Abstract
A Bayesian version of Elfving's theorem is given for the $\mathbf{c}$-optimality criterion with emphasis on the inherent geometry. Conditions under which a one-point design is Bayesian $\mathbf{c}$-optimum are described. The class of prior precision matrices $R$ for which the Bayesian $\mathbf{c}$-optimal designs are supported by the points of the classical $\mathbf{c}$-optimal design is characterized. It is proved that the Bayesian $\mathbf{c}$-optimal design, for large $n,$ is always supported by the same support points as the classical one if the number of support points and the number of regression functions are equal. Examples and a matrix analog are discussed.
Citation
Sadi M. El-Krunz. W. J. Studden. "Bayesian Optimal Designs for Linear Regression Models." Ann. Statist. 19 (4) 2183 - 2208, December, 1991. https://doi.org/10.1214/aos/1176348392
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