Knowledge Integration for Conditional Probability Assessments

TL;DR

This paper explores how to integrate and assess the consistency of two discrete conditional probability distributions, providing formulas for extending them to marginal distributions and analyzing their coherence.

Contribution

It introduces methods for analyzing the consistency of two discrete conditional probability distributions and derives explicit formulas for extending them to marginal distributions.

Findings

Identifies conditions for the coherence of two conditional probability distributions.

Provides explicit formulas for extending conditional distributions to marginals.

Analyzes special cases for consistency assessment.

Abstract

In the probabilistic approach to uncertainty management the input knowledge is usually represented by means of some probability distributions. In this paper we assume that the input knowledge is given by two discrete conditional probability distributions, represented by two stochastic matrices P and Q. The consistency of the knowledge base is analyzed. Coherence conditions and explicit formulas for the extension to marginal distributions are obtained in some special cases.