Optimal Designs for Two-Level Factorial Experiments with Binary Response
TLDR
The performance of the uniform design in the 2^2 experiment is examined and it is shown that this design is highly efficient in general and has a maximin property.Abstract:
We consider the problem of obtaining locally D-optimal designs for factorial experiments with qualitative factors at two levels each and with binary response. For the 2 factorial experiment with main-effects model, we obtain optimal designs analytically in special cases and demonstrate how to obtain a solution in the general case using cylindrical algebraic decomposition. The optimal designs are shown to be robust to the choice of the assumed values of the prior, and when there is no basis to make an informed choice of the assumed values we recommend the use of the uniform design that assigns equal number of observations to each of the four points. For the general 2 case we show that the uniform design has a maximin property.read more
Citations
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Least squares polynomial chaos expansion: A review of sampling strategies
Mohammad Hadigol,Alireza Doostan +1 more
TL;DR: A comparison between the empirical performance of the selected sampling methods applied to three numerical examples, including high-order PCE’s, high-dimensional problems, and low oversampling ratios, is presented to provide a road map for practitioners seeking the most suitable sampling technique for a problem at hand.
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OPTIMAL DESIGNS FOR 2(k) FACTORIAL EXPERIMENTS WITH BINARY RESPONSE.
TL;DR: In this paper, the author's version of a work that was accepted for publication in Statistica Sinica has been published, and a definitive version was subsequently published in the same journal.
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D-optimal Factorial Designs under Generalized Linear Models
Jie Yang,Abhyuday Mandal +1 more
TL;DR: Yang, Mandal and Majumdar as mentioned in this paper extended their results to a general setup with response belonging to a single-parameter exponential family and for multilevel predictors, and they considered full factorial and fractional factorial locally D-optimal designs for binary response and twolevel experimental factors.
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Optimal exact designs of experiments via Mixed Integer Nonlinear Programming
TL;DR: This work proposes 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.
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A note on optimal allocations for the second elementary symmetric function with applications for optimal reliability design
TL;DR: This article considers the problem of determining the optimal size allocation and optimal number of experimental conditions for a second elementary symmetric function with different coefficients to elucidate the foundation between different parametric models found in recent studies.
References
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Minima of Functions of Several Variables with Inequalities as Side Conditions
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