Combination of Upper and Lower Probabilities

TL;DR

This paper explores methods for combining different types of incomplete probabilistic information, specifically 'a priori' and evidential data, using upper and lower probabilities and possibility theory.

Contribution

It introduces new combination methods tailored for 'a priori' and evidential information, integrating convex sets of likelihood functions with possibility distributions.

Findings

Proposes methods for combining 'a priori' and evidential information.

Models evidential data as convex sets of likelihood functions.

Utilizes possibility theory to represent and process evidential information.

Abstract

In this paper, we consider several types of information and methods of combination associated with incomplete probabilistic systems. We discriminate between 'a priori' and evidential information. The former one is a description of the whole population, the latest is a restriction based on observations for a particular case. Then, we propose different combination methods for each one of them. We also consider conditioning as the heterogeneous combination of 'a priori' and evidential information. The evidential information is represented as a convex set of likelihood functions. These will have an associated possibility distribution with behavior according to classical Possibility Theory.