Publications Repository  HelmholtzZentrum DresdenRossendorf
Estimation of Parameters in Random Dynamical Systems
Konsulke, S.; van den Boogaart, K. G.; Ballani, F.; Franke, M.; Sauke, M.
In random dynamical systems, e.g. described by stochastic differential equations, it is often difficult to infer the parameters. The main difficulty is that one hand no likelihoods can be computed, excluding Maximum Likelihood, EM or Bayesian Methods and on the other hand the system is random, excluding simple least squares comparison of the observations with expected trajectories of the dynamical system. We have developed a new Rpackage ”SysStat” containing general approaches for estimation in stochastic systems based on simulation rather than likelihood computation using approximate Bayes and approximate quasilikelihood methods finding good approximations based on informed user choices and simulations of the models with varying parameters. The user choice especially includes finding functions of the data with high information contend in the sense of high quasilikelihood. Although both methods are not directly applicable to dynamic systems, there are systematic ways of constructing such informative statistics for stochastic differential equation models, allowing to construct informative functions for the local dynamic and translating these functions to informative statistics of the global dynamic by time averaging. This allows to estimate parameters of dynamic stochastic models efficiently. Our main aim is the modeling of bioleaching processes, but the method has a more general applicability for various types of processes in the geosciences including stationary and transient, spatial, temporal and spatiotemporal processes and will thus be demonstrated with simple to understand toy examples.
Keywords: Parameter estimation; dynamical systems; nonlinear methods

Contribution to proceedings
15th Annual Conference of the International Association for Mathematical Geosciences, 02.06.09.2013, Madrid, Spanien
Mathematics of Planet Earth  Proceedings of the 15th Annual Conference of the International Association for Mathematical Geosciences: Springer, 9783642324079, 843846
DOI: 10.1007/9783642324086_183 
Lecture (Conference)
15th Annual Conference of the International Association for Mathematical Geosciences, 03.09.2013, Madrid, Spanien
Permalink: https://www.hzdr.de/publications/Publ19320
Publ.Id: 19320