# Belief likelihood function for generalised logistic regression

arXiv: https://arxiv.org/abs/1808.02560 · HTML: https://mlsanity.com/paper/1808.02560/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Aug 2018.

## Built on by (most cited first, 5 of 5)

- [Random-Set Graph Neural Networks](https://mlsanity.com/paper/2605.11987/) (2026)
- [Statistical inference with belief functions: A survey](https://mlsanity.com/paper/2605.07908/) (2026)
- [Credal Large Language Models for Semantic Commitment under Uncertainty](https://mlsanity.com/paper/2608.23244/) (2026)
- [A neurosymbolic Approach with Epistemic Deep Learning for Hierarchical Image Classification](https://mlsanity.com/paper/2605.16383/) (2026)
- [XU-RS: Explaining Credal Width in Random-Set Language Models](https://mlsanity.com/paper/2609.37594/) (2026)

## Abstract (arXiv)

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.