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**Harvard**

Leander, J., Lundh, T. och Jirstrand, M. (2014) *Stochastic differential equations as a tool to regularize the parameter estimation problem for continuous time dynamical systems given discrete time measurements*.

** BibTeX **

@article{

Leander2014,

author={Leander, Jacob and Lundh, Torbjörn and Jirstrand, Mats},

title={Stochastic differential equations as a tool to regularize the parameter estimation problem for continuous time dynamical systems given discrete time measurements},

journal={Mathematical Biosciences},

issn={0025-5564},

volume={251},

pages={54-62},

abstract={In this paper we consider the problem of estimating parameters in ordinary differential equations given discrete time experimental data. The impact of going from an ordinary to a stochastic differential equation setting is investigated as a tool to overcome the problem of local minima in the objective function. Using two different models, it is demonstrated that by allowing noise in the underlying model itself, the objective functions to be minimized in the parameter estimation procedures are regularized in the sense that the number of local minima is reduced and better convergence is achieved. The advantage of using stochastic differential equations is that the actual states in the model are predicted from data and this will allow the prediction to stay close to data even when the parameters in the model is incorrect. The extended Kalman filter is used as a state estimator and sensitivity equations are provided to give an accurate calculation of the gradient of the objective function. The method is illustrated using in silico data from the FitzHugh–Nagumo model for excitable media and the Lotka–Volterra predator–prey system. The proposed method performs well on the models considered, and is able to regularize the objective function in both models. This leads to parameter estimation problems with fewer local minima which can be solved by efficient gradient-based methods.},

year={2014},

keywords={Parameter estimation; Ordinary differential equations; Stochastic differential equations; Extended Kalman filter; Lotka–Volterra; FitzHugh–Nagumo},

}

** RefWorks **

RT Journal Article

SR Electronic

ID 195122

A1 Leander, Jacob

A1 Lundh, Torbjörn

A1 Jirstrand, Mats

T1 Stochastic differential equations as a tool to regularize the parameter estimation problem for continuous time dynamical systems given discrete time measurements

YR 2014

JF Mathematical Biosciences

SN 0025-5564

VO 251

SP 54

OP 62

AB In this paper we consider the problem of estimating parameters in ordinary differential equations given discrete time experimental data. The impact of going from an ordinary to a stochastic differential equation setting is investigated as a tool to overcome the problem of local minima in the objective function. Using two different models, it is demonstrated that by allowing noise in the underlying model itself, the objective functions to be minimized in the parameter estimation procedures are regularized in the sense that the number of local minima is reduced and better convergence is achieved. The advantage of using stochastic differential equations is that the actual states in the model are predicted from data and this will allow the prediction to stay close to data even when the parameters in the model is incorrect. The extended Kalman filter is used as a state estimator and sensitivity equations are provided to give an accurate calculation of the gradient of the objective function. The method is illustrated using in silico data from the FitzHugh–Nagumo model for excitable media and the Lotka–Volterra predator–prey system. The proposed method performs well on the models considered, and is able to regularize the objective function in both models. This leads to parameter estimation problems with fewer local minima which can be solved by efficient gradient-based methods.

LA eng

DO 10.1016/j.mbs.2014.03.001

LK http://publications.lib.chalmers.se/records/fulltext/195122/local_195122.pdf

LK http://dx.doi.org/10.1016/j.mbs.2014.03.001

OL 30