Conformal Predictors Constructed from Generalized Fiducial Inference

• Activity Number: 51 - BFF: Innovation in Statistical Foundations
• Type: Topic Contributed
• Date/Time: Sunday, August 7, 2022 : 4:00 PM to 5:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Jonathan P Williams*
• Companies: North Carolina State University

Abstract

In this talk it is shown that applying the generalized fiducial (GF) inference framework to a rank-based data association leads to a model-free approach to constructing GF predictions. The resulting GF predictions lead to imprecise probabilities, and from this distribution it is shown that a conformal predictor arises. The connection to conformal predictors is important for notions of validity relating to controlling type 1 errors for finite sample sizes. An important connection between the constructed GF predictors solution and the inferential models approach to this problem is also illustrated. Theory and simulation results are provided to demonstrate the robustness of the GF predictors when the data model is misspecified in traditional GF and Bayesian approaches. Furthermore, an extension from the imprecise GF prediction probabilities to a proper prediction probability distribution is worked out for the case of univariate data. Asymptotic consistency of this univariate prediction distribution is considered for special cases.