On the number of support points of maximin and Bayesian D-optimal designs in nonlinear regression models
On the number of support points of maximin and Bayesian D-optimal designs in nonlinear regression models
复制标题
非线性回归模型中极大极小和贝叶斯 D 最优设计的支持点数
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
H. Dette
中科院分区：
文献类型：
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作者：
D. Braess;H. Dette
我们考虑非线性回归模型的极大值和贝叶斯d -最优设计。极大值准则要求为模型中的非线性参数指定一个区域，而贝叶斯最优性准则假设这些参数的先验分布是可用的。许多作者通过经验观察到，先验信息不确定性的增加（即最大准则中参数空间的范围更大或贝叶斯准则中先验分布的方差更大）会产生更多的相应优化设计的支撑点。在本文中，我们给出了这一现象的严格证明，并表明在许多非线性回归模型中，如果可用的先验信息较少，贝叶斯和最大d优化设计的支撑点数量可以变得任意大。我们的结果也解释了为什么最大d最优设计通常比贝叶斯d最优设计在更多不同的点上得到支持。
We consider maximin and Bayesian D-optimal designs for nonlinear regression models. The maximin criterion requires the specification of a region for the nonlinear parameters in the model, while the Bayesian optimality criterion assumes that a prior distribution for these parameters is available. It was observed empirically by many authors that an increase of uncertainty in the prior information (i.e. a larger range for the parameter space in the maximin criterion or a larger variance of the prior distribution in the Bayesian criterion) yields a larger number of support points of the corresponding optimal designs. In this paper we present a rigorous proof of this phenomenon and show that in many nonlinear regression models the number of support points of Bayesian- and maximin D-optimal designs can become arbitrarily large if less prior information is available. Our results also explain why maximin D-optimal designs are usually supported at more different points than Bayesian D-optimal designs.