Special Colloquium
Min Yang
University of Missouri
On the de la Garza phenomenon: a new approach of studying optimal design for nonlinear models
Abstract: Designing experiments is an integral part of the scientific process, both for discovery and verification. Resources are almost always scarce, and judicious use of the limited resources is essential. Identifying efficient and optimal designs for data collection is therefore paramount.
There is a vast literature on identifying good designs for a wide variety of linear models, but the problem is much more difficult and not nearly as well understood for nonlinear models. Nonlinear models are however very important in applications, and include the broad class of generalized linear models.
One crucial step in deriving optimal design is to determine the number of support points needed. Current tools handle this on a case-by-case basis. Each combination of model, optimality criterion and objective requires its own proof. The celebrated de la Garza phenomenon states that under a polynomial regression model, any optimal design can be based on a design with minimum number of support points. Does this conclusion also hold for nonlinear models? If the answer is yes, it would significantly simplify deriving optimal design, analytically or numerically.
In this talk, we will introduce a new approach of studying optimal designs. Using this new approach, it can be easily shown that the de la Garza phenomenon exists for many commonly studied nonlinear models.
There will be tea in SEO 300 after the colloquium.
Tuesday January 18, 2011 at 3:00 PM in SEO 636