Belief likelihood function for generalised logistic regression

TL;DR

This paper introduces a belief likelihood function for repeated trials with uncertainty modeled by belief measures, generalizing traditional likelihood and enabling belief inference in statistical data analysis.

Contribution

It develops a new belief likelihood framework, including factorisation results and analytical expressions, extending logistic regression to incorporate belief measures.

Findings

Derived analytical expressions for belief likelihoods in Bernoulli trials

Established factorisation results for conjunctive and disjunctive belief combinations

Formulated a generalized logistic regression model based on belief measures

Abstract

The notion of belief likelihood function of repeated trials is introduced, whenever the uncertainty for individual trials is encoded by a belief measure (a finite random set). This generalises the traditional likelihood function, and provides a natural setting for belief inference from statistical data. Factorisation results are proven for the case in which conjunctive or disjunctive combination are employed, leading to analytical expressions for the lower and upper likelihoods of `sharp' samples in the case of Bernoulli trials, and to the formulation of a generalised logistic regression framework.