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Definitions and notations with historical references are given for some numerical coefficients commonly used to quantify relations among collections of objects for the purpose of expressing approximate knowledge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

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.

This paper presents an application of the Dempster-Shafer evidence combination scheme in building a rule based expert system shell for diagnostic reasoning. Domain knowledge is stored as rules with associated belief functions. The reasoning component uses a combination of forward and backward inferencing mechanisms to interact with the user in a mixed initiative format.

Advanced Decision Systems Abstract We present a thorough integration of hierarchical Bayesian inference with comprehensive physical representation of objects and their relations in a system for reasoning with geometry in machine vision. Bayesian inference provides a framework (or accruing probabilities to rank order hypotheses. This is a preliminary version of visual interpretation in SUCCESSOR, an intelligent, model-based vision system integrating multiple sensors. Introduction Our design for machine vision uses an evidential accrual process, a. beginning from representation and database of a priori models o(physical objects and their photometric, geometric, and functional properties, together with their relationships and environment, b. predicting observables using models of sensors and perceptual measurement processes; c. making measurements of corresponding observables, measuring image evidence for features of objects and structures of features such as edges, vertices and regions; d. generating hypotheses of instances o(objects from those measurements and predictions; and In range imagery, measurements are 3d. There is still a difficult stage of segmenting and estimating 3d relations that disclose object structure. In 2d images, there is an additional inference from 2d projected image evidence to 3d interpretation of surfaces. System structure tends to break up into a natural hierarchy of representation and processing [Binford 80).

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.