Unit X - Subjective probability: theoretical aspects and applications

Italian version

Lecturer: Giuseppe Sanfilippo

We start by a brief critical discussion of the various approaches to probability. Then, we will introduce de Finetti’s coherence principle as a basis of subjective probability, by obtaining the classical properties of probability. We will examine several aspects of coherence, like betting scheme, penalty criterion, geometrical interpretations, proper scoring rules and probability elicitation, conditional events and conditional random quantities, logical operations among conditional events, and algorithms for imprecise probability. We will analyze the relation between Bregman divergences and proper scoring rules, by also considering the Kullback-Leibler divergence. We will model human inference within coherence-based probability logic. We will discuss formal work on nonmonotonic reasoning (retracting conclusions in the light of new evidence), conditionals (if–then statements) and compound conditionals (e.g., (if H then A) & (if K then B)).