Empirical Bayes Approach for Developing Hierarchical Probabilistic Predictive Models and Its Application to the Seismic Reliability Analysis of FRP-Retrofitted RC Bridges
Empirical Bayes Approach for Developing Hierarchical Probabilistic Predictive Models and Its Application to the Seismic Reliability Analysis of FRP-Retrofitted RC Bridges
复制标题
开发分层概率预测模型的经验贝叶斯方法及其在 FRP 加固 RC 桥梁抗震可靠性分析中的应用
DOI：
10.1061/ajrua6.0000817
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
P. Gardoni
中科院分区：
文献类型：
--
作者：
Armin Tabandeh;P. Gardoni
摘要本文提出了一种通用的公式来开发聚类数据的分层概率预测模型。在一个组内的数据之间共享的公共聚类因子导致在估计未知模型参数时需要考虑的统计依赖性。分层公式化的基本思想是，未知的模型参数被赋予取决于一组共享的底层参数的分布，并且这种构造是递归的，直到层次结构的最高级别。分层模型中方差参数的先验分布通常是不适当的，这会导致不存在的后验分布，而这些后验分布在数值模拟中可能是完全合理的。另一方面，常见的正确的无信息先验分布也可能会大大影响后验统计。相反，经验贝叶斯方法提出了客观地估计方差参数。吉布斯抽样算法是用来估计…
AbstractThis paper proposes a general formulation to develop hierarchical probabilistic predictive models for clustered data. The common clustering factor, shared among the data within a group, causes statistical dependence that needs to be accounted for in the estimation of unknown model parameters. The basic idea of the hierarchical formulation is that the unknown model parameters are endowed with distributions that depend on a set of shared underlying parameters, and this construction is recursive up to the highest level of the hierarchy. The usual improper noninformative prior distributions on variance parameters of hierarchical models can lead to nonexistent posterior distributions that may appear perfectly reasonable in numerical simulations. On the other hand, common proper noninformative prior distributions may also substantially affect posterior statistics. Instead, the empirical Bayes approach is proposed to objectively estimate the variance parameters. The Gibbs sampling algorithm is used to es...