Perspectives on the Theory and Practice of Belief Functions (1990)
| Venue: | International Journal of Approximate Reasoning |
| Citations: | 67 - 3 self |
BibTeX
@ARTICLE{Shafer90perspectiveson,
author = {Glenn Shafer},
title = {Perspectives on the Theory and Practice of Belief Functions},
journal = {International Journal of Approximate Reasoning},
year = {1990},
volume = {4},
pages = {323--362}
}
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Abstract
The theory of belief functions provides one way to use mathematical probability in subjective judgment. It is a generalization of the Bayesian theory of subjective probability. When we use the Bayesian theory to quantify judgments about a question, we must assign probabilities to the possible answers to that question. The theory of belief functions is more flexible; it allows us to derive degrees of belief for a question from probabilities for a related question. These degrees of belief may or may not have the mathematical properties of probabilities; how much they differ from probabilities will depend on how closely the two questions are related. Examples of what we would now call belief-function reasoning can be found in the late seventeenth and early eighteenth centuries, well before Bayesian ideas were developed. In 1689, George Hooper gave rules for combining testimony that can be recognized as special cases of Dempster's rule for combining belief functions (Shafer 1986a). Similar rules were formulated by Jakob Bernoulli in his Ars Conjectandi, published posthumously in 1713, and by Johann-Heinrich Lambert in his Neues Organon, published in 1764 (Shafer 1978). Examples of belief-function reasoning can also be found in more recent work, by authors
