On the number of support points of maximin and Bayesian optimal designs
On the number of support points of maximin and Bayesian optimal designs
复制标题
关于极大极小和贝叶斯最优设计的支持点数
DOI：
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发表时间：
2007
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极小和贝叶斯D-最优设计。maximin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是可用的。在区间参数空间上，许多作者根据经验观察到，先验信息中不确定性的增加（即，最大最小准则中参数空间的较大范围或贝叶斯准则中先验的较大方差）产生相应最优设计的较大数目的支持点。在本文中，我们提出了分析工具，用于证明这一现象在具体情况下。所提出的方法可以用来解释许多经验观察到的结果在文献中。此外，它解释了为什么最大最小D-最优设计通常比贝叶斯D-最优设计在更多点上得到支持。
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 for these parameters is available. On interval parameter spaces, 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 in the Bayesian criterion) yields a larger number of support points of the corresponding optimal designs. In this paper, we present analytic tools which are used to prove this phenomenon in concrete situations. The proposed methodology can be used to explain many empirically observed results in the literature. Moreover, it explains why maximin D-optimal designs are usually supported at more points than Bayesian D-optimal designs.