Optimal design and directional leverage with applications in differential equation models

We consider the problem of estimating input parameters for a differential equation model, given experimental observations of the output. As time and cost limit both the number and quality of observations, the design is critical. A generalized notion of leverage is derived and, with this, we define d...

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Bibliographic Details
Published in:Metrika 2012-10, Vol.75 (7), p.895-911
Main Authors: Burch, Nathanial, Hoeting, Jennifer A., Estep, Donald
Format: Article
Language:English
Subjects:
Economic Theory/Quantitative Economics/Mathematical Methods
Mathematics and Statistics
Probability Theory and Stochastic Processes
Statistics
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Summary:We consider the problem of estimating input parameters for a differential equation model, given experimental observations of the output. As time and cost limit both the number and quality of observations, the design is critical. A generalized notion of leverage is derived and, with this, we define directional leverage. Effective designs are argued to be those that sample in regions of high directional leverage. We present an algorithm for finding optimal designs and then establish relationships to existing design optimality criteria. Numerical examples demonstrating the performance of the algorithm are presented.
ISSN:0026-1335
1435-926X
DOI:10.1007/s00184-011-0358-4