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October 1996 Optimal Bayesian designs for models with partially specified heteroscedastic structure
Holger Dette, Weng Kee Wong
Ann. Statist. 24(5): 2108-2127 (October 1996). DOI: 10.1214/aos/1069362313

Abstract

We consider the problem of finding a nonsequential optimal design for estimating parameters in a generalized exponential growth model. This problem is solved by first considering polynomial regression models with error variances that depend on the covariate value and unknown parameters. A Bayesian approach is adopted, and optimal Bayesian designs supported on a minimal number of support points for estimating the coefficients in the polynomial model are found analytically. For some criteria, the optimal Bayesian designs depend only on the expectation of the prior, but generally their dependence includes the derivative of the logarithm of the Laplace transform of a measure induced by the prior. The optimal design for the generalized exponential growth model is then determined from these optimal Bayesian designs.

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Holger Dette. Weng Kee Wong. "Optimal Bayesian designs for models with partially specified heteroscedastic structure." Ann. Statist. 24 (5) 2108 - 2127, October 1996. https://doi.org/10.1214/aos/1069362313

Information

Published: October 1996
First available in Project Euclid: 20 November 2003

zbMATH: 0867.62062
MathSciNet: MR1421164
Digital Object Identifier: 10.1214/aos/1069362313

Subjects:
Primary: 62K05
Secondary: 65D30

Rights: Copyright © 1996 Institute of Mathematical Statistics

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Vol.24 • No. 5 • October 1996
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