Midwest Computability Seminar

XXVII
Part vii


The Midwest Computability Seminar is meeting remotely in the fall of 2021. The recurring Zoom link is:

https://notredame.zoom.us/j/99754332165?pwd=RytjK1RFZU5KWnZxZ3VFK0g4YTMyQT09

Meeting ID: 997 5433 2165

Passcode: midwest


slides    Panopto video    YouTube video


This session will be held jointly with the Computability Theory and Applications Online Seminar.


DATE: Monday, December 6th, 2021

TIME: 3:30 - 4:30 PM Central Time


SPEAKER: Francesca Zaffora Blando - Carnegie Mellon University

TITLE: Algorithmic randomness and Bayesian convergence

ABSTRACT: Much recent work in algorithmic randomness has concerned characterizations of randomness notions in terms of effectivizations of almost-everywhere convergence theorems in analysis and probability theory. In this talk, I will consider some results that are part of the basic toolkit of Bayesian epistemologists from this perspective. In particular, I will focus on certain martingale convergence theorems that form one of the cornerstones of Bayesian epistemology and that fall under the general umbrella of "Bayesian convergence-to-the-truth results". These results are standardly taken to establish that a Bayesian agent’s beliefs are guaranteed to converge to the truth with probability one as the evidence accumulates. We will see that, for computable Bayesian agents (i.e., Bayesian agents with computable priors), we not only have that convergence to the truth occurs with probability one, but we can also provide precise characterizations of the data streams along which beliefs converge to the truth: they are precisely the algorithmically random data streams. I will conclude by sketching a broader computability-theoretic approach to Bayesian epistemology suggested by these results.

This is joint work with Simon Huttegger and Sean Walsh.



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