20–24 July 2015, Pescara, Italy

Invited Speakers

photo of M. Marinacci

Massimo Marinacci

AXA-Bocconi Chair in Risk
Department of Decision Sciences
Bocconi University, Milan, Italy

Model Uncertainty

We study decision problems in which the consequences of the alternative actions depend on states determined by a generative mechanism representing some natural or social phenomenon. Model uncertainty arises as decision makers may not know such mechanism. Two types of uncertainty result, a state uncertainty within models and a model uncertainty across them. We discuss some two-stage static decision criteria proposed in the literature that address state uncertainty in the first stage and model uncertainty in the second one (by considering subjective probabilities over models). We consider two approaches to the Ellsberg-type phenomena that these decision problems feature: a Bayesian approach based on the distinction between subjective attitudes toward the two kinds of uncertainty, and a non Bayesian one that permits multiple subjective probabilities. Several applications are used to illustrate concepts as they are introduced.

photo of I. Gilboa

Itzhak Gilboa

Professor of Economics and Decision Sciences
Eitan Berglas School of Economics
Tel-Aviv University, Israel
Paris, France

A Unified Model of Inductive Reasoning

We offer a model that can capture three types of reasoning. The first, which is the most common in economic modeling, is Bayesian. An alternative mode of reasoning is case-based: The agent considers past observations and predicts the outcome that appeared more often in those past cases that are considered similar. Finally, rule-based reasoning calls for the agent to base her predictions on regularities that she believes characterize the phenomenon in question.

We present a framework that unifies these three modes of reasoning (and potentially others), allowing us to view them as special cases of a general learning process. Our model could be used to address either positive or normative questions. We focus on positive ones, describing how the reasoning process of an agent evolves as observations are gathered. Finally, the model can also be used to reason about counterfactuals.

photo of P.M. Williams

Peter M. Williams

Department of Informatics
University of Sussex, Brighton, UK
BW Mining
Brighton, UK

Early Approaches to Exact Imprecision

The 1960s and 70s were a period of widespread interest in the philosophical and mathematical foundations of probability. Bayesian ideas were recognized though not well understood, and treated with caution by mainstream statisticians. This talk surveys the intellectual climate of the period, including the impact of de Finetti's ideas, then becoming more widely known in English translation, and traces the motivation and development of non-additive measures of uncertainty, together with their impact on the then developing treatment of uncertainty in artificial intelligence.

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