Open Access
June 2015 Goodness of fit in nonlinear dynamics: Misspecified rates or misspecified states?
Giles Hooker, Stephen P. Ellner
Ann. Appl. Stat. 9(2): 754-776 (June 2015). DOI: 10.1214/15-AOAS828


This paper introduces diagnostic tests for 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, misspecification of functional forms in rate equations, and omission of dynamic variables in the description of the system. We represent lack of fit by allowing a parameter vector to vary over time, and propose generic testing procedures that do not rely on specific alternative models. Instead, different sources for lack of fit are characterized in terms of nonparametric relationships among latent variables. The tests are carried out through a combination of 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.


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Giles Hooker. Stephen P. Ellner. "Goodness of fit in nonlinear dynamics: Misspecified rates or misspecified states?." Ann. Appl. Stat. 9 (2) 754 - 776, June 2015.


Received: 1 December 2013; Revised: 1 December 2014; Published: June 2015
First available in Project Euclid: 20 July 2015

zbMATH: 06499929
MathSciNet: MR3371334
Digital Object Identifier: 10.1214/15-AOAS828

Keywords: attractor reconstruction , bootstrap , diagnostics , Differential equation , goodness of fit

Rights: Copyright © 2015 Institute of Mathematical Statistics

Vol.9 • No. 2 • June 2015
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