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Parameter estimation through ignorance

Du, Hailiang; Smith, Leonard A.


Leonard A. Smith


Dynamical modeling lies at the heart of our understanding of physical systems. Its role in science is deeper than mere operational forecasting, in that it allows us to evaluate the adequacy of the mathematical structure of our models. Despite the importance of model parameters, there is no general method of parameter estimation outside linear systems. A relatively simple method of parameter estimation for nonlinear systems is introduced, based on variations in the accuracy of probability forecasts. It is illustrated on the logistic map, the Henon map, and the 12-dimensional Lorenz96 flow, and its ability to outperform linear least squares in these systems is explored at various noise levels and sampling rates. As expected, it is more effective when the forecast error distributions are non-Gaussian. The method selects parameter values by minimizing a proper, local skill score for continuous probability forecasts as a function of the parameter values. This approach is easier to implement in practice than alternative nonlinear methods based on the geometry of attractors or the ability of the model to shadow the observations. Direct measures of inadequacy in the model, the “implied ignorance,” and the information deficit are introduced.


Du, H., & Smith, L. A. (2012). Parameter estimation through ignorance. Physical review E: Statistical, nonlinear, and soft matter physics, 86(1), Article 016213.

Journal Article Type Article
Online Publication Date Jul 16, 2012
Publication Date 2012
Deposit Date Jul 31, 2018
Journal Physical Review E
Print ISSN 1539-3755
Electronic ISSN 1550-2376
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 86
Issue 1
Article Number 016213