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Inference in dynamic systems using B‐splines and quasilinearized ODE penalties
Author(s) -
Frasso Gianluca,
Jaeger Jonathan,
Lambert Philippe
Publication year - 2016
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.201500082
Subject(s) - ode , ordinary differential equation , mathematical optimization , nonlinear system , spline (mechanical) , smoothing , mathematics , smoothing spline , inference , computer science , differential equation , spline interpolation , mathematical analysis , bilinear interpolation , statistics , artificial intelligence , engineering , physics , structural engineering , quantum mechanics
Nonlinear (systems of) ordinary differential equations (ODEs) are common tools in the analysis of complex one‐dimensional dynamic systems. We propose a smoothing approach regularized by a quasilinearized ODE‐based penalty. Within the quasilinearized spline‐based framework, the estimation reduces to a conditionally linear problem for the optimization of the spline coefficients. Furthermore, standard ODE compliance parameter(s) selection criteria are applicable. We evaluate the performances of the proposed strategy through simulated and real data examples. Simulation studies suggest that the proposed procedure ensures more accurate estimates than standard nonlinear least squares approaches when the state (initial and/or boundary) conditions are not known.