We present a version of Elfving's theorem for the Bayesian D-optimality criterion in nonlinear regression models. The Bayesian optimal design can be characterized as a design which allows a representation of a (uniquely determined) boundary point of a convex subset of $L^2$-integrable functions. A similar characterization is given for the Bayesian c-optimality criterion where a (possible) nonlinear function of the unknown parameters has to be estimated. The results are illustrated in the example of an exponential growth model using a gamma prior distribution.
@article{1032526965,
author = {Dette, Holger},
title = {A note on Bayesian c- and D-optimal designs in nonlinear regression models},
journal = {Ann. Statist.},
volume = {24},
number = {6},
year = {1996},
pages = { 1225-1234},
language = {en},
url = {http://dml.mathdoc.fr/item/1032526965}
}
Dette, Holger. A note on Bayesian c- and D-optimal designs in nonlinear regression models. Ann. Statist., Tome 24 (1996) no. 6, pp. 1225-1234. http://gdmltest.u-ga.fr/item/1032526965/