Student Seminar Series - June 22, 2006
University of Minnesota
School of Statistics
College of Liberal Arts
Bayesian
Approaches to Model Robust and Model Discrimination Designs
Vincent
Kokouvi Agboto
Thursday, June 22, 2006
3:00 PM, B29
Ford Hall
Minneapolis, East Bank Campus
Refreshments at 2:30 PM
300 Ford Hall
Abstract
In industrial experiments, cost considerations will sometimes make
it impractical to design experiments so that effects of all the
factors can be estimated simultaneously. Therefore experimental
designs are frequently constructed to estimate main effects and a
few pre-specified interactions. A criticism frequently associated
with the use of many optimality criteria is the specific reliance on
an assumed statistical model. One way to deal with such a criticism
may be to assume that instead the true model is an approximation of
an unknown element of a known set of models. In this thesis, we
consider a class of designs that are robust for change in model
specification.
This thesis is motivated by the belief that appropriate
Bayesian
approaches may also perform well in constructing model robust
designs and by the limitation of such approaches in the literature.
We introduce an idea that uses the traditional Bayesian design
method for parameter estimation and incorporates a discrete prior
probability on the set of models of interest. We also introduce some
model discrimination approaches that maximize the capability of a
design for discriminating among competing models. Two-levels
orthogonal designs and designs derived from orthogonal starting
designs were used in the examples. Our model discrimination approaches
could be seen as extensions of the approach developed by Atkinson &
Federov (1975a, 1975b) and the approach of Li, Jones, Nachtsheim and Ye
(2006).
Comparisons and evaluations of our constructed designs with
designs from existing approaches and under similar conditions will be
provided.