IDS Seminar: A generalization of the de Finetti—Hewitt—Savage Theorem on exchangeable processes
Venue: Inno Wing II / Zoom
Mode: Hybrid. Seats for on-site participants are limited. A confirmation email will be sent to participants who have successfully registered.
Abstract
De Finetti proved the classical theorem that a sequence of (real) random variables is mixed iid iff it is exchangeable.
The theorem was consecutively generalized: Ryll-Nardzewski showed in the same setting that exchangeability is also equivalent to being conditionally iid. By a well-known argument, these theorems generalize immediately to any sequence of random variables taking values in (so-called) standard Borel spaces. The conditions on the space where the process takes its values were further relaxed in work of Hewitt—Savage, Fremlin, and recently, Alam. The guiding question has been: To what extent can one get rid of the topological restrictions? In the opposite direction, Dubins and Freedman gave examples of ill-behaved process where these equivalences fail. There constructions have a decidedly set-theoretic flavor.
In recent joint work with PETER POTAPTCHIK and DANIEL M. ROY, we prove a generalization of the above theorems:
Given an exchangeable sequence of random elements, the sequence is conditionally i.i.d. if and only if each random element admits a regular conditional distribution given the exchangeable σ-algebra (equivalently, the shift invariant or the tail algebra). We use this result, which holds without any regularity or technical conditions, to demonstrate that any exchangeable sequence of random elements whose common distribution is Radon is conditional iid.
Speaker
Professor David Schrittesser currently holds the position of Professor at the Institute for Advanced Studies in Mathematics at Harbin Institute of Technology. Before that, he was a Research Associate in statistics and mathematics at the University of Toronto. During his time at UoT, he served as a main organizer of the Set Theory Seminar at the Fields Institute. He received his PhD degree from the Kurt Gödel Research Center, University of Vienna.
His research interest is in mathematical logic; his primary interests are descriptive set theory, as well as infinite combinatorics, forcing, definability, and inner models. He is also interested in non-standard analysis and its applications, especially in probability theory and statistical decision theory.
For full biography of Prof. Schrittesser, please refer to: https://logicdavid.github.io/
Moderator
Prof. Boris Babic is HKU-100 Associate Professor at the University of Hong Kong, jointly appointed in the Musketeers Foundation Institute of Data Science, the Department of Philosophy, and (by courtesy) the Faculty of Law, from Fall 2023. He also serves as an occasional visiting professor in the Decision Sciences department at INSEAD.
Prof. Babic’s primary research interests are in Bayesian inference and decision-making, ethics, law, and policy of artificial intelligence and machine learning, especially in medical applications. His research has been published extensively in leading journals such as Science, Nature Machine Intelligence, Nature Digital Medicine, and the Harvard Business Review.
For full biography of Prof. Babic, please refer to: https://datascience.hku.hk/people/boris-babic/
For information, please contact:
Email: datascience@hku.hk