Perhaps malapropos for the NBA Finals, Prof. Michael Jordan gave the first plenary talk at ISIT. It was a great overview of nonparametric Bayesian modeling. In particular, he covered his favorite Chinese restaurant process (also known as the Pitman-Yor stick-breaking process), hierarchical Dirichlet priors, and all the other jargon-laden elements of modeling. At the end he covered some of the rather stunning successes of this approach in applications with lots of data to learn from. What was missing for me was a sense of how these approaches worked in the data-poor regime, so I asked a question (foolishly) about sample complexity. Alas, since that is a “frequentist” question and Jordan is a “Bayesian,” I didn’t quite get the answer to the question I was trying to ask, but that’s what happens when you don’t phrase things properly.
One nice thing that I learned was the connection to Kingman’s earlier work on characterizing random measures via non-homogeneous Poisson processes. Kingman has been popping up all over the place in my reading, from urn processes to exchangeable partition processes (also known as paintbox processes). When I get back to SD, it will be back to the classics for me!