Scholarly Communications Project


Bayesian Two Stage Design Under Model Uncertainty

by

Angela R. Neff

Dissertation submitted to the Faculty of the Virginia Tech in partial fulfillment of the requirements for the degree of

Ph.D.

in

Statistics

Approved

Raymond Myers, Co-Chair
Keying Ye, Co-Chair
Jesse Arnold
Robert Foutz
Marvin Lentner

January 16, 1997
Blacksburg, Virginia


Abstract

Traditional single stage design optimality procedures can be used to efficiently generate data for an assumed model. The model assumptions include the model form, the set of regressors and the error distribution. The nature of the response often provides information about the model form and the error distribution. It is more difficult to know, apriori, the specific set of regressors which will best explain the relationship between the response and a set of design (control) variables. Misspecification of regressors will result in a design which is efficient, but for the wrong model. A Bayesian two stage design approach makes it possible to efficiently design experiments when initial regressor knowledge is poor. This is accomplished by using a Bayesian optimality criterion in the first stage which is robust to model uncertainty. Bayesian analysis of first stage data reduces regressor uncertainty, enabling the remaining design points (second stage design) to be chosen with greater efficiency. The second stage design is then generated from an optimality procedure which incorporates the improved model knowledge. Using this approach, numerous two stage design procedures have been developed for the normal linear model. Extending this concept, a Bayesian design augmentation procedure has been developed for the purpose of efficiently obtaining data for variance modeling, when initial knowledge of the variance model is poor.

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