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首页> 外文期刊>Journal of Microscopy >EDGE-CORRECTED ESTIMATORS OF THE NEAREST-NEIGHBOUR DISTANCE DISTRIBUTION FUNCTION FOR THREE-DIMENSIONAL POINT PATTERNS
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EDGE-CORRECTED ESTIMATORS OF THE NEAREST-NEIGHBOUR DISTANCE DISTRIBUTION FUNCTION FOR THREE-DIMENSIONAL POINT PATTERNS

机译：三维点模式的近邻距离分布函数的边缘校正估计

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In multiphase systems consisting of 'particles' embedded in a matrix the three-dimensional spatial distribution of the particles may represent important structural information. In systems where the matrix is transparent or translucent recent developments in microscopy allow the three-dimensional location of particles to be recorded. Using these data a spatial statistical, or second-order stereological, analysis can be carried out. In second-order stereology functions of interparticle distances are used as,summary statistics of the spatial distributions. These statistics show whether the particles are randomly arranged or, more commonly, either clustered together or inhibited from close approach to each other. This paper focuses on the estimation of one of these spatial statistics, the nearest-neighbour distance distribution function or G-function. In practice, estimation of the G-function is plagued by an 'edge-effect' bias introduced by the sampling process itself. There exist a number of G-function estimators that tackle this edge effect problem; for single sample 'bricks' it can be shown that these estimators become increasingly accurate as the brick size increases, i.e. they are consistent. However, in many practical cases the size of a sampling brick is fixed by experimental constraints and in these circumstances the only way to increase sample size is to take replicated sampling regions. In this paper we review a number of existing G-function estimators and propose a new estimator. These estimators are compared using the criterion of how well they overcome the edge-effect when they are applied to replicated samples of a fixed size of brick. These comparisons were made using Monte-Carlo simulation methods; the results show that three existing estimators are clearly unsuitable for estimating the G-function from replicated sample bricks. Of the other estimators the recommended estimator depends upon the number of replicates taken; however, we conclude that if a total of more than about 800 points are analysed then the bias in the pooled estimate of the G-function can be reduced to tolerable levels. [References: 25]
机译：在由嵌入在矩阵中的“粒子”组成的多相系统中，粒子的三维空间分布可能代表重要的结构信息。在基质是透明或半透明的系统中，显微镜的最新发展允许记录颗粒的三维位置。使用这些数据，可以进行空间统计或二阶立体分析。在二阶立体学中，粒子间距离的函数用作空间分布的摘要统计。这些统计数据表明粒子是随机排列的还是更常见的是聚集在一起或被抑制为彼此靠近的方式。本文着重于对这些空间统计之一，最近邻距离分布函数或G函数的估计。在实践中，G函数的估计受到采样过程本身引入的“边缘效应”偏差的困扰。有许多G函数估计器可以解决这一边缘效应问题。对于单个样本``砖块''，可以证明这些估计量随着砖块大小的增加而变得越来越准确，即它们是一致的。但是，在许多实际情况下，采样砖的大小由实验约束决定，在这些情况下，增加样本大小的唯一方法是获取重复的采样区域。在本文中，我们回顾了许多现有的G函数估计量，并提出了一个新的估计量。使用将这些估算器应用于固定大小的砖块的复制样本时克服边缘效应的程度的标准来比较这些估算器。这些比较是使用蒙特卡洛模拟方法进行的;结果表明，三个现有的估计量显然不适合从复制的样本块中估计G函数。在其他估计量中，推荐的估计量取决于所进行的重复次数。但是，我们得出的结论是，如果总共分析了约800个以上的点，则可以将G函数的合并估计中的偏差减少到可容忍的水平。 [参考：25]

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