Goodness of Fit in Nonlinear Dynamics: Mis-specified Rates or Mis-specified States? Giles Hooker, Stephen P. Ellner, 12-2-13

Goodness of Fit in Nonlinear Dynamics: Mis-specified Rates or Mis-specified States?

Giles Hooker, Stephen P. Ellner(Submitted on 2 Dec 2013)

This paper introduces tests to uncover the nature of lack of fit in ordinary differential equation models (ODEs) proposed for data. We present a hierarchy of three possible sources of lack of fit: unaccounted-for stochastic variation, mis-specification of functional forms in the rate equations, and missing dynamical variables in the description of the system. We represent lack of fit by allowing some parameters to vary over time, and propose generic testing procedures that do not rely on specific alternative models. Our hypotheses are expressed in terms of nonparametric relationships among latent variables, and the tests are carried out through a combined residual bootstrap and permutation methods. We demonstrate the effectiveness of these tests on simulated data, and on real data from laboratory ecological experiments and electro-cardiogram data.

Comments: 20 pages, 5 figuresSubjects: Methodology (stat.ME)Cite as: arXiv:1312.0294 [stat.ME]  (or arXiv:1312.0294v1 [stat.ME] for this version)