A Simple Bayesian Modification of D -Optimal Designs to Reduce Dependence on an Assumed Model

William DuMouchel · Bradley Jones

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Optimal Experimental Design Methods Statistical Methods and Bayesian Inference Advanced Statistical Methods and Models

Abstract

D-optimal and other computer-generated experimental designs have been criticized for being too dependent on an assumed statistical model. To address this criticism, we introduce the notion of empirical models that have both primary and potential terms. Combining this idea with the Bayesian paradigm, this article proposes a modification of the D-optimal approach that preserves the flexibility and ease of use of algorithmic designs while being more resistant to the biases caused by an incorrect model. These designs provide a Bayesian justification for resolution IV designs. Several theoretical examples and a practical example from the literature demonstrate the advantages of the proposed method.

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References

1979Statistics for Experimenters 1988Empirical Model Building and Response Surfaces 1992Design and Analysis of Experiments 1988Empirical Model-Building and Response Surfaces.1956On a Measure of the Information Provided by an Experiment 1984Experiments with Mixtures: Designs, Models, and the Analysis of Mixture Data.1959A Basis for the Selection of a Response Surface Design 1978Curve Fitting and Optimal Design for Prediction

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