Belief likelihood function for generalised logistic regression
This work addresses a foundational issue in statistical inference for researchers dealing with uncertainty encoded by belief measures, though it appears incremental as it builds on existing belief measure theory.
The paper tackles the problem of generalizing traditional likelihood functions for statistical inference by introducing a belief likelihood function for repeated trials under belief measures, and presents a generalised logistic regression framework with analytical expressions for lower and upper likelihoods in Bernoulli trials.
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.