Control Strategies for hierarchical tree-like probabilistic inference networks are formulated and investigated. Strategies that utilize staged look-ahead and temporary focus on subgoals are formalized and refined using the Depth Vector concept that serves as a tool for defining the 'virtual tree' regarded by the control strategy. The concept is illustrated by four types of control strategies for three-level trees that are characterized according to their Depth Vector, and according to the way they consider intermediate nodes and the role that they let these nodes play. INFERENTI is a computerized inference system written in Prolog, which provides tools for exercising a variety of control strategies. The system also provides tools for simulating test data and for comparing the relative average performance under different strategies.

Several different uncertain inference systems (UISs) have been developed for representing uncertainty in rule-based expert systems. Some of these, such as Mycin's Certainty Factors, Prospector, and Bayes' Networks were designed as approximations to probability, and others, such as Fuzzy Set Theory and DempsterShafer Belief Functions were not. How different are these UISs in practice, and does it matter which you use? When combining and propagating uncertain information, each UIS must, at least by implication, make certain assumptions about correlations not explicily specified. The maximum entropy principle with minimum cross-entropy updating, provides a way of making assumptions about the missing specification that minimizes the additional information assumed, and thus offers a standard against which the other UISs can be compared. We describe a framework for the experimental comparison of the performance of different UISs, and provide some illustrative results.

Three paediatric cardiologists assessed nearly 1000 imprecise subjective conditional probabilities for a simple belief network representing congenital heart disease, and the quality of the assessments has been measured using prospective data on 200 babies. Quality has been assessed by a Brier scoring rule, which decomposes into terms measuring lack of discrimination and reliability. The results are displayed for each of 27 diseases and 24 questions, and generally the assessments are reliable although there was a tendency for the probabilities to be too extreme. The imprecision allows the judgements to be converted to implicit samples, and by combining with the observed data the probabilities naturally adapt with experience. This appears to be a practical procedure even for reasonably large expert systems.

Knowledge elicitation is one of the major bottlenecks in expert system design. Systems based on Bayes nets require two types of information--network structure and parameters (or probabilities). Both must be elicited from the domain expert. In general, parameters have greater opacity than structure, and more time is spent in their refinement than in any other phase of elicitation. Thus, it is important to determine the point of diminishing returns, beyond which further refinements will promise little (if any) improvement. Sensitivity analyses address precisely this issue--the sensitivity of a model to the precision of its parameters. In this paper, we report the results of a sensitivity analysis of Pathfinder, a Bayes net based system for diagnosing pathologies of the lymph system. This analysis is intended to shed some light on the relative importance of structure and parameters to system performance, as well as the sensitivity of a system based on a Bayes net to noise in its assessed parameters.

In this paper the elicitation of probabilities from human experts is considered as a measurement process, which may be disturbed by random 'measurement noise'. Using Bayesian concepts a second order probability distribution is derived reflecting the uncertainty of the input probabilities. The algorithm is based on an approximate sample representation of the basic probabilities. This sample is continuously modified by a stochastic simulation procedure, the Metropolis algorithm, such that the sequence of successive samples corresponds to the desired posterior distribution. The procedure is able to combine inconsistent probabilities according to their reliability and is applicable to general inference networks with arbitrary structure. Dempster-Shafer probability mass functions may be included using specific measurement distributions. The properties of the approach are demonstrated by numerical experiments.

Bayesian inference systems should be able to explain their reasoning to users, translating from numerical to natural language. Previous empirical work has investigated the correspondence between absolute probabilities and linguistic phrases. This study extends that work to the correspondence between changes in probabilities (updates) and relative probability phrases, such as "much more likely" or "a little less likely." Subjects selected such phrases to best describe numerical probability updates. We examined three hypotheses about the correspondence, and found the most descriptively accurate of these three to be that each such phrase corresponds to a fixed difference in probability (rather than fixed ratio of probabilities or of odds). The empirically derived phrase selection function uses eight phrases and achieved a 72% accuracy in correspondence with the subjects' actual usage.

Many AI researchers argue that probability theory is only capable of dealing with uncertainty in situations where a full specification of a joint probability distribution is available, and conclude that it is not suitable for application in knowledge-based systems. Probability intervals, however, constitute a means for expressing incompleteness of information. We present a method for computing such probability intervals for probabilities of interest from a partial specification of a joint probability distribution. Our method improves on earlier approaches by allowing for independency relationships between statistical variables to be exploited.

A method for computing probabilistic propositions is presented. It assumes the availability of a single external routine for computing the probability of one instantiated variable, given a conjunction of other instantiated variables. In particular, the method allows belief network algorithms to calculate general probabilistic propositions over nodes in the network. Although in the worst case the time complexity of the method is exponential in the size of a query, it is polynomial in the size of a number of common types of queries.

The comparisons of uncertainty calculi from the last two Uncertainty Workshops have all used theoretical probabilistic accuracy as the sole metric. While mathematical correctness is important, there are other factors which should be considered when developing reasoning systems. These other factors include, among other things, the error in uncertainty measures obtainable for the problem and the effect of this error on the performance of the resulting system.

Expert systems applications that involve uncertain inference can be represented by a multidimensional contingency table. These tables offer a general approach to inferring with uncertain evidence, because they can embody any form of association between any number of pieces of evidence and conclusions. (Simpler models may be required, however, if the number of pieces of evidence bearing on a conclusion is large.) This paper presents a method of using these tables to make uncertain inferences without assumptions of conditional independence among pieces of evidence or heuristic combining rules. As evidence is accumulated, new joint probabilities are calculated so as to maintain any dependencies among the pieces of evidence that are found in the contingency table. The new conditional probability of the conclusion is then calculated directly from these new joint probabilities and the conditional probabilities in the contingency table.