In this paper, the feasibility of using finite totally ordered probability models under Alelinnas's Theory of Probabilistic Logic [Aleliunas, 1988] is investigated. The general form of the probability algebra of these models is derived and the number of possible algebras with given size is deduced. Based on this analysis, we discuss problems of denominator-indifference and ambiguity-generation that arise in reasoning by cases and abductive reasoning. An example is given that illustrates how these problems arise. The investigation shows that a finite probability model may be of very limited usage.

The most difficult task in probabilistic reasoning may be handling directed cycles in belief networks. To the best knowledge of this author, there is no serious discussion of this problem at all in the literature of probabilistic reasoning so far.

This study compares the inherent intuitiveness or usability of the most prominent methods for managing uncertainty in expert systems, including those of EMYCIN, PROSPECTOR, Dempster-Shafer theory, fuzzy set theory, simplified probability theory (assuming marginal independence), and linear regression using probability estimates. Participants in the study gained experience in a simple, hypothetical problem domain through a series of learning trials. They were then randomly assigned to develop an expert system using one of the six Uncertain Inference Systems (UISs) listed above. Performance of the resulting systems was then compared. The results indicate that the systems based on the PROSPECTOR and EMYCIN models were significantly less accurate for certain types of problems compared to systems based on the other UISs. Possible reasons for these differences are discussed.

We present a new, deterministic, distributed MAP estimation algorithm for Markov Random Fields called Local Highest Confidence First (Local HCF). The algorithm has been applied to segmentation problems in computer vision and its performance compared with stochastic algorithms. The experiments show that Local HCF finds better estimates than stochastic algorithms with much less computation.

An algorithm for automated construction of a sparse Bayesian network given an unstructured probabilistic model and causal domain information from an expert has been developed and implemented. The goal is to obtain a network that explicitly reveals as much information regarding conditional independence as possible. The network is built incrementally adding one node at a time. The expert's information and a greedy heuristic that tries to keep the number of arcs added at each step to a minimum are used to guide the search for the next node to add. The probabilistic model is a predicate that can answer queries about independencies in the domain. In practice the model can be implemented in various ways. For example, the model could be a statistical independence test operating on empirical data or a deductive prover operating on a set of independence statements about the domain.

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.

This paper discusses a new measure that is adaptable to certain intervalic probability frameworks, possibility theory, and belief theory. As such, it has the potential for wide use in knowledge engineering, expert systems, and related problems in the human sciences. This measure (denoted here by F) has been introduced in Smithson (1988) and is more formally discussed in Smithson (1989a)o Here, I propose to outline the conceptual basis for F and compare its properties with other measures of second-order uncertainty. I will argue that F is an indicator of nonspecificity or alternatively, of freedom, as distinguished from either ambiguity or vagueness.

We derive axiomatically the probability function that should be used to make decisions given any form of underlying uncertainty.

A number of algorithms have been developed to solve probabilistic inference problems on belief networks. These algorithms can be divided into two main groups: exact techniques which exploit the conditional independence revealed when the graph structure is relatively sparse, and probabilistic sampling techniques which exploit the "conductance" of an embedded Markov chain when the conditional probabilities have non-extreme values. In this paper, we investigate a family of "forward" Monte Carlo sampling techniques similar to Logic Sampling [Henrion, 1988] which appear to perform well even in some multiply connected networks with extreme conditional probabilities, and thus would be generally applicable. We consider several enhancements which reduce the posterior variance using this approach and propose a framework and criteria for choosing when to use those enhancements.

The arc reversal/node reduction approach to probabilistic inference is extended to include the case of instantiated evidence by an operation called "evidence reversal." This not only provides a technique for computing posterior joint distributions on general belief networks, but also provides insight into the methods of Pearl [1986b] and Lauritzen and Spiegelhalter [1988]. Although it is well understood that the latter two algorithms are closely related, in fact all three algorithms are identical whenever the belief network is a forest.