Support and Plausibility Degrees in Generalized Functional Models

TL;DR

This paper introduces generalized functional models that extend traditional models by allowing multiple compatible parameter values, using support and plausibility functions for reasoning under uncertainty, inspired by Fisher's fiducial probability.

Contribution

It proposes a new framework for modeling reasoning under uncertainty with support and plausibility functions, relaxing the uniqueness requirement of traditional models.

Findings

Supports modeling multiple compatible parameter values

Uses support and plausibility functions instead of probability distributions

Inspired by Fisher's fiducial probability theory

Abstract

By discussing several examples, the theory of generalized functional models is shown to be very natural for modeling some situations of reasoning under uncertainty. A generalized functional model is a pair (f, P) where f is a function describing the interactions between a parameter variable, an observation variable and a random source, and P is a probability distribution for the random source. Unlike traditional functional models, generalized functional models do not require that there is only one value of the parameter variable that is compatible with an observation and a realization of the random source. As a consequence, the results of the analysis of a generalized functional model are not expressed in terms of probability distributions but rather by support and plausibility functions. The analysis of a generalized functional model is very logical and is inspired from ideas already put forward by R.A. Fisher in his theory of fiducial probability.