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A Bayesian A-optimal and model robust design criterion.

Xiaojie Zhou·Lawrence Joseph·David B Wolfson·Patrick Bélisle
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Abstract

Suppose that the true model underlying a set of data is one of a finite set of candidate models, and that parameter estimation for this model is of primary interest. With this goal, optimal design must depend on a loss function across all possible models. A common method that accounts for model uncertainty is to average the loss over all models; this is the basis of what is known as Läuter's criterion. We generalize Läuter's criterion and show that it can be placed in a Bayesian decision theoretic framework, by extending the definition of Bayesian A-optimality. We use this generalized A-optimality to find optimal design points in an environmental safety setting. In estimating the smallest detectable trace limit in a water contamination problem, we obtain optimal designs that are quite different from those suggested by standard A-optimality.

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Xiaojie Zhou, Lawrence Joseph, David B Wolfson, Patrick Bélisle. 2003. A Bayesian A-optimal and model robust design criterion.. https://doi.org/10.1111/j.0006-341x.2003.00124.x

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