√n-consistent parameter estimation for systems of ordinary differential equations : bypassing numerical integration via smoothing
By S. Gugushvili, Chris A. J. Klaassen. 2010
80 citations recorded by the source corpus.
We consider the problem of parameter estimation for a system of ordinary differential equations from noisy observations on a solution of the system. In case the system is nonlinear, as it typically is in practical applications, an analytic solution to it usually does not exist. Consequently, straightforward estimation methods like the ordinary least squares method depend on repetitive use of numerical integration in order to determine the solution of the system for each of the parameter values considered, and to find subsequently the parameter estimate that minimises the objective function. This induces a huge computational load to such estimation methods. We study the consistency of an alternative estimator that is defined as a minimiser of an appropriate distance between a nonparametrically estimated derivative of the solution and the righthand side of the system applied to a nonparametrically estimated solution. This smooth and match estimator (SME) bypasses numerical integration altogether and reduces the amount of computational time drastically compared to ordinary least squares. Moreover, we show that under suitable regularity conditions this smooth and match estimation procedure leads to a √ n-consistent estimator of the parameter of interest.
Subfields: Artificial Intelligence, Control and Systems Engineering
View Paper: https://www.semanticscholar.org/paper/0e173cea49530a401aaad52db1496569a023d34a
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In Artificial Intelligence
- Mark A. Girolami
- David Alexander Campbell
- Oksana A. Chkrebtii
- Ben Calderhead
- Niels Richard Hansen
- Frederik Vissing Mikkelsen
- Chris J. Oates
- Michael Betancourt
In Control and Systems Engineering
Citations in the corpus
- Learning Large Scale Ordinary Differential Equation Systems (2017, methodology): “This requires numerical integration, which is often more stable than numerical differentiation, and under certain assumptions √ n-consistency is guaranteed, as by Gugushvili & Klaassen (2012).”
- Bayesian Solution Uncertainty Quantification for Differential Equations (2013, background): “…, given measurements of the model states (Bock, 1983; Ionides et al., 2006; Dowd, 2007; Ramsay et al., 2007; Xue et al., 2010; Brunel, 2008; Liang and Wu, 2008; Calderhead and Girolami, 2011; Campbell and Steele, 2011; Gugushvili and Klaassen, 2012; Campbell and Chkrebtii, 2013; Xun et al., 2013).”