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On the selection of ordinary differential equation models with application to predator‐prey dynamical models
Author(s) -
Zhang Xinyu,
Cao Jiguo,
Carroll Raymond J.
Publication year - 2015
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/biom.12243
Subject(s) - ode , ordinary differential equation , mathematics , context (archaeology) , ordinary least squares , selection (genetic algorithm) , model selection , estimator , population , estimation theory , population model , mathematical optimization , differential equation , computer science , statistics , artificial intelligence , mathematical analysis , demography , sociology , biology , paleontology
Summary We consider model selection and estimation in a context where there are competing ordinary differential equation (ODE) models, and all the models are special cases of a “full” model. We propose a computationally inexpensive approach that employs statistical estimation of the full model, followed by a combination of a least squares approximation (LSA) and the adaptive Lasso. We show the resulting method, here called the LSA method, to be an (asymptotically) oracle model selection method. The finite sample performance of the proposed LSA method is investigated with Monte Carlo simulations, in which we examine the percentage of selecting true ODE models, the efficiency of the parameter estimation compared to simply using the full and true models, and coverage probabilities of the estimated confidence intervals for ODE parameters, all of which have satisfactory performances. Our method is also demonstrated by selecting the best predator‐prey ODE to model a lynx and hare population dynamical system among some well‐known and biologically interpretable ODE models.