Using Computer Experiments and Gaussian Process Emulation to Facilitate Bayesian Optimal Design for Physical Models Derived from Ordinary Differential Equations

• Activity Number: 220
• Type: Invited
• Date/Time: Monday, August 1, 2016 : 2:00 PM to 3:50 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): David Woods* and Antony Overstall and Benjamin Parker
• Companies: University of Southampton and University of Glasgow and University of Southampton
• Keywords: Decision-theoretic design of experiments ; Non-linear modelling ; Uncertainty quantification

Abstract

Bayesian optimal design for many realistic and practically important experiments is complicated by the need to evaluate an expected loss over all a priori unknown and unobserved quantities for each prospective design. For nonlinear statistical models, this expected loss is typically analytically intractable; for many physical models, evaluation of the expected loss is further complicated by the need for numerical solutions to the underpinning ordinary differential equations (ODEs). Hence, finding an optimal design for such models via minimisation of the expected loss is challenging. We present a methodology for finding optimal designs that (i) employs a probabilistic solution to the system of ODEs and (ii) treats a Monte Carlo approximation of the expected loss as an unknown black-box function and conducts a computer experiment. The potentially high-dimensional nature of the problem is mitigated via application of the coordinate exchange algorithm and conditional emulation of the expected loss for each coordinate (value of a single controllable variable in a single experimental run). The work is motivated by, and demonstrated on, examples from the biological sciences.