However, the theory has not been implemented for reasoning in expert systems due to.its difficulty dealing with uncertain rules. More recently, several extenstions to the theory has been proposed to overcome this difficulty [Yen, 1986a] [Liu, 1986]. Based on Yen's extended DS theory, we have implemented a prototype expert system, named GERTIS (General Evidential Reasoning Tool for Intelligent Systems), that diagnoses rheumatoid arthritis. We chose unspecified polyarthritis as the area of our medical consultation system because the diagnoses form a disease hierarchy, which fits Dempster-Shafer based reasoning best. GERTIS uses the knowledge base of OADIAG-2, a medical expert system developed by Peter Adlassnig [Adlassnig, 1985a,b]. Through the use of OADIAG-2's knowledge base, relevant evidence and rules have been already identified for the area of arthritis. In order to suit the needs of our model, however, the rules of OADIAG-2 were modified and reorganized.

This paper considers the problem of invoking auxiliary, unobservable variables to facilitate the structuring of causal tree models for a given set of continuous variables. Paralleling the treatment of bi-valued variables in [Pearl 1986], we show that if a collection of coupled variables are governed by a joint normal distribution and a tree-structured representation exists, then both the topology and all internal relationships of the tree can be uncovered by observing pairwise dependencies among the observed variables (i.e., the leaves of the tree). Furthermore, the conditions for normally distributed variables are less restrictive than those governing bi-valued variables. The result extends the applications of causal tree models which were found useful in evidential reasoning tasks.

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.

Definitions and notations with historical references are given for some numerical coefficients commonly used to quantify relations among collections of objects for the purpose of expressing approximate knowledge and probabilistic reasoning.

A distinction is sometimes made between "statistical" and "subjective" probabilities. This is based on a distinction between "unique" events and "repeatable" events. We argue that this distinction is untenable, since all events are "unique" and all events belong to "kinds", and offer a conception of probability for A1 in which (1) all probabilities are based on -- possibly vague -- statistical knowledge, and (2) every statement in the language has a probability. This conception of probability can be applied to very rich languages.

This paper describes NAIVE, a low-level knowledge representation language and inferencing process. NAIVE has been designed for reasoning about nondeterministic dynamic systems like those found in medicine. Knowledge is represented in a graph structure consisting of nodes, which correspond to the variables describing the system of interest, and arcs, which correspond to the procedures used to infer the value of a variable from the values of other variables. The value of a variable can be determined at an instant in time, over a time interval or for a series of times. Information about the value of a variable is expressed as a probability density function which quantifies the likelihood of each possible value. The inferencing process uses these probability density functions to propagate uncertainty. NAIVE has been used to develop medical knowledge bases including over 100 variables.

Bayes belief networks and influence diagrams are tools for constructing coherent probabilistic representations of uncertain knowledge. The process of constructing such a network to represent an expert's knowledge is used to illustrate a variety of techniques which can facilitate the process of structuring and quantifying uncertain relationships. These include some generalizations of the "noisy OR gate" concept. Sensitivity analysis of generic elements of Bayes' networks provides insight into when rough probability assessments are sufficient and when greater precision may be important.

David Beckerman and Holly Jimison Medical Computer Science Group Knowledge Systems Laboratory Stanford University Medical School Office Building, Room 215 Stanford, California 94305 We examine a Bayesian approach for accommodating beliefs and preferences that are held with partial confidence. An important notion highlighted by the method is that additional modeling can be valuable when complete confidence is lacking. We develop a meta-decision-analytic approach to balance the benefits of additional modeling with associated costs. We show how the approach can be used during knowledge acquisition to focus the attention of a knowledge engineer or expert on parts of a decision model that deserve additional refinement.

We present a program that manages a database of temporally scoped beliefs. The basic functionality of the system includes maintaining a network of constraints among time points, supporting a variety of fetches, mediating the application of causal rules, monitoring intervals of time for the addition of new facts, and managing data dependencies that keep the database consistent. At this level the system operates independent of any measure of belief or belief calculus. We provide an example of how an application program mi9ght use this functionality to implement a belief calculus.

This paper examines Bayesian belief network inference using simulation as a method for computing the posterior probabilities of network variables. Specifically, it examines the use of a method described by Henrion, called logic sampling, and a method described by Pearl, called stochastic simulation. We first review the conditions under which logic sampling is computationally infeasible. Such cases motivated the development of the Pearl's stochastic simulation algorithm. We have found that this stochastic simulation algorithm, when applied to certain networks, leads to much slower than expected convergence to the true posterior probabilities. This behavior is a result of the tendency for local areas in the network to become fixed through many simulation cycles. The time required to obtain significant convergence can be made arbitrarily long by strengthening the probabilistic dependency between nodes. We propose the use of several forms of graph modification, such as graph pruning, arc reversal, and node reduction, in order to convert some networks into formats that are computationally more efficient for simulation.