Stability estimates for the expected utility in Bayesian optimal experimental design

TL;DR

This paper investigates the stability of the expected utility function in Bayesian optimal experimental design, establishing convergence rates under likelihood perturbations in a non-parametric setting and validating results through numerical examples.

Contribution

It introduces a framework for stability analysis in Bayesian experimental design, providing sharp convergence rates and demonstrating applicability to non-linear inverse problems with Gaussian likelihoods.

Findings

Convergence rate of expected utility under likelihood perturbations

Stability of expected utility in non-linear Bayesian inverse problems

Numerical validation in three different examples

Abstract

We study 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 prove 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 three different examples.