Inference in Nonlinear Systems with Unscented Kalman Filters

Giurghita, D. and Husmeier, D. (2016) Inference in Nonlinear Systems with Unscented Kalman Filters. In: 22nd International Conference on Computational Statistics (COMPSTAT 2016), Oviedo, Spain, 23-26 Aug 2016, pp. 383-393. ISBN 9789073592360

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 di↵erential 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. The present study investigates 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.

• Item Type: Conference Proceedings
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Husmeier, Professor Dirk
• Authors: Giurghita, D., and Husmeier, D.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Statistics
• ISBN: 9789073592360
• Copyright Holders: Copyright © 2016 The International Statistical Institute/International Association for Statistical Computing
• First Published: First published in 22nd International Conference on Computational Statistics (COMPSTAT 2016): 383-393
• Publisher Policy: Reproduced with the permission of the Publisher

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