STAT C206B (= MATH C223B) Spring 2013: David Aldous

STAT 206, with catalog description Advanced Topics in Probability and Stochastic Processes, is intended to have a different subject each semester. My subject is

Exchangeability and related topics

See the list of possibly-relevant papers for many more works than are mentioned on this page.

We will first review classical theory, centered upon de Finetti's theorem. In the late 1970s there were several developments, discussed in Aldous (1983) (200 typed pages). In particular we will discuss two topics initiated around that time

Topic 1. The Poisson-Dirichlet distribution on partitions

Topic 2. Representation theorems for partially exchangeable arrays

As one can infer from Google Scholar's time series of citations to that article, the subject remained quiet until around 2005 but has subsequently attracted considerable interest from several opposite directions.

Topic 1. On the one hand this has influenced extensive work concerning prior distributions on categorical data for Bayesian machine learning -- see e.g. Teh at al (2006). Developments on the mathematical side appear in the monograph Feng (2010).

Topic 2. This theory was treated in detail in the monograph Kallenberg (2005). Around that time it was being rediscovered in several "pure math" contexts

My own personal current interest is in the general idea of representations of complex random structures Aldous (2010) via induced substructures on randomly sampled points. In particular there is a challenging project Aldous (2012a) on a conjectured compactification of some finite reversible Markov chains.


Lecture times: MWF 1.00 - 2.00pm room 344 EVANS

Office Hours: Wednesdays 2.00-3.00 in 351 Evans.

If you email me ( put "STAT 206" in subject line.

Requirements for students. Students taking course for credit need to do one of the following.

Class-by-class schedule

This will mostly be a debriefing of what I have done, rather than a plan for the future......