Bayesian optimal blocking of factorial designs |
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Authors: | Mingyao Ai Lulu Kang V Roshan Joseph |
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Institution: | 1. LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China;2. School of Industrial and Systems Engineering, Georgia Institute of Technology, 755 Ferst Drive NW, Atlanta, GA 30332-0205, USA |
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Abstract: | The presence of block effects makes the optimal selection of fractional factorial designs a difficult task. The existing frequentist methods try to combine treatment and block wordlength patterns and apply minimum aberration criterion to find the optimal design. However, ambiguities exist in combining the two wordlength patterns and therefore, the optimality of such designs can be challenged. Here we propose a Bayesian approach to overcome this problem. The main technique is to postulate a model and a prior distribution to satisfy the common assumptions in blocking and then, to develop an optimal design criterion for the efficient estimation of treatment effects. We apply our method to develop regular, nonregular, and mixed-level blocked designs. Several examples are presented to illustrate the advantages of the proposed method. |
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Keywords: | Block design Bayesian method Combined wordlength pattern Minimum aberration |
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