TY - JOUR
T1 - Bayesian D-optimal designs on a fixed number of design points for heteroscedastic polynomial models
AU - Dette, Holger
AU - Wong, Weng Kee
N1 - Funding Information:
Parts of the paper were written while H. Dette was visiting the University of Goettingen. This author would like to thank the Institut fur Mathematische Stochastik for its hospitality. The research of W. K. Wong was partially supported by a University of California, Los Angeles Faculty Career Development Award and a National Institutes of Health First award. We also wish to thank the editor, the associate editor and referees for their helpful comments on earlier versions of this paper.
PY - 1998
Y1 - 1998
N2 - We consider design issues in a polynomial regression model where the variance of the response depends on the independent variable exponentially. However, this dependence is not known precisely and additional parameters are required in the model. Our design criteria permit various subsets of the parameters to be estimated with different emphasis. Bayesian D-optimal designs on a compact interval, with the number of support points restricted to be one more than the degree of the polynomial, are found analytically for a large class of priors. These designs may or may not be optimal within the class of all designs, depending on the prior distribution.
AB - We consider design issues in a polynomial regression model where the variance of the response depends on the independent variable exponentially. However, this dependence is not known precisely and additional parameters are required in the model. Our design criteria permit various subsets of the parameters to be estimated with different emphasis. Bayesian D-optimal designs on a compact interval, with the number of support points restricted to be one more than the degree of the polynomial, are found analytically for a large class of priors. These designs may or may not be optimal within the class of all designs, depending on the prior distribution.
UR - https://www.scopus.com/pages/publications/0000376239
UR - https://www.scopus.com/pages/publications/0000376239#tab=citedBy
U2 - 10.1093/biomet/85.4.869
DO - 10.1093/biomet/85.4.869
M3 - Article
AN - SCOPUS:0000376239
SN - 0006-3444
VL - 85
SP - 869
EP - 882
JO - Biometrika
JF - Biometrika
IS - 4
ER -