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.

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.

Kutato is a system that takes as input a database of cases and produces a belief network that captures many of the dependence relations represented by those data. This system incorporates a module for determining the entropy of a belief network and a module for constructing belief networks based on entropy calculations. Kutato constructs an initial belief network in which all variables in the database are assumed to be marginally independent. The entropy of this belief network is calculated, and that arc is added that minimizes the entropy of the resulting belief network. Conditional probabilities for an arc are obtained directly from the database. This process continues until an entropy-based threshold is reached. We have tested the system by generating databases from networks using the probabilistic logic-sampling method, and then using those databases as input to Kutato. The system consistently reproduces the original belief networks with high fidelity.

This is a preliminary version of visual interpretation integrating multiple sensors in SUCCESSOR, an intelligent, model-based vision system. We pursue a thorough integration of hierarchical Bayesian inference with comprehensive physical representation of objects and their relations in a system for reasoning with geometry, surface materials and sensor models in machine vision. Bayesian inference provides a framework for accruing_ probabilities to rank order hypotheses.

As the technology for building knowledge based systems has matured, important lessons have been learned about the relationship between the architecture of a system and the nature of the problems it is intended to solve. We are implementing a knowledge engineering tool called BART that is designed with these lessons in mind. BART is a Bayesian reasoning tool that makes belief networks and other probabilistic techniques available to knowledge engineers building classificatory problem solvers. BART has already been used to develop a decision aid for classifying ship images, and it is currently being used to manage uncertainty in systems concerned with analyzing intelligence reports. This paper discusses how state-of-the-art probabilistic methods fit naturally into a knowledge based approach to classificatory problem solving, and describes the current capabilities of BART.

An efficient algorithm is developed that identifies all independencies implied by the topology of a Bayesian network. Its correctness and maximality stems from the soundness and completeness of d-separation with respect to probability theory. The algorithm runs in time O (l E l) where E is the number of edges in the network.

This paper demonstrates a methodology for examining the accuracy of uncertain inference systems (UIS), after their parameters have been optimized, and does so for several common UIS's. This methodology may be used to test the accuracy when either the prior assumptions or updating formulae are not exactly satisfied. Surprisingly, these UIS's were revealed to be no more accurate on the average than a simple linear regression. Moreover, even on prior distributions which were deliberately biased so as give very good accuracy, they were less accurate than the simple probabilistic model which assumes marginal independence between inputs. This demonstrates that the importance of updating formulae can outweigh that of prior assumptions. Thus, when UIS's are judged by their final accuracy after optimization, we get completely different results than when they are judged by whether or not their prior assumptions are perfectly satisfied.