Imprecise Sampling Models for Modelling Unobserved Heterogeneity? Basic Ideas of a Credal Likelihood Concept

Thomas Augustin

Abstract: In this research note, we sketch the idea to use (aspects of) imprecise probability models to handle unobserved heterogeneity in statistical (regression) models. Unobserved heterogeneity (frailty) is a frequent issue in many applications, arising whenever the underlying probability distributions depend on unobservable individual characteristics (like personal attitudes or hidden genetic dispositions). We consider imprecise sampling models where the likelihood contributions depend on individual parameters, varying in an interval (cuboid). Based on this, and a hyperparameter controlling the amount of ambiguity, we directly fit a credal set to the data. We introduce the basic concepts of this credal maximum likelihood approach, sketch first aspects of practical calculation of the resulting estimators by constrained optimization, derive some first general properties and finally discuss some ideas of a data-dependent choice of the hyperparameter.