Possibilistic inferential models: a review

Abstract

An inferential model (IM) is a model describing the construction of provably reliable, data-driven uncertainty quantification and inference about relevant unknowns. IMs and Fisher's fiducial argument have similar objectives, but a fundamental distinction between the two is that the former doesn't require that uncertainty quantification be probabilistic, offering greater flexibility and allowing for a proof of its reliability. Important recent developments have been made thanks in part to newfound connections with the imprecise probability literature, in particular, possibility theory. The brand of possibilistic IMs studied here are straightforward to construct, have very strong frequentist-like reliability properties, and offer fully conditional, Bayesian-like (imprecise) probabilistic reasoning. This paper reviews these key recent developments, describing the new theory, methods, and computational tools. A generalization of the basic possibilistic IM is also presented, making new and unexpected connections with ideas in modern statistics and machine learning, e.g., bootstrap and conformal prediction.

References in corpus (16)

• Inferential models: A framework for prior-free posterior probabilistic inference
• Is Bayes Posterior just Quick and Dirty Confidence?
• Marginal inferential models: prior-free probabilistic inference on interest parameters
• Conditional inferential models: combining information for prior-free probabilistic inference
• Fiducial theory and optimal inference
• Satellite conjunction analysis and the false confidence theorem
• Plausibility functions and exact frequentist inference
• On an inferential model construction using generalized associations
• A note on p-values interpreted as plausibilities
• Valid inferential models for prediction in supervised learning problems
• Validity, consonant plausibility measures, and conformal prediction
• Possibility-theoretic statistical inference offers performance and probativeness assurances
• Direct and approximately valid probabilistic inference on a class of statistical functionals
• Asymptotic efficiency of inferential models and a possibilistic Bernstein--von Mises theorem
• Computationally efficient variational-like approximations of possibilistic inferential models
• Partial Conditioning for Inference of Many-Normal-Means with Hölder Constraints