Bayesian D-Optimal and Model Robust Designs in Linear Regression Models
Bayesian D-Optimal and Model Robust Designs in Linear Regression Models
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DOI：
10.1080/02331889308802429
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发表时间：
1993
期刊：
影响因子：
1.9
通讯作者：
H. Dette
中科院分区：
文献类型：
--
作者：
H. Dette
本文考虑了一般线性回归模型中的贝叶斯最优设计问题。针对模型鲁棒贝叶斯c-最优性准则，证明了Elfving定理的一个版本。最优设计最小化加权乘积，其中因子与不同模型中参数线性组合的贝叶斯估计量的预期后验风险成比例。几何特征被用来说明充分条件，保证经典和贝叶斯最优设计是支持在同一组点或相同。贝叶斯D-最优设计问题出现作为一个特殊的情况下，在这种设置考虑“嵌套”模型和特殊的线性组合的参数的“最高系数”在不同的模型。从而得到了贝叶斯D-最优设计与经典最优设计在同一点集上得到支持或完全相同的先验分布精度矩阵的充分条件。结果是生病……
We consider the Bayesian optimal design problem in the usual linear regression model. A version of Elfving’s Theorem is proved for a model robust Bayesian c-optimality criterion. The optimal design minimizes a weighted product where the factors are proportional to the expected posterior risks of the Bayesian estimators for the linear combinations of the parameters in different models. The geometric characterizations are used to state sufficient conditions which guarantee that the classical and the Bayesian optimal designs are supported at the same set of points or are identical. The Bayesian D-optimal design problem appears as a special case in this setup considering “nested” models and special linear combinations for the paramater of the “highest coefficients” in different models. Thus sufficient conditions on the precision matrices of the prior distribution are found that the Bayesian D-optimal and the classical optimal design are supported at the same set of points or are identical. The results are ill...