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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/25461

Title: Fast derivatives of likelihood functionals for ODE based models using adjoint-state method
Authors: Melicher, Valdemar
Haber, Tom
Vanroose, Wim
Issue Date: 2017
Citation: COMPUTATIONAL STATISTICS, 32(4), p. 1621-1643
Abstract: We consider time series data modeled by ordinary differential equations (ODEs), widespread models in physics, chemistry, biology and science in general. The sensitivity analysis of such dynamical systems usually requires calculation of various derivatives with respect to the model parameters. We employ the adjoint state method (ASM) for efficient computation of the first and the second derivatives of likelihood functionals constrained by ODEs with respect to the parameters of the underlying ODE model. Essentially, the gradient can be computed with a cost (measured by model evaluations) that is independent of the number of the ODE model parameters and the Hessian with a linear cost in the number of the parameters instead of the quadratic one. The sensitivity analysis becomes feasible even if the parametric space is high-dimensional. The main contributions are derivation and rigorous analysis of the ASM in the statistical context, when the discrete data are coupled with the continuous ODE model. Further, we present a highly optimized implementation of the results and its benchmarks on a number of problems. The results are directly applicable in (e.g.) maximum-likelihood estimation or Bayesian sampling of ODE based statistical models, allowing for faster, more stable estimation of parameters of the underlying ODE model.
Notes: [Melicher, Valdemar; Vanroose, Wim] Univ Antwerp, Dept Math & Comp Sci, Middelheimlaan 1, B-3590 Diepenbeek, Belgium. [Haber, Tom] Hasselt Univ, Expertise Ctr Digital Media, Wetenschapspk 2, B-3590 Diepenbeek, Belgium.
URI: http://hdl.handle.net/1942/25461
Link to publication: https://arxiv.org/pdf/1606.04406v3.pdf
DOI: 10.1007/s00180-017-0765-8
ISI #: 000413025300019
ISSN: 0943-4062
Category: A1
Type: Journal Contribution
Appears in Collections: Research publications

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