Stability estimates for the expected utility in Bayesian optimal experimental design

Abstract

We study the 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.

Bayesian experimental design for linear elasticity

“…Assuming a zero mean for α can be motivated by appropriately choosing the background Lamé parameter pair τ 0 . On the other hand, if the mean of the noise were not initially zero, it could be subtracted from both sides of (17), thus redefining the measurement and a new zero-mean noise term. Be that as it may, neither of these means affects the target function of A-optimality introduced below.…”

“…Moreover, one can also aim to avoid discretizing the problem setting before employing OED; see, e.g., the series of papers on Bayesian OED in the framework of infinite-dimensional inverse problems [2,3,4,5]. The stability of the expected utility under approximations, such as linearization and discretization, in Bayesian OED has recently been investigated in [17]. For general reviews on the topic of Bayesian OED, we refer to [1,14,49,50].…”