Title: Bayesian design of physical experiments for nonlinear and computational models
Authors: Tim Waite - University of Manchester (United Kingdom) [presenting]
David Woods - University of Southampton (United Kingdom)
Yiolanda Englezou - University of Cyprus (Cyprus)
Abstract: The purpose is to discuss Bayesian decision-theoretic optimal design of physical experiments for parameter estimation in nonlinear models, including models that incorporate an expensive computer simulator. In the Bayesian approach, one key challenge is the presence of analytically intractable nested integrals in the expected utility (e.g. expected Shannon information gain) of any proposed design. We propose new Monte Carlo approaches for approximate numerical integration of the expected utility that give reduced bias and computational expense compared to several existing methods. Another challenge is that, when the model incorporates an expensive computer simulator, it is prohibitively costly to use an expected utility estimate that relies on direct evaluations of the simulator. Hence in order to perform design optimization for the physical experiment, and also to conduct subsequent inference, one must use a computationally cheap surrogate model in place of the simulator. We accomplish this using a Gaussian process emulator built with pre-existing training data from a computer experiment, thereby extending the analysis framework from the calibration literature to the design problem. The proposed fully Bayesian framework enables uncertainty about the simulator output at untested input combinations to be incorporated when designing the physical experiment.