Bayesian Reasoning:
A New Science of Knowledge

Instructor: Anna Longo Date & Time: Saturdays February 6, 13, 20, 27, March 6, 13, 20, 27 11:00 to 13:30 ET

DESCRIPTION: Bayesian statistical inference and theory of decision are widely employed today in many different domains of enquiry such as physics, social sciences, economics, medicine, law, cognitive sciences and artificial intelligence. Even though Thomas Bayes wrote the theorem for conditioning the probability of hypothesis during the 18 th century, it has been difficult to use it in scientific induction until the introduction of algorithmic techniques that rendered the calculation practically accessible and suitable for make any sort of prediction based on big data exploration. Bayesianism is much more than a theory of probability: it is a paradigm for reasoning and learning that allows to explain how knowledge evolve, how beliefs converge towards the most reliable hypothesis and how conventional rules for coordinating practices can emerge to support collective interests. Moreover, Bayesian decision theory provides the model of rational agent in economics and for programming artificial intelligence. However, despite the remarkable achievement and the promises, Bayesianism has been criticized for being a normative and idealizing perspective on rationality that do not take into account real computational limits and the logical impossibility of achieving inductive certainty. The seminar aims to provide the basic tools to understand Bayesian methods and to grasp their potentialities and limitations. We will explore the history of probability theory and we will compare different interpretations (von Mises, Carnap, Keynes, Ramsey, de Finetti) and their application to scientific induction in order to situate bayesianism within the wider epistemological turn at the beginning of the 20 th Century. We will introduce algorithmic probability (Ray Solomonff) and the hypothesis of “Bayesian brain” in cognitive sciences (Friston, Dehaene) to understand why it has been considered as suitable for programming artificial intelligence. We will deal with the game theoretic perspective on decision theory (von Neumann and Morgestern, Harsanyi, Lewis) that supports economic modeling (Savage, Friedman) and automated trading. Finally, we will turn to criticism (evolutionary game theory) and we will try to think about the philosophical implications of Bayesian epistemology.

IMAGE: Laura Stack, Untitled, 2017

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