非线性混合效应模型的最优与稳健设计

项目名称： 非线性混合效应模型的最优与稳健设计

项目编号： No.11471216

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 岳荣先

作者单位： 上海师范大学

项目金额： 68万元

中文摘要： 非线性混合效应模型广泛用于分析相关数据，如纵向数据和重复测量数据等。近十多年来关于非线性混合效应模型的最优试验设计的研究正受到越来越多的关注。文献中对于非线性混合效应模型试验设计问题通常是在一定的模型假设下研究基于Fisher信息阵一阶Taylor近似的局部最优设计，但这些设计在精确度和稳健性等方面存在一定局限性。本项目较系统地研究单响应和多响应非线性混合效应模型的两类设计，一类是具有更高精确度的最优设计，另一类是关于模型不确定性具有一定稳健性的设计，并通过理论和数值研究展示这些设计的理论性质。主要研究包括：获得更高精确度的近似信息阵和置信域体积，建立在不同模型假设和不同优良准则下的最优设计，研究在不同先验下的贝叶斯设计，提出能抵御模型参数不确定性、模型形式不确定性、方差-协方差结构不确定性以及试验方案实施过程不确定性的稳健设计方法。

中文关键词： 混合效应模型；非线性；最优设计；稳健设计；贝叶斯设计

英文摘要： Nonlinear mixed effects models are often applied for the analysis of correlated data, such as longitudinal data, repeated measures data, etc. The research on optimal designs for nonlinear mixed effects models has been paid more and more attention in last decade. Most of the work in the optimal design literature for nonlinear models concerns the local optimal designs based on an approximate Fisher information matrix via a first order Taylor series expansion for the specified model. Such local optimal designs may lose their accuracy and robustness. This project provides a systematic and comprehensive study of two kinds of designs for single-response and milti-response nonlinear mixed effects models, which are more accurate and robust. Advantages of the proposed designs are demonstrated through both theoretical and numerical studies. The main research includes：Find an approximate Fisher information matrix and an approximate volume of the confidence region more accurately, develop optimal designs under different model assumptions and different optimality criteria, investigate the Bayesian optimal designs for various prior distributions, and propose robust design methods to against the uncertainty in the parameter space, uncertainty in the model space, uncertainty in the variance-covariance structure, and uncertainty in the design execution.

英文关键词： Mixed effects model;Nonlinear;Optimal design;Robust design;Baysian design