This paper presents a new approach for computing posterior probabilities in Bayesian nets, which sidesteps the triangulation problem. The current state of art is the clique tree propagation approach. When the underlying graph of a Bayesian net is triangulated, this approach arranges its cliques into a tree and computes posterior probabilities by appropriately passing around messages in that tree. The computation in each clique is simply direct marginalization. When the underlying graph is not triangulated, one has to first triangulated it by adding edges. Referred to as the triangulation problem, the problem of finding an optimal or even a ?good? triangulation proves to be difficult. In this paper, we propose to first decompose a Bayesian net into smaller components by making use of Tarjan's algorithm for decomposing an undirected graph at all its minimal complete separators. Then, the components are arranged into a tree and posterior probabilities are computed by appropriately passing around messages in that tree. The computation in each component is carried out by repeating the whole procedure from the beginning. Thus the triangulation problem is sidestepped.

In a previous paper [Pearl and Verma, 1991] we presented an algorithm for extracting causal influences from independence information, where a causal influence was defined as the existence of a directed arc in all minimal causal models consistent with the data. In this paper we address the question of deciding whether there exists a causal model that explains ALL the observed dependencies and independencies. Formally, given a list M of conditional independence statements, it is required to decide whether there exists a directed acyclic graph (dag) D that is perfectly consistent with M, namely, every statement in M, and no other, is reflected via dseparation in D. We present and analyze an effective algorithm that tests for the existence of such a day, and produces one, if it exists.

Although the notion of diagnostic problem has been extensively investigated in the context of static systems, in most practical applications the behavior of the modeled system is significantly variable during time. The goal of the paper is to propose a novel approach to the modeling of uncertainty about temporal evolutions of time-varying systems and a characterization of model-based temporal diagnosis. Since in most real world cases knowledge about the temporal evolution of the system to be diagnosed is uncertain, we consider the case when probabilistic temporal knowledge is available for each component of the system and we choose to model it by means of Markov chains. In fact, we aim at exploiting the statistical assumptions underlying reliability theory in the context of the diagnosis of timevarying systems. We finally show how to exploit Markov chain theory in order to discard, in the diagnostic process, very unlikely diagnoses.

Bayes nets are relatively recent innovations. As a result, most of their theoretical development has focused on the simplest class of single-author models. The introduction of more sophisticated multiple-author settings raises a variety of interesting questions. One such question involves the nature of compromise and consensus. Posterior compromises let each model process all data to arrive at an independent response, and then split the difference. Prior compromises, on the other hand, force compromise to be reached on all points before data is observed. This paper introduces prior compromises in a Bayes net setting. It outlines the problem and develops an efficient algorithm for fusing two directed acyclic graphs into a single, consensus structure, which may then be used as the basis of a prior compromise.

We recently described a formalism for reasoning with if-then rules that re expressed with different levels of firmness [18]. The formalism interprets these rules as extreme conditional probability statements, specifying orders of magnitude of disbelief, which impose constraints over possible rankings of worlds. It was shown that, once we compute a priority function Z+ on the rules, the degree to which a given query is confirmed or denied can be computed in O(log n`) propositional satisfiability tests, where n is the number of rules in the knowledge base. In this paper, we show that computing Z+ requires O(n2 X log n) satisfiability tests, not an exponential number as was conjectured in [18], which reduces to polynomial complexity in the case of Horn expressions. We also show how reasoning with imprecise observations can be incorporated in our formalism and how the popular notions of belief revision and epistemic entrenchment are embodied naturally and tractably.

Jeffrey's rule has been generalized by Wagner to the case in which new evidence bounds the possible revisions of a prior probability below by a Dempsterian lower probability. Classical probability kinematics arises within this generalization as the special case in which the evidentiary focal elements of the bounding lower probability are pairwise disjoint. We discuss a twofold extension of this generalization, first allowing the lower bound to be any two-monotone capacity and then allowing the prior to be a lower envelope.

The ideal Bayesian agent reasons from a global probability model, but real agents are restricted to simplified models which they know to be adequate only in restricted circumstances. Very little formal theory has been developed to help fallibly rational agents manage the process of constructing and revising small world models. The goal of this paper is to present a theoretical framework for analyzing model management approaches. For a probability forecasting problem, a search process over small world models is analyzed as an approximation to a larger-world model which the agent cannot explicitly enumerate or compute. Conditions are given under which the sequence of small-world models converges to the larger-world probabilities.

We describe how we selectively reformulate portions of a belief network that pose difficulties for solution with a stochastic-simulation algorithm. With employ the selective conditioning approach to target specific nodes in a belief network for decomposition, based on the contribution the nodes make to the tractability of stochastic simulation. We review previous work on BNRAS algorithms- randomized approximation algorithms for probabilistic inference. We show how selective conditioning can be employed to reformulate a single BNRAS problem into multiple tractable BNRAS simulation problems. We discuss how we can use another simulation algorithm-logic sampling-to solve a component of the inference problem that provides a means for knitting the solutions of individual subproblems into a final result. Finally, we analyze tradeoffs among the computational subtasks associated with the selective conditioning approach to reformulation.

This paper describes some results of research on associate systems: knowledge-based systems that flexibly and adaptively support their human users in carrying out complex, time-dependent problem-solving tasks under uncertainty. Based on principles derived from decision theory and decision analysis, a problem-solving approach is presented which can overcome many of the limitations of traditional expert-systems. This approach implements an explicit model of the human user's problem-solving capabilities as an integral element in the overall problem solving architecture. This integrated model, represented as an influence diagram, is the basis for achieving adaptive task sharing behavior between the associate system and the human user. This associate system model has been applied toward ongoing research on a Mars Rover Manager's Associate (MRMA). MRMA's role would be to manage a small fleet of robotic rovers on the Martian surface. The paper describes results for a specific scenario where MRMA examines the benefits and costs of consulting human experts on Earth to assist a Mars rover with a complex resource management decision.

An expert classification system having statistical information about the prior probabilities of the different classes should be able to use this knowledge to reduce the amount of additional information that it must collect, e.g., through questions, in order to make a correct classification. This paper examines how best to use such prior information and additional information-collection opportunities to reduce uncertainty about the class to which a case belongs, thus minimizing the average cost or effort required to correctly classify new cases.