Author:

Keywords:

Quasi-Monte Carlo, Bayesian inversion, Uncertainty quantification

Abstract:

We investigate the problem of parameter identification of a mathematical model using uncertain data. In particular, we consider the human insulin-glucose system which can be modelled by a system of parameter-dependent differential equations and aim to estimate parameters such as insulin sensitivity. To identify the desired parameters, we apply the concept of Bayesian inversion in combination with quasi-Monte Carlo point sets in the sense of Stuart (2010), Stuart and Schwab (2012) and Dick, Gantner, Le Gia and Schwab (2016). In contrast to often used Markov chain Monte Carlo (MCMC) methods, we aim for QMC methods that can achieve much faster convergence rates of O(1/Nα), with α>1/2, to estimate the occurring high-dimensional integrals. The used data is uncertain in several ways as we deal with noisy measurement data, uncertain inputs to the ODE and modelling uncertainties and assumptions.