Bayesian optimal design for estimating physical parameters of computer models based on systems of ODEs with application to measuring transportation properties of human placentas Seminar

We consider Bayesian optimal design for estimating the physical parameters of computer models, in particular, those derived from the numerical solution to a system of ordinary differential equations (ODEs).

Bayesian optimal design requires the maximisation of the expectation (over all unobserved quantities) of an appropriately chosen utility function. Typically, this expectation is intractable. In our case, a further complication arises from the computational expense of the numerical solution to the ODEs. We propose a strategy that includes employing statistical emulators to approximate 1) the expected utility function employed to find the optimal design; and 2) the solution to the ODEs. These steps substantially reduce the computational expense of finding an optimal design.

We apply the strategy to data from a medical experiment involving modelling the transport of the amino acid serine across the membranes of a human placenta. The behaviour of the concentration of serine at various time points can be described by a system of ODEs. A full understanding of serine transport requires that we determine the value of several unknown physical parameters which control the system of ODEs. The goal is to design an experiment to minimise uncertainty in the expected posterior distribution of the physical parameters.