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Boiger, R.* ; Hasenauer, J. ; Hross, S. ; Kaltenbacher, B.*

Integration based profile likelihood calculation for PDE constrained parameter estimation problems.

Inverse Probl. 32:125009 (2016)
Publ. Version/Full Text Postprint DOI
Open Access Green
Partial differential equation (PDE) models are widely used in engineering and natural sciences to describe spatio-temporal processes. The parameters of the considered processes are often unknown and have to be estimated from experimental data. Due to partial observations and measurement noise, these parameter estimates are subject to uncertainty. This uncertainty can be assessed using profile likelihoods, a reliable but computationally intensive approach. In this paper, we present the integration based approach for the profile likelihood calculation developed by (Chen and Jennrich 2002 J. Comput. Graph. Stat. 11 714-32) and adapt it to inverse problems with PDE constraints. While existing methods for profile likelihood calculation in parameter estimation problems with PDE constraints rely on repeated optimization, the proposed approach exploits a dynamical system evolving along the likelihood profile. We derive the dynamical system for the unreduced estimation problem, prove convergence and study the properties of the integration based approach for the PDE case. To evaluate the proposed method, we compare it with state-of-the-art algorithms for a simple reaction-diffusion model for a cellular patterning process. We observe a good accuracy of the method as well as a significant speed up as compared to established methods. Integration based profile calculation facilitates rigorous uncertainty analysis for computationally demanding parameter estimation problems with PDE constraints.
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Publication type Article: Journal article
Document type Scientific Article
Keywords Parameter Estimation ; Partial Differential Equations ; Uncertainty Quantification ; Profile Likelihood; Practical Identifiability Analysis; Confidence-intervals; Systems Biology; Models; Gradient
ISSN (print) / ISBN 0266-5611
e-ISSN 1361-6420
Quellenangaben Volume: 32, Issue: 12, Pages: , Article Number: 125009 Supplement: ,
Publisher Institute of Physics Publishing (IOP)
Publishing Place Bristol
Reviewing status