April 4, 2022

Extended probabilities and their application to statistical inference

Michele Caprio, Duke

Abstract: We propose a new, more general definition of extended probability measures. We study their properties and provide a behavioral interpretation. We use them in an inference procedure, whose environment is canonically represented by the probability space ​(Ω,F,P), when both ​P and the composition of Ω are unknown. We develop an ex-ante analysis — taking place before the statistical analysis requiring knowledge of Ω — in which we progressively learn the true composition of Ω. We provide an example in the field of ecology.