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Approximate and exact D-optimal designs for $2^k$ factorial experiments for Generalized Linear Models via SOCP

Zitieren Sie bitte immer diese URN: urn:nbn:de:0297-zib-66256
  • We propose (Mixed Integer) Second Order Cone Programming formulations to find approximate and exact $D-$optimal designs for $2^k$ factorial experiments for Generalized Linear Models (GLMs). Locally optimal designs are addressed with Second Order Cone Programming (SOCP) and Mixed Integer Second Order Cone Programming (MISOCP) formulations. The formulations are extended for scenarios of parametric uncertainty employing the Bayesian framework for \emph{log det} $D-$optimality criterion. A quasi Monte-Carlo sampling procedure based on the Hammersley sequence is used for integrating the optimality criterion in the parametric region. The problems are solved in \texttt{GAMS} environment using \texttt{CPLEX} solver. We demonstrate the application of the algorithm with the logistic, probit and complementary log-log models and consider full and fractional factorial designs.

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Metadaten
Verfasserangaben:Belmiro P.M. Duarte, Guillaume Sagnol
Dokumentart:ZIB-Report
MSC-Klassifikation:62-XX STATISTICS / 62Kxx Design of experiments [See also 05Bxx] / 62K05 Optimal designs
Datum der Erstveröffentlichung:20.12.2017
Schriftenreihe (Bandnummer):ZIB-Report (18-02)
ISSN:1438-0064
DOI:https://doi.org/10.1007/s00362-018-01075-7
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