Validity, consonant plausibility measures, and conformal prediction

Prediction of future observations is an important and challenging problem. The two mainstream approaches for quantifying prediction uncertainty use regions predictive distributions, respectively, with the latter believed to be more informative because it can perform other prediction-related tasks. standard notion validity, what we refer here as Type-1 focuses on coverage probability regions, while a validity relevant tasks performed by distributions lacking. Here present new notion, called Type-2 these We establish connections between coherence properties, show that imprecise considerations are required in order achieve it. go both types achieved interpreting conformal output contour function consonant plausibility measure. also offer alternative characterization prediction, based nonparametric inferential model construction, wherein appearance consonance natural, prove its validity.