Session I.6 - Mathematical Foundations of Data Assimilation and Inverse Problems
Poster
Stability for the optimal experimental design problem in Bayesian inverse problems
Duc-Lam Duong
LUT University, Finland - This email address is being protected from spambots. You need JavaScript enabled to view it.
We study some stability properties of the expected utility function in Bayesian optimal experimental design. We provide a framework for this problem in a non-parametric setting and prove a convergence rate of the expected utility with respect to a likelihood perturbation. This rate is uniform over the design space and its sharpness in the general setting is demonstrated by proving a lower bound in a special case. To make the problem more concrete we proceed by considering non-linear Bayesian inverse problems with Gaussian likelihood and verify that the assumptions set out for the general case are satisfied and regain the stability of the expected utility with respect to perturbations to the observation map. Theoretical convergence rates are demonstrated numerically in different examples.
Joint work with Tapio Helin (LUT University, Finland) and Rodrigo Rojo-Garcia (LUT University, Finland).