Bayesian Two Stage Design Under Model Uncertainty

Abstract

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.