Optimal designs for nonlinear regression models with respect to non-informative priors
Loading...
Date
2013-10-25
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
In nonlinear regression models the Fisher information depends on the parameters of
the model. Consequently, optimal designs maximizing some functional of the information
matrix cannot be implemented directly but require some preliminary knowledge about
the unknown parameters. Bayesian optimality criteria provide an attractive solution to
this problem. These criteria depend sensitively on a reasonable specification of a prior
distribution for the model parameters which might not be available in all applications.
In this paper we investigate Bayesian optimality criteria with non-informative prior distributions.
In particular, we study the Jeffreys and the Berger-Bernardo prior for which
the corresponding optimality criteria are not necessarily concave. Several examples are
investigated where optimal designs with respect to the new criteria are calculated and
compared to Bayesian optimal designs based on a uniform and a functional uniform prior.
Description
Table of contents
Keywords
Bayesian optimality criteria, canonical moments, heteroscedasticity, Jeffreys prior, non-informative prior, optimal design, polynomial regression, reference prior