The interpretation and applicationof belief functions

As is well known, the Dempster-Shafer mathematical theory of evidence, which employs the use of belief Junctions, has been used to perform uncertain inference in expert systems andartificial 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 usingonly probability theory to perform uncertain inference; (2) As shown by a number of authors, mechanical applications of belief Junctions can lead to quite unacceptable results. In a 1990special issue of the International Journal of Approximate Reasoning, which was devoted to adiscussion of belief Junctions, these criticisms were forwarded and various interpretations ofbelief fimctions were offered. In his response to the discussion in the special issue, Shafershowed the problems with these criticisms and interpretations, and he once again explainedhow he meant for belief functions to be interpreted. In this article, this defense is furthered intwo ways: (1) It is shown that belief Junctions, as Shafer intends them to be interpreted, useprobability theory in the same way as the traditional statistical tool, significance testing; and(2) A problem is given for which an application of belief Junctions yields a meaningfulsolution while a Bayesian analysis does not.