Department of Statistics, The Ohio State University
Statistics and Biostatistics Colloquium Series

In many modelling situations the Fisher information matrix depends on certain of the unknown parameters. Thus, in order to construct designs which in some sense optimize a function of the information matrix, it is common either to assume a "best guess" for the unknown parameters and to construct a "locally'" optimal design, or to invoke a Bayesian approach and to average an appropriate criterion based on the information matrix over a prior distribution on the parameters, or to adopt a maximin strategy and, specifically, to consider maximizing the minimum of a function of the information matrix taken over a specified range of the unknown parameters. Maximin criteria are not differentiable however and as a consequence the problem of constructing the associated maximin optimal designs is a challenging one.

In the present talk the construction of locally, Bayesian and maximin optimal designs for a specific weighted polynomial regression model is discussed. In particular the relationship between maximin optimal designs and designs optimal with respect to a class of differentiable Bayesian criteria is explored and a general methodology for the construction of maximin optimal designs developed.

*This work is joint with Holger Dette and Lorens Imhof of Germany.