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A Bayesian A ‐Optimal and Model Robust Design Criterion
Author(s) -
Zhou Xiaojie,
Joseph Lawrence,
Wolfson David B.,
Bélisle Patrick
Publication year - 2003
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.0006-341x.2003.00124.x
Subject(s) - bayesian probability , trace (psycholinguistics) , optimal design , set (abstract data type) , mathematical optimization , mathematics , limit (mathematics) , function (biology) , optimality criterion , basis (linear algebra) , bayesian experimental design , bayesian inference , computer science , statistics , bayesian statistics , mathematical analysis , philosophy , linguistics , geometry , evolutionary biology , biology , programming language
Summary . 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.