A problem in cascaded inference: Determining the inferential impact of confirming and conflicting reports from several unreliable sources

Abstract

The occurrence or nonoccurrence of an event D has inferential significance. We query n sources or sensors who make individual reports about the occurrence or nonoccurrence of D. Their reports are either mutually confirming or there is some pattern of conflict among them. In this paper we develop expressions termed adjusted likelihood ratios which prescribe the inferential or diagnostic impact of the joint confirming or conflicting reports from the n sources. These expressions combine information about the inferential impact of D (and its complement ) with information about the reliability of each source. We only consider the case in which the reporting behavior of any subset of the sources is not itself an inferentially significant event. Appropriate independence and conditional independence assumptions are necessary. Our formulations of adjusted likelihood ratio are applicable to a variety of medical, legal, military, and other inferential tasks.