Optimal Design of Experiments for Implicit Models | PERPUSTAKAAN UNIVERSITAS KATOLIK PARAHYANGAN

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Optimal Design of Experiments for Implicit Models

Duarte, Belmiro P. M. - Nama Orang; Atkinson, Anthony C. - Nama Orang; Granjo, Jose F. O. - Nama Orang; Oliveira, Nuno M. C. - Nama Orang;

Explicit models representing the response variables as functions of the control variables are standard in virtually all scientific fields. For these models, there is a vast literature on the optimal design of experiments (ODoE) to provide good estimates of the parameters with the use of minimal resources. Contrarily, the ODoE for implicit models is more complex and has not been systematically addressed. Nevertheless, there are practical examples where the models relating the response variables, the parameters and the factors are implicit or hardly convertible into an explicit form. We propose a general formulation for developing the theory of the ODoE for implicit algebraic models to specifically find continuous local designs. The treatment relies on converting the ODoE problem into an optimization problem of the nonlinear programming (NLP) class which includes the construction of the parameter sensitivities and the Cholesky decomposition of the Fisher information matrix. The NLP problem generated has multiple local optima, and we use global solvers, combined with an equivalence theorem from the theory of ODoE, to ensure the global optimality of our continuous optimal designs. We consider D- and A-optimality criteria and apply the approach to five examples of practical interest in chemistry and thermodynamics. Supplementary materials for this article are available online.

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Informasi Detail

Judul Seri: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION (JASA); Vol.117 No.539 September 2022
No. Panggil: -
Penerbit: : .,
Deskripsi Fisik: p. 1424-1437
Bahasa: English
ISBN/ISSN: -
Klasifikasi: NONE
Tipe Isi: -
Tipe Media: -
Tipe Pembawa: -
Edisi: -
Subjek: NONLINEAR PROGRAMMING
IMPLICIT MODELS
CONTINUOUS DESIGNS
MODEL-BASED OPTIMAL DESIGNS
Info Detail Spesifik: https://doi.org/10.1080/01621459.2020.1862670
Pernyataan Tanggungjawab: Belmiro P. M. Duarte, Anthony C. Atkinson, José F. O. Granjo, Nuno M. C. Oliveira

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