Research Project: Statistical Inference with Belief Likelihood
Given a sample space X, the traditional likelihood function is equal to the conditional probability of the data given a parameter theta in Theta, i.e., a family of probability distribution functions (PDFs) over X parameterised by theta:


As originally proposed by Shafer and Wasserman [28, 32, 33], belief functions can indeed be built from traditional likelihood functions. However, as we argue here, one can directly define a belief likelihood function, mapping a sample observation x in X to a real number, as a natural set-valued generalisation of the conventional likelihood. It is natural to define such a belief likelihood function as family of belief functions on X, BelX(.|theta), parameterised by theta in Theta. As the latter take values on sets of outcomes, A X, of which singleton outcomes are mere special cases, they provide a natural setting for computing likelihoods of set-valued observations, in accordance with the random set philosophy.
Relevant papers:
  •   Fabio Cuzzolin
    The geometry of uncertainty - The geometry of imprecise probabilities
    Artificial Intelligence: Foundations, Theory, and Algorithms (http://www.springer.com/series/13900), Springer-Verlag, 2018 (in press)
    The geometry of uncertainty
  • Fabio Cuzzolin
    Belief likelihood function for generalised logistic regression
    Submitted to Uncertainty in Artificial Intelligence (UAI 2018)
  • Fabio Cuzzolin
    The statistics of belief functions
    Invited talk at the 4th BFAS Summer School on Belief Functions