Colloquium Series: Bodhisattva Sen

Our upcoming event for the Statistics Colloquium Series is scheduled for Monday, October 26th from 12:00 – 1:00pm (ET) and will be an in-person presentation at Maxwell-Dworkin, Room 119. Lunch will be provided to guests following the talk. This week's speaker will be Bodhisattva Sen, Professor and Chair of Statistics at Columbia University. 

Wasserstein-Cramér-Rao Theory of Unbiased Estimation

Abstract: The quantity of interest in the classical Cramér-Rao theory of unbiased estimation—including the Cramér-Rao lower bound, exact efficiency in exponential families, and asymptotic efficiency of maximum likelihood estimation—is the variance, which measures the instability of an estimator across independently sampled data sets from the same distribution. In this talk, we consider a different measure of instability: the change in an estimator under an infinitesimal additive perturbation of the original data set. We refer to this quantity as the “sensitivity” of an estimator. The resulting theory of sensitivity is based on Wasserstein geometry, just as the classical theory of variance is based on Fisher-Rao (equivalently, Hellinger) geometry. This connection leads to analogues of classical results: a Wasserstein-Cramér-Rao lower bound for the sensitivity of unbiased estimators, a characterization of models admitting unbiased estimators that attain the bound exactly, and results establishing asymptotic attainment of the bound by Wasserstein projection estimators. We illustrate the theory through statistical examples, revealing new optimality properties of existing estimators and suggesting new estimators. This is joint work with Nicolás García Trillos (University of Wisconsin–Madison) and Adam Jaffe (Columbia University), based on the paper: https://arxiv.org/pdf/2511.07414.

Speaker's Bio: Bodhi Sen is Professor and Chair of Statistics at Columbia University in New York. He received his Ph.D. in Statistics from the University of Michigan, Ann Arbor, in 2008, and his B.Stat. (2002) and M.Stat. (2004) from the Indian Statistical Institute, Kolkata. His research interests include nonparametric inference, shape-constrained estimation, empirical Bayes methods, and optimal transport. His honors include an NSF CAREER Award (2012) and the Young Statistical Scientist Award in the Theory and Methods category from the International Indian Statistical Association. He is a Fellow of the Institute of Mathematical Statistics (IMS) and an elected member of the International Statistical Institute (ISI), and delivered an IMS Medallion Lecture in 2026.