Possibilistic Radial Transport for Approximate IM Inference

Abstract

Probing the hypothesis space after seeing the data remains valid under possibilistic inferential models (IMs), provided the significance level stays fixed. The price is computation, as each plausibility is a supremum of the possibility contour over the hypothesis, and the contour itself is approximated at each queried parameter value. We propose a possibilistic radial transport, which hides the contour value of a parameter in the radius of its source point. When a transport that maximizes within-shell entropy is picked, sampling parameters covering a confidence cut becomes a matter of truncating the radius. We provide a deep learning algorithm that enforces the contour depth condition while maximizing the entropy within each shell. Our amortization makes coverage and power assessments of the learned approximation practical as well as predictive check of new datasets. We also use the sampler to construct a Bel-Pl spectrum for comparing and selecting interpretable hypotheses that satisfy a prescribed Bel-Pl decision criterion. In simulations the learned contours match or improve on ellipsoidal approximations to the cuts, while the coverage and power track the exact reference. Finally, we probe hypotheses about ovarian aging using synthetic AMH records, asking for each woman how many more years her median AMH level will remain above a specified reference value.