Further Study of the Old Evidence Problem

University Of Tennessee Knoxville, Knoxville TN

Investigators

Abstract

SES 99-84005 - Carl G. Wagner (University of Tennessee) "Further Study of the Old Evidence Problem" Several years ago Richard Jeffrey devised a probability revision method, called reparation, that increases the probability of hypothesis H when it is discovered that H implies previously known evidence E. The P.I. subsequently generalized this method to apply to uncertain old evidence and probabilistic new explanation, identifying several conditions sufficient to guarantee the confirmation of H in this more general context. This generalization was based on the principle that explanation-based revisions should preserve certain Bayes factors. A plausible alternative principle dictates that explanation- and observation-based revisions should commute. One formulation of this principle is equivalent to the uniformity of Bayes factors, but another is not. In this project the P.I. will investigate these competing revision principles to determine if one has a superior claim to ground a generalization of reparation (and thus to capture the essence of Jeffrey's method), or if each might be appropriate to a separate class of uncertain old evidence problems. Comparison of these principles will be based both on further mathematical analysis of their properties, and on the development of certain benchmark problems sufficiently concrete to enable one to determine decisively the principle applicable to their solution. Problems of classification and diagnosis having a formal old evidence/new explanation structure, but a closer connection to relative frequencies than the typical judgmental probabilities of scientific explanation, appear to be promising candidates. To the extent that old evidence problems in the realm of scientific explanation can then be assimilated to one or more of these benchmarks, insight into their solution may be expected.