Bayesian Inference and Optimal Design for Differential Equation Models with Application to Chemical Kinetics

• Activity Number: 307
• Type: Invited
• Date/Time: Tuesday, August 5, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Antony Overstall*+ and David Woods
• Companies: University of St. Andrews and University of Southampton
• Keywords: differential equations ; emulators ; optimal design

Abstract

We consider Bayesian inference and optimal design for data-generating processes that can be described by a system of ordinary differential equations (ODEs). Typically, the ODEs do not have an analytic solution and numerical methods must be employed.

Bayesian inference and optimal design are complicated by the computational expense of the numerical solution to the ODEs. We propose a strategy that employs statistical emulators to approximate 1) the expected utility function employed to find the optimal design; and 2) the solution to the ODEs which improves the efficiency of the MCMC methods used to explore the posterior distribution.

We apply the strategy to data from a pharmaceutical experiment involving a series of chemical reactions and a multivariate response (the concentration of three chemicals). The behaviour of the concentrations can be described by a system of ODEs derived from chemical kinetics and which incorporates temperature dependency through the Arrehnius equation. The goal is to find a set of design variables such that the probability of the responses from a future experiment satisfying given constraints is greater than a specified constant.