Abstract
Abstract As is well known, the Dempster-Shafer mathematical theory of evidence, which employs the use of belief functions, has been used to perform uncertain inference in expert systems and artificial intelligence. As is also well known, many fault this discipline for two reasons: (1) Dempster-Shafer theory is not probability theory, and there exist cogent arguments for using only probability theory to perform uncertain inference; (2) As shown by a number of authors, mechanical applications of belief functions can lead to quite unacceptable results. In a 1990 special issue of the International Journal of Approximate Reasoning, which was devoted to a discussion of belief functions, these criticisms were forwarded and various interpretations of belief functions were offered. In his response to the discussion in the special issue, Shafer showed the problems with these criticisms and interpretations, and he once again explained how he meant for belief functions to be interpreted. In this article, this defense is furthered in two ways: (1) It is shown that belief functions, as Shafer intends them to be interpreted, use probability theory in the same way as the traditional statistical tool, significance testing; and (2) A problem is given for which an application of belief functions yields a meaningful solution while a Bayesian analysis does not.
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