Direct and approximately valid probabilistic inference on a class of statistical functionals

Uncertainty Quantification in Logistic Regression Using Random Fuzzy Sets and Belief Functions

“…As shown in [40], π θ|y verifies the following "strong validity" property, ). An in-depth discussion of this method can be found in [3]. Possibility distribution π θ|y does not satisfy requirements R 1 and R 2 : in particular, a "valid" possibility distribution computed from two independent samples cannot be obtained by combining the valid possibility distributions from each of the two samples using a formal rule such as the product-intersection operator.…”

“…Another approach, which will be adopted here, is to consider decision rules with rejection, and to compare error rates for various rejection rates obtained with predictive belief functions on the one hand, and estimated posterior probabilities on the other hand. As a given rejection rate is achieved by comparing the maximum degree belief or plausibility to some threshold, the error-reject curve, by considering all possible thresholds, characterizes the "information content" of the predictive belief function better than the error rate without rejection alone 3 . The datasets and the experimental settings will first be described in Section 5.1.…”