Optimal exact designs of experiments via Mixed Integer Nonlinear Programming

Optimal exact designs are problematic to find and study because there is no unified theory for determining them and studying their properties. Each has its own challenges and when a method exists to confirm the design optimality, it is invariably applicable to the particular problem only. We propose...

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Bibliographic Details
Published in:Statistics and computing Vol. 30; no. 1; pp. 93 - 112
Main Authors: Duarte, Belmiro P. M., Granjo, José F. O., Wong, Weng Kee
Format: Journal Article
Language:English
Published: New York Springer US 01.02.2020
Springer Nature B.V
Subjects:
Artificial Intelligence
Design optimization
Fisher information
Mathematics and Statistics
Mixed integer
Nonlinear programming
Probability and Statistics in Computer Science
Statistical Theory and Methods
Statistics
Statistics and Computing/Statistics Programs
62K05
Model-based optimal designs
90C47
Constrained designs
Mixed Integer Nonlinear Programming
Global Optimization
Exact designs
ISSN:0960-3174, 1573-1375
Online Access:Get full text
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Summary:Optimal exact designs are problematic to find and study because there is no unified theory for determining them and studying their properties. Each has its own challenges and when a method exists to confirm the design optimality, it is invariably applicable to the particular problem only. We propose a systematic approach to construct optimal exact designs by incorporating the Cholesky decomposition of the Fisher Information Matrix in a Mixed Integer Nonlinear Programming formulation. As examples, we apply the methodology to find D - and A -optimal exact designs for linear and nonlinear models using global or local optimizers. Our examples include design problems with constraints on the locations or the number of replicates at the optimal design points.
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ISSN:0960-3174
1573-1375
DOI:10.1007/s11222-019-09867-z