CRSC Projects: Estimation and Inference for Nonlinear Dynamical Systems

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Estimation and Inference for Nonlinear Dynamical Systems

Nonlinear dynamical systems can behave in ways that look random but aren't, a phenomenon called ``chaos''. Claims of evidence for chaotic vs. random dynamics in ecology (population dynamics), economics (stock market prices, exchange rates, unemployment rates), geology (earthquake times and magnitudes) and medicine (EEG and ECG), are active scientific controversies. It is now recognized that the conventional methods of analyzing such data, largely developed within theoretical physics, require unrealistically large amounts of data for many of these application areas, and moreover require a completely noise-free system, or they may give unreliable results.
CRSC investigators have developed methods based on nonparametric function estimation, which require 80-90% less data than conventional methods, and remain accurate at much higher levels of noise. Current research is focusing on: (1) increasing the reliability of numerical methods for data-based model selection; (2) estimation of short-term predictability as a function of current state; and (3) applications to global climate modeling, using our methods as tools for summarizing the behavior of complex models and for model validations. Efficient computational methods are essential for simulation studies to validate proposed methods, and we are interested in implementations on parallel machines, and the use of regularization methods to accelerate model fitting. An important direction for future research is methods for multivariate rather than scalar data, in particular situations where spatially replicated measurements are available, such as satellite monitoring of terrestrial climate and environmental variables.
CRSC investigators include S. Ellner, in collaboration with D. Nychka and A.R. Gallant in the Statistics Department at NCSU, and with H. Abarbanel (UC San Diego) and S. Koonin (Cal Tech) on climatology applications.

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