Optimal experiment design for practical parameter inference and model selection

Mathematical models are seeing increasing use in understanding the dynamical mechanisms underlying biological systems. The accuracy and reliability of the predictions and insights offered by such models depend on our ability to confidently estimate the values of unknown parameters in the model from available data, referred to as parameter identifiability, and the ability to distinguish competing biological hypotheses represented by different models, a problem known as model discrimination. A well-designed experiment can produce data that are much more informative for reducing uncertainty in parameter values. In this talk, we present methods for optimal experiment design that aims both to improve parameter identifiability, and to perform model discrimination. We focus on cases where an external stimulus can be used as a control input to probe the behaviour of the system, and explore techniques for optimally designing such a control for a given experiment. We demonstrate these techniques in the context of ordinary differential equation models for population growth, use profile likelihoods to quantify parameter uncertainty, and apply Pontryagin's Maximum Principle to solve the optimal control problem.