Finding Bayesian Optimal Designs for Nonlinear Models: A Semidefinite Programming-Based Approach.
Finding Bayesian Optimal Designs for Nonlinear Models: A Semidefinite Programming-Based Approach.
复制标题
寻找非线性模型的贝叶斯最优设计：基于半定规划的方法。
DOI：
10.1111/insr.12073
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
Wong,WengKee
中科院分区：
文献类型：
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作者：
Duarte,BelmiroPM;Wong,WengKee
本文利用半定规划（SDP）构造非线性回归模型的贝叶斯最优设计。这里的设置扩展的最优设计问题的制定为SDP问题从线性到非线性模型。高斯求积公式（GQF）用于计算贝叶斯设计准则中的期望值，例如D-、A-或E-最优性。作为一个说明性的例子，我们使用幂逻辑模型演示了该方法，并比较了文献中的结果。此外，我们研究如何影响最优设计的设计空间，不同数量的不确定性的参数值，不同的选择GQF和不同的先验分布的模型参数的向量，包括正常的先验和不相关的组件的不同的离散化方案。进一步的应用，以寻找贝叶斯D-最优设计与两个回归的logistic模型和两个变量的广义线性模型与伽玛分布的响应进行了讨论，我们的方法的一些局限性。
This paper uses semidefinite programming (SDP) to construct Bayesian optimal design for nonlinear regression models. The setup here extends the formulation of the optimal designs problem as an SDP problem from linear to nonlinear models. Gaussian quadrature formulas (GQF) are used to compute the expectation in the Bayesian design criterion, such as D‐, A‐ or E‐optimality. As an illustrative example, we demonstrate the approach using the power‐logistic model and compare results in the literature. Additionally, we investigate how the optimal design is impacted by different discretising schemes for the design space, different amounts of uncertainty in the parameter values, different choices of GQF and different prior distributions for the vector of model parameters, including normal priors with and without correlated components. Further applications to find Bayesian D‐optimal designs with two regressors for a logistic model and a two‐variable generalised linear model with a gamma distributed response are discussed, and some limitations of our approach are noted.