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CMX Lunch Seminar

Wednesday, January 29, 2020
12:00pm to 1:00pm
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Annenberg 213
Statistical Guarantees for MAP Estimators in PDE-Constrained Regression Problems
Sven Wang, Department of Pure Mathematics and Mathematical Statistics, University of Cambridge,

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.

For more information, please contact Jolene Brink by phone at 6263952813 or by email at jbrink@caltech.edu or visit CMX Website.