A Bayesian Reliability Approach to Multiple Response Optimization with Seemingly Unrelated Regression Models
A Bayesian Reliability Approach to Multiple Response Optimization with Seemingly Unrelated Regression Models
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DOI：
10.1080/16843703.2009.11673204
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发表时间：
2009-01
影响因子：
2.8
通讯作者：
John J. Peterson;Guillermo Miró-Quesada;Enrique del Castillo
中科院分区：
文献类型：
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作者：
John J. Peterson;Guillermo Miró-Quesada;Enrique del Castillo
摘要本文提出了一种多响应优化实验的贝叶斯预测方法。它以两种方式概括了Peterson [33]的工作，使其在应用程序中更灵活。首先，看似无关的回归模型的多变量后验预测分布用于通过评估所需多变量响应的可靠性来确定最佳因子水平。结果表明，它是可能的最佳平均响应面出现令人满意的，但与不满意的整体过程的可靠性。其次，使用多元正态分布的回归误差项的向量推广到（重尾）多元t分布。这提供了关于中等离群值的贝叶斯敏感性分析。通过前验分析也考虑了增加设计点的影响。用两个真实的例子说明了这种方法的优点。
Abstract This paper presents a Bayesian predictive approach to multiresponse optimization experiments. It generalizes the work of Peterson [33] in two ways that make it more flexible for use in applications. First, a multivariate posterior predictive distribution of seemingly unrelated regression models is used to determine optimum factor levels by assessing the reliability of a desired multivariate response. It is shown that it is possible for optimal mean response surfaces to appear satisfactory yet be associated with unsatisfactory overall process reliabilities. Second, the use of a multivariate normal distribution for the vector of regression error terms is generalized to that of the (heavier tailed) multivariate t-distribution. This provides a Bayesian sensitivity analysis with regard to moderate outliers. The effect of adding design points is also considered through a preposterior analysis. The advantages of this approach are illustrated with two real examples.