The optimal selection of experimental conditions is essential to maximizing
the value of data for inference and prediction, particularly in situations
where experiments are time-consuming and expensive to conduct. We propose a
general mathematical framework and an algorithmic approach for optimal
experimental design with nonlinear simulation-based models; in particular, we
focus on finding sets of experiments that provide the most information about
targeted sets of parameters.
Our framework employs a Bayesian statistical setting, which provides a
foundation for inference from noisy, indirect, and incomplete data, and a
natural mechanism for incorporating heterogeneous sources of information. An
objective function is constructed from information theoretic measures,
reflecting expected information gain from proposed combinations of experiments.
Polynomial chaos approximations and a two-stage Monte Carlo sampling method are
used to evaluate the expected information gain. Stochastic approximation
algorithms are then used to make optimization feasible in computationally
intensive and high-dimensional settings. These algorithms are demonstrated on
model problems and on nonlinear parameter estimation problems arising in
detailed combustion kinetics.Comment: Preprint 53 pages, 17 figures (54 small figures). v1 submitted to the
Journal of Computational Physics on August 4, 2011; v2 submitted on August
12, 2012. v2 changes: (a) addition of Appendix B and Figure 17 to address the
bias in the expected utility estimator; (b) minor language edits; v3
submitted on November 30, 2012. v3 changes: minor edit
