title: On the selection of ordinary differential equation models with application to predator-prey dynamical models.
abstract: 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.
authors.affiliation: International School of Economics and Management, Capital University of Economics and Business, Beijing, 100070, China.
authors.forename: Xinyu
authors.initials: X
authors.lastname: Zhang
authors.affiliation: Department of Statistics and Actuarial Science, Simon Fraser University, Burnaby, BC, Canada, V5A1S6.
authors.forename: Jiguo
authors.initials: J
authors.lastname: Cao
authors.affiliation: Department of Statistics, Texas A&M University, 3143 TAMU, College Station, TX, 77843-3143, U.S.A.|Department of Mathematics and Statistics, University of Technology, P.O. Box 123, Broadway, Sydney, New South Wales, 2007, Australia.
authors.forename: Raymond J
authors.initials: RJ
authors.lastname: Carroll
mesh_terms: D000465:Algorithms; D000818:Animals; D001699:Biometry / Q000379:methods*; D003198:Computer Simulation; D006801:Humans; D046008:Lynx / Q000502:physiology*; D008954:Models, Biological; D015233:Models, Statistical; D011235:Predatory Behavior / Q000502:physiology*; D011817:Rabbits / Q000502:physiology*
keywords: Adaptive LASSO; Least squares approximation; Spline modeling; Variable selection