An algorithm for automated construction of a sparse Bayesian network given an unstructured probabilistic model and causal domain information from an expert has been developed and implemented. The goal is to obtain a network that explicitly reveals as much information regarding conditional independence as possible. The network is built incrementally adding one node at a time. The expert's information and a greedy heuristic that tries to keep the number of arcs added at each step to a minimum are used to guide the search for the next node to add. The probabilistic model is a predicate that can answer queries about independencies in the domain. In practice the model can be implemented in various ways. For example, the model could be a statistical independence test operating on empirical data or a deductive prover operating on a set of independence statements about the domain.

The multiple extension problem arises frequently in diagnostic and default inference. That is, we can often use any of a number of sets of defaults or possible hypotheses to explain observations or make Predictions. In default inference, some extensions seem to be simply wrong and we use qualitative techniques to weed out the unwanted ones. In the area of diagnosis, however, the multiple explanations may all seem reasonable, however improbable. Choosing among them is a matter of quantitative preference. Quantitative preference works well in diagnosis when knowledge is modelled causally. Here we suggest a framework that combines probabilities and defaults in a single unified framework that retains the semantics of diagnosis as construction of explanations from a fixed set of possible hypotheses. We can then compute probabilities incrementally as we construct explanations. Here we describe a branch and bound algorithm that maintains a set of all partial explanations while exploring a most promising one first. A most probable explanation is found first if explanations are partially ordered.

Dempster's rule of combination has been the most controversial part of the Dempster-Shafer (D-S) theory. In particular, Zadeh has reached a conjecture on the noncombinability of evidence from a relational model of the D-S theory. In this paper, we will describe another relational model where D-S masses are represented as conditional granular distributions. By comparing it with Zadeh's relational model, we will show how Zadeh's conjecture on combinability does not affect the applicability of Dempster's rule in our model.

We describe a method for incrementally constructing belief networks. We have developed a network-construction language similar to a forward-chaining language using data dependencies, but with additional features for specifying distributions. Using this language, we can define parameterized classes of probabilistic models. These parameterized models make it possible to apply probabilistic reasoning to problems for which it is impractical to have a single large static model.

After a brief introduction to causal probabilistic networks and the HUGIN approach, the problem of conflicting data is discussed. A measure of conflict is defined, and it is used in the medical diagnostic system MUNIN. Finally, it is discussed how to distinguish between conflicting data and a rare case.

Unaided human decision making appears to systematically violate consistency constraints imposed by normative theories; these biases in turn appear to justify the application of formal decision-analytic models. It is argued that both claims are wrong. In particular, we will argue that the "confirmation bias" is premised on an overly narrow view of how conflicting evidence is and ought to be handled. Effective decision aiding should focus on supporting the contral processes by means of which knowledge is extended into novel situations and in which assumptions are adopted, utilized, and revised. The Non- Monotonic Probabilist represents initial work toward such an aid.

A model of knowledge representation is described in which propositional facts and the relationships among them can be supported by other facts. The set of knowledge which can be supported is called the set of cognitive units, each having associated descriptions of their explicit and implicit support structures, summarizing belief and reliability of belief. This summary is precise enough to be useful in a computational model while remaining descriptive of the underlying symbolic support structure. When a fact supports another supportive relationship between facts we call this meta-support. This facilitates reasoning about both the propositional knowledge. and the support structures underlying it.

We define a new notion of conditional belief, which plays the same role for Dempster-Shafer belief functions as conditional probability does for probability functions. Our definition is different from the standard definition given by Dempster, and avoids many of the well-known problems of that definition. Just as the conditional probability Pr (lB) is a probability function which is the result of conditioning on B being true, so too our conditional belief function Bel (lB) is a belief function which is the result of conditioning on B being true. We define the conditional belief as the lower envelope (that is, the inf) of a family of conditional probability functions, and provide a closed form expression for it. An alternate way of understanding our definition of conditional belief is provided by considering ideas from an earlier paper [Fagin and Halpern, 1989], where we connect belief functions with inner measures. In particular, we show here how to extend the definition of conditional probability to non measurable sets, in order to get notions of inner and outer conditional probabilities, which can be viewed as best approximations to the true conditional probability, given our lack of information. Our definition of conditional belief turns out to be an exact analogue of our definition of inner conditional probability.

The Dempster-Shafer theory has been extended recently for its application to expert systems. However, implementing the extended D-S reasoning model in rule-based systems greatly complicates the task of generating informative explanations. By implementing GERTIS, a prototype system for diagnosing rheumatoid arthritis, we show that two kinds of knowledge are essential for explanation generation: (l) taxonomic class relationships between hypotheses and (2) pointers to the rules that significantly contribute to belief in the hypothesis. As a result, the knowledge represented in GERTIS is richer and more complex than that of conventional rule-based systems. GERTIS not only demonstrates the feasibility of rule-based evidential-reasoning systems, but also suggests ways to generate better explanations, and to explicitly represent various useful relationships among hypotheses and rules.

Our previous work on classifying complex ship images [1,2] has evolved into an effort to develop software tools for building and solving generic classification problems. Managing the uncertainty associated with feature data and other evidence is an important issue in this endeavor. Bayesian techniques for managing uncertainty [7,12,13] have proven to be useful for managing several of the belief maintenance requirements of classification problem solving. One such requirement is the need to give qualitative explanations of what is believed. Pearl [11] addresses this need by computing what he calls a belief commitment-the most probable instantiation of all hypothesis variables given the evidence available. Before belief commitments can be computed, the straightforward implementation of Pearl's procedure involves finding an analytical solution to some often difficult optimization problems. We describe an efficient implementation of this procedure using tensor products that solves these problems enumeratively and avoids the need for case by case analysis. The procedure is thereby made more practical to use in the general case.