22-24 September 2021
Alpen-Adria-Universität Klagenfurt
Europe/Vienna timezone

Consistency of Bayesian inference with Gaussian process priors for a parabolic inverse problem

24 Sep 2021, 10:20
HS 1 (Alpen-Adria-Universität Klagenfurt)

HS 1

Alpen-Adria-Universität Klagenfurt


Dr Hanne Kekkonen (Delft University of Technology)


We consider the statistical nonlinear inverse problem of recovering the absorption term f > 0 in the heat equation, with given boundary and initial value functions, from N discrete noisy point evaluations of the solution u_f. We study the statistical performance of Bayesian nonparametric procedures based on Gaussian process priors, that are often used in practice. We show that, as the number of measurements increases, the resulting posterior distributions concentrate around the true parameter f* that generated the data, and derive a convergence rate for the reconstruction error of the associated posterior means. We also consider the optimality of the contraction rates and prove a lower bound for the minimax convergence rate for inferring f from the data, and show that optimal rates can be achieved with truncated Gaussian priors.

Primary author

Dr Hanne Kekkonen (Delft University of Technology)

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