Priors and Likelihood Ratios as Evidence
David H. Krantz, John M. Miyamoto · Journal of the American Statistical Association · 1983
Arguments based on diagnostic data concerning a particular case, and ones based on prior experience with like cases, can be represented by belief functions and combined by Dempster's Rule. In limiting cases, the belief functions depend on likelihood ratio or on prior odds, and when these limiting cases occur together, Bayes' Theorem is applicable as is Dempster's Rule. The resulting functional equations lead to a single-parameter family of functions relating belief strength to probability and to likelihood ratio. The parameter can be measured by studying the belief strength produced by conceptually independent dissonant arguments that point to a common conclusion. This provides one possible solution to the problem of fundamental measurement for Shafer's theory of belief.