Dear Colleagues,

We would like to invite you to the following seminar: On Frequentist Coverage of Bayes Posteriors for Non Linear Inverse Problems by Youngsoo Baek (Duke University)

The seminar will take place on THU, 11.07.2024 at 14:00 CET in Aula Seminari, Dipartimento di Matematica, UNIPI and streamed online at this linkhttps://meet.google.com/gji-phwo-vbg.

Katerina Papagiannouli

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Abstract: We present two new results on the frequentist coverage of Bayes posteriors when estimating linear functionals of the unknown parameter in a nonlinear, PDE-based inverse problem. The results are valid for Gaussian process priors under sufficiently strong smoothness assumptions on the model. They provide a characterization of asymptotic coverage and Gaussian geometry for the standard posterior credible bands based on the first two moments, irrespective of whether Bernstein von-Mises (BvM) theorem holds or not. In the case it does hold, our sufficient conditions are sharper than previous known results. The proof is based on a particular choice of a least favorable transformation of the parameter and an injectivity estimate on the prior RKHS. As an application, we study the case of estimating diffusivity coefficient in a Darcy flow problem, where necessary conditions of BvM breaks down. This is a joint work with Katerina Papagiannouli.