a set of admissible alternatives for each decision variable and a set of bounds on expected value based on the imprecision in the input. The procedure can be viewed as an approximation to a full e-dimensional sensitivity analysis where n are the number of imprecise probability distributions in the input. We show the transformations are optimal and sound. The performance of the algorithm on an influence diagrams is investigated and compared to an exact algorithm.

We introduce a new heuristic algorithm for the problem of finding minimum size loop cutsets in multiply connected belief networks. We compare this algorithm to that proposed in [Suemmondt and Cooper, 1988]. We provide lower bounds on the performance of these algorithms with respect to one another and with respect to optimal. We demonstrate that no heuristic algorithm for this problem cam be guaranteed to produce loop cutsets within a constant difference from optimal. We discuss experimental results based on randomly generated networks, and discuss future work and open questions.