Ranking and Estimation of Related Means in the Presence of a Covariate—A Bayesian Approach
有协变量时相关均值的排序与估计：贝叶斯方法AI 解读 ↓
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有协变量时相关均值的排序与估计：贝叶斯方法
- 研究问题
- 存在协变量且不同组斜率可能不同时，如何估计相关均值并判断在指定协变量取值下哪个均值最大，表达选择的不确定性？
- 方法与思路
- 作者采用分层贝叶斯多斜率模型，计算参数后验均值、标准差及各均值最大的后验概率，并以Monte Carlo处理复杂积分。
- 材料陈述的贡献
- 摘要称，最大均值的后验概率向量提供易理解的选择依据；论文给出高效积分算法，并通过淀粉薄膜强度与厚度数据展示应用。
- 阅读关注点
- 应核对层级先验、协变量取值对排序的影响、不平衡设计和未知方差的处理，以及后验计算误差与先验敏感性分析。
- 阅读边界
- 仅据OpenAlex索引摘要，稿件版本未注明。摘要未列明先验及模型条件；所报计算时间依赖特定数据与历史硬件，不能直接外推到当前任务。
原文摘要
Choosing the largest of several means can be a demanding problem, especially in the presence of a covariate. A hierarchical Bayesian approach to ranking and selection, as well as estimation of related means in the presence of a covariate, is considered. For the multiple slopes model we compute, in addition to the posterior means and standard deviations of the parameters, the posterior probabilities that each mean, at a given value of the covariate, is the largest. The vector of posterior probabilities thus obtained provides an easily understandable answer to the selection problem. Although calculation of the posterior probabilities may involve four-dimensional numerical integration in the difficult unbalanced design and unknown variance case, an efficient Monte Carlo method of evaluation has been developed and is given in the article. By reanalyzing a well-known data set on the breaking strength and thickness of starch films, we illustrate how our Bayesian approach produces meaningful conclusions, some of which would perhaps be difficult to obtain otherwise. For the starch film example, we found that it took only 1.4 seconds to compute the quantities of interest using an IBM 3090–600S machine. Because the computation time is quite small, it is apparent that the Bayesian procedure can be implemented for everyday use.