  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.
