Bayesian Optimal Design for Ordinary Differential Equation Models

Overstall, A. M., Woods, D. C. and Parker, B. M. (2015) Bayesian Optimal Design for Ordinary Differential Equation Models. Working Paper. University of Glasgow. (Unpublished)

Abstract

Bayesian optimal design is considered for experiments where it is hypothesised that the responses are described by the intractable solution to a system of non-linear ordinary differential equations (ODEs). Bayesian optimal design is based on the minimisation of an expected loss function where the expectation is with respect to all unknown quantities (responses and parameters). This expectation is typically intractable even for simple models before even considering the intractability of the ODE solution. New methodology is developed for this problem that involves minimising a smoothed stochastic approximation to the expected loss and using a state-of-the-art stochastic solution to the ODEs, by treating the ODE solution as an unknown quantity. The methodology is demonstrated on three illustrative examples and a real application involving estimating the properties of human placentas.

• Item Type: Research Reports or Papers (Working Paper)
• Status: Unpublished
• Refereed: No
• Glasgow Author(s) Enlighten ID: Overstall, Dr Antony
• Authors: Overstall, A. M., Woods, D. C., and Parker, B. M.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Statistics
• Publisher: University of Glasgow
• Copyright Holders: Copyright © 2015 The Authors
• Publisher Policy: Reproduced with permission of Authors

Related URLs

• arXiv