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Inference for nonlinear dynamical systems
Open accessAbstract
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.
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Cites
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Malaria early warnings based on seasonal climate forecasts from multi-model ensembles
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Cited by
Li, R., Pei, S., Chen, B., Song, Y., Zhang, T., Yang, W., & Shaman, J. (2020) · Science · doi:10.1126/science.abb3221 · Cited by 3,633
Riemann manifold langevin and hamiltonian monte carlo methods
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Modelling the influence of human behaviour on the spread of infectious diseases: a review
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Parameter estimation for differential equations: a generalized smoothing approach
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Forecasting seasonal outbreaks of influenza
Shaman, J., & Karspeck, A. (2012) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1208772109 · Cited by 420
Metadata
- Authors
- Ionides, E. L., Bretó, C., & King, A. A.
- Venue
- Proceedings of the National Academy of Sciences
- Published
- 2006-12-05
- Volume
- 103
- Issue
- 49
- Pages
- 18438-18443
- ISSN
- 0027-8424 (ISSN-L)
- 1091-6490
- OpenAlex
- W2065266611
- Cited by
- 459
- References
- 7
- FWCI
- 29.72
- Type
- journal article
- Language
- en
- Open access
- green
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