Tutorials

Barbara Vantaggi

Associate professor of Probability and Mathematical Statistics

“La Sapienza” University of Rome, Italy

De Finetti coherence and Beyond

We present the concept of coherence, which dates back to de Finetti, by showing its role in modelling uncertainty. One of the main peculiarities is that a coherent assessment can always be extended, generally not in a unique way, to any superset, giving rise to a class of coherent extensions and its lower and upper envelopes.

The main features of de Finetti's coherence are discussed in connection with its "generalizations" to imprecise probabilities, essentially given by Williams and Walley.

Some examples coming from applications will be used to illustrate key concepts.

Gregory Wheeler

Assistant Professor of Philosophy

Munich Center for Mathematical Philosophy
Ludwig-Maximilians-Universität München, Germany

Introduction to the Philosophical Foundations of Imprecise Probabilities

In this tutorial we will introduce several topics in the foundations of imprecise probabilities through a review of key historical figures, including John Maynard Keynes, B.O. Koopman, and I.J. Good, Henry Kyburg, Terrence Fine and Isaac Levi, and their reactions to the subjectivist-rationalist tradition associated with Ramsey, de Finetti, and Savage, and the later developments associated with Peter Williams and Peter Walley. We will end with a short overview of Epistemic Decision Theory, which aims to reinterpret the machinery of strictly proper scoring rules as measures of “epistemic accuracy,” and the issues which arise from impossibility theorems which indicate that there are no strictly IP proper scoring rules.