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research-article

Optimal Experimental Design Using A Consistent Bayesian Approach

[+] Author and Article Information
Scott Walsh

University of Colorado Denver, Department of Mathematical and Statistical Sciences
scott.walsh@ucdenver.edu

Timothy Wildey

Sandia National Laboratories, Center for Computing Research
tmwilde@sandia.gov

John D Jakeman

Sandia National Laboratories, Center for Computing Research
jdjakem@sandia.gov

1Corresponding author.

ASME doi:10.1115/1.4037457 History: Received October 04, 2016; Revised June 26, 2017

Abstract

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.

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