Nonlinear Bayesian optimal experimental design using logarithmic Sobolev inequalities

The optimal experimental design (OED) problem arises in numerous settings, with applications ranging from combustion kinetics Huan & Marzouk (2013), sensor placement for weather prediction Krause et al. (2008), containment source identification Attia et al. (2018), to pharmaceutical trials Djuris et al. (2024). A commonly addressed version of the OED problem centers on the fundamental question of selecting an optimal subset of k observations from a total pool of n possible candidates, with the goal of learning the parameters of a statistical model for the observations. In the Bayesian framework, these parameters are endowed with a prior distribution to represent our state of knowledge before seeing the data. A posterior distribution on the parameters is obtained by conditioning on the observations. A commonly used experimental design criterion is then the mutual information (MI) between the parameters and the selected observations or, equivalently, the expected information gain from prior to posterior, which should be maximized.