Abstract Finding Bayesian optimal designs for nonlinear models is a difficult task because the optimality criterion typically requires us to evaluate complex integrals before we perform a constrained optimization. We propose a hybridized method where we combine an adaptive multidimensional integration algorithm and a metaheuristic algorithm called imperialist competitive algorithm to find Bayesian optimal designs. We apply our numerical method to a few challenging design problems to demonstrate its efficiency. They include finding D-optimal designs for an item response model commonly used in education, Bayesian optimal designs for survival models, and Bayesian optimal designs for a four-parameter sigmoid Emax dose response model. Supplementary materials for this article are available online and they contain an R package for implementing the proposed algorithm and codes for reproducing all the results in this article.

中文翻译：

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一种用于寻找非线性模型贝叶斯最优设计的基于元启发式自适应 Cubature 的算法

摘要 为非线性模型寻找贝叶斯最优设计是一项艰巨的任务，因为最优性标准通常要求我们在执行约束优化之前评估复杂的积分。我们提出了一种混合方法，将自适应多维积分算法和称为帝国主义竞争算法的元启发式算法相结合，以找到贝叶斯最优设计。我们将我们的数值方法应用于一些具有挑战性的设计问题，以证明其效率。它们包括寻找教育中常用的项目响应模型的 D 最优设计、生存模型的贝叶斯最优设计以及四参数 sigmoid Emax 剂量响应模型的贝叶斯最优设计。