论文标题
maximin $φ_{p} $ - 多元GLM的高效设计
A Maximin $Φ_{p}$-Efficient Design for Multivariate GLM
论文作者
论文摘要
广义线性模型（GLM）的实验设计通常取决于模型的规范，包括链接函数，预测因子和未知参数，例如回归系数。为了处理这些模型规范的不确定性，重要的是在这种不确定性下以高效率构建最佳设计。贝叶斯实验设计等现有方法通常使用模型规格的先前分布，将模型不确定性纳入设计标准。另外，人们可以通过优化模型规范的不确定性来获得最差的设计效率来获得设计。在这项工作中，我们提出了一种新的最大值$φ_p$ - 效率（或简短的MM- $φ_P$）设计，旨在最大程度地提高模型不确定性下的最低$φ_P$ - 效率。基于提出标准的理论属性，我们开发了一种具有声音收敛属性的有效算法来构建MM $ $φ_P$设计。通过几个数值示例评估了建议的MM-$ $ $φ_P$设计的性能。
Experimental designs for a generalized linear model (GLM) often depend on the specification of the model, including the link function, the predictors, and unknown parameters, such as the regression coefficients. To deal with uncertainties of these model specifications, it is important to construct optimal designs with high efficiency under such uncertainties. Existing methods such as Bayesian experimental designs often use prior distributions of model specifications to incorporate model uncertainties into the design criterion. Alternatively, one can obtain the design by optimizing the worst-case design efficiency with respect to uncertainties of model specifications. In this work, we propose a new Maximin $Φ_p$-Efficient (or Mm-$Φ_p$ for short) design which aims at maximizing the minimum $Φ_p$-efficiency under model uncertainties. Based on the theoretical properties of the proposed criterion, we develop an efficient algorithm with sound convergence properties to construct the Mm-$Φ_p$ design. The performance of the proposed Mm-$Φ_p$ design is assessed through several numerical examples.
