Event Date
Mathematics-Statistics Joint Colloquium 2026
Speaker: Persi Diaconis, Mary V. Sunery Professor of Statistics / Professor of Mathematics, Stanford University
Title: "Estimating the Size of a Finite Set"
Abstract: Suppose you have a large finite set S of interest (the set of I x J integer arrays with given row and column sums or the set of unlabeled trees on n vertices). You have the ability to sample randomly from the set and want to estimate its size. With no structure, about all you can do is wait for repeats and use the birthday problem. This requires a sample of size |S|1/2, which can be prohibitive in applications. In joint work with Sourav Chatterjee and Susan Holmes, we found that useful improvements using the structure of S are available. Examples include the unseen species problem (how many words did Shakespeare know?), the German tank problem (when S is a poset), and the problem of estimating the volume of a convex set in R^d. A general, non-asymptotic theory is developed; I will try to explain all this to a general audience “in English.”
Faculty webpage (links to Stanford)
The annual Math / Stats Colloquium is jointly hosted by the Department of Mathematics and the Department of Statistics at UC Davis.