Dorph-Petersen K A, Gundersen H J, Jensen E B
Stereological Research Laboratory, Institute of Experimental Clinical Research, University Institute of Pathology and 2nd University Clinic of Internal Medicine, University of Aarhus, Denmark.
J Microsc. 2000 Nov;200(Pt 2):148-57. doi: 10.1046/j.1365-2818.2000.00750.x.
Non-uniform systematic sampling designs in stereology are studied. Various methods of constructing non-uniform systematic sampling points from prior knowledge of the measurement function are presented. As an example, we consider area estimation from lengths of linear intercepts. The efficiency of two area estimators, based on non-uniform sampling of parallel lines, is compared to that of the classical 2D Cavalieri estimator, based on uniform sampling, in a sample of planar profiles from transverse sections of 41 small myelinated axons. The comparison is based on simulations. It is concluded that for profiles of this type one of the non-uniform sampling schemes is more efficient than the traditional uniform sampling scheme. Other examples where non-uniform systematic sampling may be used are in area estimation from lines emanating from a fixed point, area estimation from concentric circles or spirals and curve length estimation from sweeping lines. It is shown that proportional-to-size sampling is a special case of non-uniform systematic sampling. Finally, the effect of noise in the observations is discussed.
本文研究了体视学中的非均匀系统抽样设计。提出了多种根据测量函数的先验知识构建非均匀系统抽样点的方法。例如，我们考虑从线性截距的长度进行面积估计。在来自41个小髓鞘轴突横切面的平面轮廓样本中，将基于平行线非均匀抽样的两种面积估计器的效率与基于均匀抽样的经典二维卡瓦列里估计器的效率进行了比较。该比较基于模拟。得出的结论是，对于这种类型的轮廓，其中一种非均匀抽样方案比传统的均匀抽样方案更有效。非均匀系统抽样可用于其他示例的情况包括：从固定点发出的线进行面积估计、从同心圆或螺旋线进行面积估计以及从扫描线进行曲线长度估计。结果表明，按大小比例抽样是非均匀系统抽样的一种特殊情况。最后，讨论了观测值中的噪声影响。
