CMX Lunch Seminar

Wednesday January 29, 2020 12:00 PM

Statistical Guarantees for MAP Estimators in PDE-Constrained Regression Problems

Speaker: Sven Wang, Department of Pure Mathematics and Mathematical Statistics, University of Cambridge
Location: Annenberg 213

The main topic of the talk are convergence rates for penalised least squares (PLS) estimators in non-linear statistical inverse problems, which can also be interpreted as Maximum a Posteriori (MAP) estimators for certain Gaussian Priors. Under general conditions on the forward map, we prove convergence rates for PLS estimators.

In our main example, the parameter f is an unknown heat conductivity function in a steady state heat equation [a second order elliptic PDE]. The observations consist of a noisy version of the solution u[f] to the boundary value corresponding to f. The PDE-constrained regression problem is shown to be solved a minimax-optimal way.

This is joint work with S. van de Geer and R. Nickl. If time permits, we will mention some related work on the non-parametric Bayesian approach, as well as computational questions for the Bayesian posterior.

Series CMX Lunch Series

Contact: Jolene Brink at 6263952813 jbrink@caltech.edu
For more information visit: http://cmx.caltech.edu/