Inference for Nonlinear Dynamical Systems

Nonlinear stochastic dynamical systems are widely used to model systems across the sciences and engineering. Such models are natural to formulate and can be analyzed mathematically and numerically. However, difficulties associated with inference from time-series data about unknown parameters in thes...

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Bibliographic Details
Published in:Proceedings of the National Academy of Sciences - PNAS 2006-12, Vol.103 (49), p.18438-18443
Main Authors: Ionides, E. L., Bretó, C., King, A. A.
Format: Article
Language:English
Subjects:
Analysis
Biological Sciences
Cholera
Cholera - diagnosis
Cholera - epidemiology
Cholera - mortality
Computer Simulation
Confidence Intervals
Disease models
Disease reservoirs
Disease transmission
Dynamical systems
Ecological modeling
Humans
Incidence
Inference
Likelihood Functions
Maximum likelihood estimation
Maximum likelihood estimators
Modeling
Models, Biological
Mortality
Nonlinear Dynamics
Nonlinear programming
Physical Sciences
Stochastic models
Stochastic Processes
Time series
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Summary:Nonlinear stochastic dynamical systems are widely used to model systems across the sciences and engineering. Such models are natural to formulate and can be analyzed mathematically and numerically. However, difficulties associated with inference from time-series data about unknown parameters in these models have been a constraint on their application. We present a new method that makes maximum likelihood estimation feasible for partially-observed nonlinear stochastic dynamical systems (also known as state-space models) where this was not previously the case. The method is based on a sequence of filtering operations which are shown to converge to a maximum likelihood parameter estimate. We make use of recent advances in nonlinear filtering in the implementation of the algorithm. We apply the method to the study of cholera in Bangladesh. We construct confidence intervals, perform residual analysis, and apply other diagnostics. Our analysis, based upon a model capturing the intrinsic nonlinear dynamics of the system, reveals some effects overlooked by previous studies.
ISSN:0027-8424
1091-6490
DOI:10.1073/pnas.0603181103