Algorithmic randomness and Bayesian convergence

Francesca Zaffora Blando (Carnegie Mellon University)

06-Dec-2021, 21:30-22:30 (2 years ago)

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.

logic

Audience: researchers in the topic


Computability theory and applications

Series comments: Description: Computability theory, logic

The goal of this endeavor is to run a seminar on the platform Zoom on a weekly basis, perhaps with alternating time slots each of which covers at least three out of four of Europe, North America, Asia, and New Zealand/Australia. While the meetings are always scheduled for Tuesdays, the timezone varies, so please refer to the calendar on the website for details about individual seminars.

Organizers: Damir Dzhafarov*, Vasco Brattka*, Ekaterina Fokina*, Ludovic Patey*, Takayuki Kihara, Noam Greenberg, Arno Pauly, Linda Brown Westrick
*contact for this listing

Export talk to