The size of the connected components of excursion sets of χ2, t and F fields
The size of the connected components of excursion sets of χ2, t and F fields
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DOI：
10.1239/aap/1029955192
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发表时间：
1999-09-01
影响因子：
1.2
通讯作者：
Cao, J
中科院分区：
文献类型：
--
作者：
Cao, J
在高、低阈值的极限下，对平稳的χ（2）、t和F场，导出了漂移集的一个连通分量和最大连通分量的大小分布。这推广了以前关于平稳高斯场（Nosko 1969，Adler 1981）和一维和二维chi（2）场（Aronowich and Adler 1986，1988）的结果。这是一个应用程序，以检测区域变化的正电子发射断层扫描（PET）图像的血流在人脑中，使用的最大连接组件的偏移集的大小作为检验统计量。
The distribution of the size of one connected component and the largest connected component of the excursion set is derived for stationary chi(2), t and F fields, in the limit of high or low thresholds. This extends previous results for stationary Gaussian fields (Nosko 1969, Adler 1981) and for chi(2) fields in one and two dimensions (Aronowich and Adler 1986, 1988). An application of this is to detect regional changes in positron emission tomography (PET) images of blood flow in human brain, using the size of the largest connected component of the excursion set as a test statistic.