Predictive Inference and Discontinuities

Abstract

The purpose of this note is to study the consequences, mainly in the form of simple examples, which the fundamental ideas of deFinetti on predictive inference and exchangeable random variables have in the context of reliability problems. In particular, the role of unpredictable observations, or innovations, is related to discontinuities in the process of learning from the data. It is argued that probabilistic quantification of subjective uncertainties is an intrinsic element of realistic modeling. The presentation is mainly of an expository nature.