An Axiomatic Framework for Propagating Uncertainty in Directed Acyclic Networks

This paper presents an axiomatic system for propagating uncertainty in Pearl's causal networks, (Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference, 1988 [7]). The main objective is to study all aspects of knowledge representation and reasoning in causal networks from an abstract point of view, independent of the particular theory being used to represent information (probabilities, belief functions or upper and lower probabilities). This is achieved by expressing concepts and algorithms in terms of valuations, an abstract mathematical concept representing a piece of information, introduced by Shenoy and Sharer [1, 2]. Three new axioms are added to Shenoy and Shafer's axiomatic framework [1, 2], for the propagation of general valuations in hypertrees. These axioms allow us to address from an abstract point of view concepts such as conditional information (a generalization of conditional probabilities) and give rules relating the decomposition of global information with the concept of independence (a generalization of probability rules allowing the decomposition of a bidimensional distribution with independent marginals in the product of its two marginals). Finally, Pearl's propagation algorithms are also developed and expressed in terms of operations with valuations.Commission of the European Communities under ESPRIT BRA 3085: DRUM

A probabilistic reasoning and learning system based on Bayesian belief networks

SIGLEAvailable from British Library Document Supply Centre- DSC:DX173015 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

The role of causal reasoning in understanding Simpson's paradox, Lord's paradox, and the suppression effect: covariate selection in the analysis of observational studies

Tu et al present an analysis of the equivalence of three paradoxes, namely, Simpson's, Lord's, and the suppression phenomena. They conclude that all three simply reiterate the occurrence of a change in the association of any two variables when a third variable is statistically controlled for. This is not surprising because reversal or change in magnitude is common in conditional analysis. At the heart of the phenomenon of change in magnitude, with or without reversal of effect estimate, is the question of which to use: the unadjusted (combined table) or adjusted (sub-table) estimate. Hence, Simpson's paradox and related phenomena are a problem of covariate selection and adjustment (when to adjust or not) in the causal analysis of non-experimental data. It cannot be overemphasized that although these paradoxes reveal the perils of using statistical criteria to guide causal analysis, they hold neither the explanations of the phenomenon they depict nor the pointers on how to avoid them. The explanations and solutions lie in causal reasoning which relies on background knowledge, not statistical criteria

ARTIFICIAL INTELLIGENCE DIALECTS OF THE BAYESIAN BELIEF REVISION LANGUAGE

Rule-based expert systems must deal with uncertain data, subjective expert opinions, and inaccurate decision rules. Computer scientists and psychologists have proposed and implemented a number of belief languages widely used in applied systems, and their normative validity is clearly an important question, both on practical as well on theoretical grounds. Several well-know belief languages are reviewed, and both previous work and new insights into their Bayesian interpretations are presented. In particular, the authors focus on three alternative belief-update models the certainty factors calculus, Dempster-Shafer simple support functions, and the descriptive contrast/inertia model. Important "dialectsâ of these languages are shown to be isomorphic to each other and to a special case of Bayesian inference. Parts of this analysis were carried out by other authors; these results were extended and consolidated using an analytic technique designed to study the kinship of belief languages in general.Information Systems Working Papers Serie