  We consider the utilization of a computational model to guide the optimal
acquisition of experimental data to inform the stochastic description of model
input parameters. Our formulation is based on the recently developed consistent
Bayesian approach for solving stochastic inverse problems which seeks a
posterior probability density that is consistent with the model and the data in
the sense that the push-forward of the posterior (through the computational
model) matches the observed density on the observations almost everywhere.
Given a set a potential observations, our optimal experimental design (OED)
seeks the observation, or set of observations, that maximizes the expected
information gain from the prior probability density on the model parameters. We
discuss the characterization of the space of observed densities and a
computationally efficient approach for rescaling observed densities to satisfy
the fundamental assumptions of the consistent Bayesian approach. Numerical
results are presented to compare our approach with existing OED methodologies
using the classical/statistical Bayesian approach and to demonstrate our OED on
a set of representative PDE-based models.
