The Annals of Statistics

Optimal Bayesian designs for models with partially specified heteroscedastic structure

Holger Dette and Weng Kee Wong

Full-text: Open access

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.

Article information

Source
Ann. Statist., Volume 24, Number 5 (1996), 2108-2127.

Dates
First available in Project Euclid: 20 November 2003

Permanent link to this document
https://projecteuclid.org/euclid.aos/1069362313

Digital Object Identifier
doi:10.1214/aos/1069362313

Mathematical Reviews number (MathSciNet)
MR1421164

Zentralblatt MATH identifier
0867.62062

Subjects
Primary: 62K05: Optimal designs
Secondary: 65D30: Numerical integration

Keywords
Approximate designs design efficiency efficiency functions Laplace transform Bayesian design

Citation

Dette, Holger; Wong, Weng Kee. Optimal Bayesian designs for models with partially specified heteroscedastic structure. Ann. Statist. 24 (1996), no. 5, 2108--2127. doi:10.1214/aos/1069362313. https://projecteuclid.org/euclid.aos/1069362313


Export citation