S ince the early days of probability theory, there has been a distinction between probabilities that are given, as in a game of chance, and probabilities that are not given, but reflect a subjective degree of belief; Hacking (1975) and Shafer (1978) offer historical surveys. In economics, Knight (1921) is typically credited with the distinction between situations of “risk” and of “uncertainty.”...

The modeling of epistemic knowledge is a necessity of most systems dealing with some sort of artificial reasoning. There a re several formalisms able to mathematically model someone’s degrees of belief. A very popular one is the Bayesian Theory, which is based on a prior knowledge of a probability distribution. Another model is the Theory of Evidence, or DempskrShafer Theory, which provides a m...

Standard logic and probability theory are both beset with fundamental problems if used as adequacy criteria for relating logical propositions to learning data. We discuss the problems of exception, of sample size, and of inclusion. Bayesian pattern logic (‘Bayesian logic’ or BL for short) has been proposed as a possible rational resolution of these problems. BL can also be taken as psychologica...

Ewens’s sampling formula exemplifies the harmony of mathematical theory, statistical application, and scientific discovery. The formula not only contributes to the foundations of evolutionary molecular genetics, the neutral theory of biodiversity, Bayesian nonparametrics, combinatorial stochastic processes, and inductive inference but also emerges from fundamental concepts in probability theory...

The determination of low-energy constants from data is an important component of most effective field theory programs, including that of chiral perturbation theory. We propose a novel method based on Bayesian probability theory which allows us to address several shortcomings of the standard approach to parameter extraction. Using a toy-model we argue that the Bayesian approach is ideally suited...

There is a long philosophical tradition of addressing questions in philosophy of science and epistemology by means of the tools of Bayesian probability theory (see Earman (1992) and Howson and Urbach (1993)). In the late '70s, an axiomatic approach to conditional independence was developed within a Bayesian framework. This approach in conjunction with developments in graph theory are the two pi...

This paper presents a clinical diagnosis support system which combines the advantages of Dempster-Shafer theory with Bayesian networks in order to simulate the uncertain medical reasoning. We propose a hierarchical structure using Dempster-Shafer at the upper level for evaluating more general hypothesis (disease groups) and Bayesian networks at the lower level for a more accurate analysis of sp...