基于形状理论的介数度量与推理
A Measurement of In-Betweenness and Inference Based on Shape Theories
摘要：
我们提出了一个统计框架，调查是否一个给定的子群体之间的其他两个子群体在多元特征空间。这种方法的动机是来自合作者的一个生物学问题：一种新发现的细胞类型在几个给定的特征中是否介于两种已知类型之间？我们提出了两个介数指数（IBI）来量化由三个亚群的汇总统计量形成的随机三角形所表现出的介数。为三角形和IBI度量提供了统计推断方法。我们的方法的应用在三个例子中得到了证明：经典的虹膜数据集，三种乳腺癌亚型复发风险的研究，以及具有测量电生理特征的激励神经元细胞数据。
英文摘要：
We propose a statistical framework to investigate whether a given subpopulation lies between two other subpopulations in a multivariate feature space. This methodology is motivated by a biological question from a collaborator: Is a newly discovered cell type between two known types in several given features? We propose two in-betweenness indices (IBI) to quantify the in-betweenness exhibited by a random triangle formed by the summary statistics of the three subpopulations. Statistical inference methods are provided for triangle shape and IBI metrics. The application of our methods is demonstrated in three examples: the classic Iris data set, a study of risk of relapse across three breast cancer subtypes, and the motivating neuronal cell data with measured electrophysiological features.
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