Finding a Posterior Domain Probability Distribution by Specifying Nonspecific Evidence

TL;DR

This paper extends previous work on nonspecific evidence within Dempster-Shafer theory to derive a posterior probability distribution over the number of evidence subsets, integrating evidence support with prior domain probabilities.

Contribution

It introduces a method to compute a posterior domain probability distribution for the number of evidence subsets using support degrees and prior distributions within Dempster-Shafer theory.

Findings

Derived a bpa for the number of subsets based on evidence support

Combined support-based bpa with prior distribution to obtain posterior

Enhanced evidence partitioning with probabilistic subset count estimation

Abstract

This article is an extension of the results of two earlier articles. In [J. Schubert, On nonspecific evidence, Int. J. Intell. Syst. 8 (1993) 711-725] we established within Dempster-Shafer theory a criterion function called the metaconflict function. With this criterion we can partition into subsets a set of several pieces of evidence with propositions that are weakly specified in the sense that it may be uncertain to which event a proposition is referring. In a second article [J. Schubert, Specifying nonspecific evidence, in Cluster-based specification techniques in Dempster-Shafer theory for an evidential intelligence analysis of multiple target tracks, Ph.D. Thesis, TRITA-NA-9410, Royal Institute of Technology, Stockholm, 1994, ISBN 91-7170-801-4] we not only found the most plausible subset for each piece of evidence, we also found the plausibility for every subset that this piece of evidence belongs to the subset. In this article we aim to find a posterior probability distribution regarding the number of subsets. We use the idea that each piece of evidence in a subset supports the existence of that subset to the degree that this piece of evidence supports anything at all. From this we can derive a bpa that is concerned with the question of how many subsets we have. That bpa can then be combined with a given prior domain probability distribution in order to obtain the sought-after posterior domain distribution.