Probability and statistics
Probability and statistics
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DOI：
10.1201/b17767-22
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发表时间：
2012-08
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影响因子：
--
通讯作者：
Francis Albarede
中科院分区：
文献类型：
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作者：
Francis Albarede
从历史的角度来看，统计学理论是最近才发展起来的。从大量测量数据中计算平均值的方法最早是在1581年采用的，但即使是这个今天被大多数人理解的简单方法，直到18世纪末仍然存在很大争议。传统上，地壳的上部一直被视为一个复杂的三维马赛克的许多岩石单元具有不同的成分和年龄。然而，正如本章所强调的，许多地质特征显示出随机特征，可以通过采用数理统计方法进行建模。可以从统计总体中随机抽取样本来估计参数的想法仍然至关重要。地学数据的主要参数是其均值和方差。频率分布分析适用于许多不同类型的地质数据。离散分布包括二项分布和泊松分布，但也包括几何分布和负二项分布。正态分布和对数正态分布在连续数据建模中是最重要的，尽管Pareto分布由于其与分形建模的密切联系而变得越来越重要。许多统计推断的方法，包括学生t检验、方差分析和卡方检验的拟合优度都是基于正态分布的。这些统计方法在地质学中仍然很重要，如果以探索的方式使用，因为考虑的随机变量通常不是独立同分布的（iid），这是在大多数其他科学领域中实践的统计问题解决的要求。特别是，由于大多数地质变量的连续性，统计检验中常用的自由度的数量受到空间自相关的强烈影响。
From a historical perspective, the theory of statistics was developed relatively recently. Calculating the mean from a number of measurements was a procedure first practiced in 1581 but even this simple method, which is understood by most people to-day, remained highly controversial until the end of the eighteenth century. Traditionally, the upper part of the Earth’s crust has been viewed as a complex three-dimensional mosaic of numerous rock units with different compositions and ages. However, as emphasized in this chapter, many geological features display random characteristics that can be modeled by adapting methods of mathematical statistics. The idea that random samples can be taken from statistical populations for the estimation of parameters remains paramount. The main parameters of geoscience data to be estimated are their mean and variance. Frequency distribution analysis is applicable to many different types of geological data. Discrete distributions include the binomial and Poisson, but also the geometric and negative binomial distributions. The normal and lognormal distributions are most important in modeling continuous data although the Pareto distribution is becoming increasingly important because of its close connection to fractal modeling. Many methods of statistical inference including Student’s t-test, analysis of variance and the chi-squared test for goodness of fit are based on the normal distribution. These statistical methods remain important in geology if used in an exploratory manner because the random variables considered often are not independent and identically distributed (iid), which is a requirement for statistical problem-solving as practiced in most other fields of science. Especially, numbers of degrees of freedom commonly used in statistical tests are strongly affected by spatial autocorrelation due to the continuous nature of most geological variables.