From imprecise probability assessments to conditional probabilities with quasi additive classes of conditioning events

TL;DR

This paper develops a method to derive coherent conditional probabilities from imprecise assessments using quasi additive classes of conditioning events, ensuring consistency through linear system solutions.

Contribution

It introduces a novel approach to construct coherent conditional probabilities from interval assessments via quasi additivity and g-coherence theory.

Findings

Constructs conditional probabilities consistent with initial assessments

Uses solutions of linear systems to ensure coherence

Provides a finite sequence approach for probability updates

Abstract

In this paper, starting from a generalized coherent (i.e. avoiding uniform loss) intervalvalued probability assessment on a finite family of conditional events, we construct conditional probabilities with quasi additive classes of conditioning events which are consistent with the given initial assessment. Quasi additivity assures coherence for the obtained conditional probabilities. In order to reach our goal we define a finite sequence of conditional probabilities by exploiting some theoretical results on g-coherence. In particular, we use solutions of a finite sequence of linear systems.