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September, 1991 Robust Bayesian Experimental Designs in Normal Linear Models
A. DasGupta, W. J. Studden
Ann. Statist. 19(3): 1244-1256 (September, 1991). DOI: 10.1214/aos/1176348247

Abstract

We address the problem of finding a design that minimizes the Bayes risk with respect to a fixed prior subject to being robust with respect to misspecification of the prior. Uncertainty in the prior is formulated in terms of having a family of priors instead of one single prior. Two different classes of priors are considered: $\Gamma_1$ is a family of conjugate priors, and a second family of priors $\Gamma_2$ is induced by a metric on the space of nonnegative measures. The family $\Gamma_1$ has earlier been suggested by Leamer and Polasek, while $\Gamma_2$ was considered by DeRobertis and Hartigan and Berger. The setup assumed is that of a canonical normal linear model with independent homoscedastic errors. Optimal robust designs are considered for the problem of estimating the vector of regression coefficients or a linear combination of the regression coefficients and also for testing and set estimation problems. Concrete examples are given for polynomial regression and completely randomized designs. A very surprising finding is that for $\Gamma_2$, the same design is optimal for a variety of different problems with different loss structures. In general, the results for $\Gamma_2$ are significantly more substantive. Our results are applicable to group decision making and reconciliation of opinions among experts with different priors.

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A. DasGupta. W. J. Studden. "Robust Bayesian Experimental Designs in Normal Linear Models." Ann. Statist. 19 (3) 1244 - 1256, September, 1991. https://doi.org/10.1214/aos/1176348247

Information

Published: September, 1991
First available in Project Euclid: 12 April 2007

zbMATH: 0744.62099
MathSciNet: MR1126323
Digital Object Identifier: 10.1214/aos/1176348247

Subjects:
Primary: 62F15
Secondary: 62F35 , 62K05

Keywords: Robust Bayesian design

Rights: Copyright © 1991 Institute of Mathematical Statistics

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Vol.19 • No. 3 • September, 1991
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