CMStatistics 2021: Start Registration
View Submission - CMStatistics
B0863
Title: False confidence, imprecise probability, and valid statistical inference Authors:  Ryan Martin - North Carolina State University (United States) [presenting]
Abstract: Statistical inference aims to quantify uncertainty about unknowns based on data. To formalize this, an inferential model (IM) is a function that maps data, etc., to a capacity on the parameter space assigning data-dependent degrees of belief to assertions about the unknowns; this covers Bayes, fiducial, and other distributional inference approaches. Important questions include: what statistical properties should an IM satisfy, and what do these statistical properties imply about the mathematical structure of its capacity? We will define a ``validity'' property which, among other things, implies strong frequentist error rate control. Then we will summarize two recent results saying that (a) an IM whose capacity is a precise/additive probability suffers from false confidence and, therefore, cannot be valid, and (b) validity can be achieved by IMs whose capacities belong to a simple class of imprecise/non-additive probabilities, namely, possibility measures. We will end with illustrations and a discussion of practical implications and open questions.