Title: Inference in nonlinear systems with unscented Kalman filters
Authors: Diana Giurghita - University of Glasgow (United Kingdom) [presenting]
Dirk Husmeier - Biomathematics and Statistics Scotland, Edinburgh (UK)
Abstract: An increasing number of scientific disciplines, most notably the life sciences and health care, have become more quantitative, describing complex systems with coupled nonlinear differential equations. While powerful algorithms for numerical simulations from these systems have been developed, statistical inference of the system parameters is still a challenging problem. A promising approach is based on the unscented Kalman filter (UKF), which has seen a variety of recent applications, from soft tissue mechanics to chemical kinetics. We investigate the dependence of the accuracy of parameter estimation on the initialisation. Based on three toy systems that capture typical features of real-world complex systems - limit cycles, chaotic attractors and intrinsic stochasticity - we carry out repeated simulations on a large range of independent data instantiations. Our study allows a quantification of the accuracy of inference, measured in terms of two alternative distance measures in function and parameter space, in dependence on the initial deviation from the ground truth.