2014-2015 II semestre: H. Hosney: An Introduction to Bayesian Rationality
Corsi Dottorato - II semestre 2014-2015
An Introduction to Bayesian Rationality
Docente Prof. H. Hosney
Lunedì 6 Luglio
10:00 - 12:00: From Rational Choice to Rational Degrees of Belief
14:00 - 16:00: From Rational Degrees of Belief to Rational Decision
Martedì 7 Luglio
10:00 - 13:00: The Rational Selection of Probabilities
Mercoledì 8 Luglio
10:00 - 13:00: Descriptive and Normative Challenges
Uncertainty is ubiquitous and affects virtually all of our reasoning and decision-making, both practical and scientific. This clearly raises a two-fold question of fundamental epistemological importance:
/How should we reason and act so as to be rational in the face of uncertainty?/
The cross-disciplinary framework which is generally referred to as Bayesian Theory puts forward a two-fold reply:
/Rational agents should reason probabilistically and their actions should maximise the agent's subjective expected utility./
The purpose of this course is to provide the formal and conceptual tools required (i) to formulate the Bayesian norms of rationality with some precision and (ii) to assess them as the key elements of a /theory/ of rationality.
The course is divided into two main parts. The first focusses on the choice-theoretic roots of Bayesian theory. Both Probability and Expected Utility maximisation are derived as norms rationality from suitable formalisations of choice-theoretic consistency. As paradigmatic illustrations of those derivations we will consider de Finetti's Dutch Book Argument and, in somewhat less detail, Savage's representation theorem.
The second part of the course aims at evaluating critically the epistemological status of Bayesian Theory. As a key normative challenge to Bayesian theory we will tackle the question of the rational selection of subjective
probabilities. This, in short, amounts to challenging the (pure) subjectivist view which identifies rational belief with /any/ consistent probability distribution. This question is best framed in the context of probability logic, the basics of which will be introduced to the extent needed for our present purposes. Then we will consider (a necessarily small sample of) the descriptive challenges to Bayesian theory posed by the vast experimental literature which has become available in the past few decades, spanning economics and the cognitive sciences.
In conclusion I will emphasise how the descriptive and normative criticisms illustrated concur to raising a set of epistemologically deep questions which undoubtedly will keep the foundations of uncertain reasoning
thriving, as a cross-disciplinary research area, for the years to come.
(Acquaintance with classical propositional logic will be useful, though not necessary. Otherwise the course will be self-contained.)