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In this paper, we describe an abstract framework and axioms under which exact local computation of marginals is possible. The primitive objects of the framework are variables and valuations. The primitive operators of the framework are combination and marginalization. These operate on valuations. We state three axioms for these operators and we derive the… (More)

- Glenn Shafer
- 1996

Probability and causality must live together because both involve contingency. When I assign a probability to a coin's falling heads, I am saying that how it will fall is contingent. When I say the wind caused a tree to topple, I am saying that the wind and the toppling were contingent. The tree might have remained standing had the wind been less severe.… (More)

This article gives an algorithm for the exact implementation of Demp-ster's rule in the case of hierarchical evidence. This algorithm is computationally efficient, and it makes the approximation suggested by Gordon and Shortliffe unnecessary. The algorithm itself is simple, but its derivation depends on a detailed understanding of the interaction of… (More)

Conformal prediction uses past experience to determine precise levels of confidence in new predictions. Given an error probability ǫ, together with a method that makes a predictionˆy of a label y, it produces a set of labels, typically containingˆy, that also contains y with probability 1 − ǫ. Conformal prediction can be applied to any method for… (More)

- Glenn Shafer
- UAI
- 1985

This paper is concerned with two theories of probability judgment: the Bayesian theory and the theory of belief functions. It illustrates these theories with some simple examples and discusses some of the issues that arise when we try to implement them in expert systems. The Bayesian theory is well known; its main ideas go back to the work of Thomas Bayes… (More)