Application of Copulas in Geostatistics
Application of Copulas in Geostatistics
复制标题
Copula在地统计学中的应用
DOI：
10.1007/978-90-481-2322-3_34
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
András Bárdossy
中科院分区：
文献类型：
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作者：
Haslauer;Claus P;Jing Li;András Bárdossy
本文演示了经验Copula如何以最纯粹的形式描述和建模真实世界环境数据集的空间相关结构，以及如何将这样的Copula模型用作插值和相关不确定性估计的底层结构，使用Copula，通过使用均匀边际分布函数的变量的联合累积分布来建模多变量分布的相关性。均匀边缘分布是通过使用变量的秩对边缘分布进行单调变换的结果。由于边际分布的均匀性，Copula函数表达了变量的依赖结构，与变量的边际分布无关，这意味着Copula函数以最纯粹的形式显示了变量之间的相互依赖关系。这一性质也意味着原始数据的边缘分布对空间依赖结构没有影响，不能“掩盖”部分空间依赖结构。此外，变量的不同分位数之间的依赖程度的差异很容易通过经验copula密度的轮廓形状来识别。关于不确定性的量化，copula提供了一个显着的优势：在每个插值点处的插值参数的完整分布函数是可用的。不确定性的大小不仅取决于观测网络的密度，而且还取决于测量值的大小以及测量值大小的梯度。这意味着对于相同配置的观测网络，内插两个具有非常相似的边缘分布的事件，两个事件的置信区间看起来明显不同。
This paper demonstrates how empirical copulas can be used to describe and model spatial dependence structures of real-world environmental datasets in the purest form and how such a copula model can be employed as the underlying structure for interpolation and associated uncertainty estimates.Using copulas, the dependence of multivariate distributions is modelled by the joint cumulative distribution of the variables using uniform marginal distribution functions. The uniform marginal distributions are the effect of transforming the marginal distributions monotonically by using the ranks of the variables. Due to the uniform marginal distributions, copulas express the dependence structure of the variables independent of the variables’ marginal distributions which means that copulas display interdependence between variables in its purest form. This property also means that marginal distributions of the original data have no influence on the spatial dependence structure and can not “cover up” parts of the spatial dependence structure. Additionally, differences in the degree of dependence between different quantiles of the variables are readily identified by the shape of the contours of an empirical copula density.Regarding the quantification of uncertainties, copulas offer a significant advantage: the full distribution function of the interpolated parameter at every interpolation point is available. The magnitude of uncertainty does not depend on the density of the observation network only, but also on the magnitude of the measurements as well as on the gradient of the magnitude of the measurements. That means for the same configuration of the observation network, interpolating two events with very similar marginal distribution, the confidence intervals look significantly different for both events.
DOI：
10.1007/978-1-4757-3076-0
发表时间：
1998-10
期刊：
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影响因子：
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作者：
通讯作者：
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影响因子：
5.4
作者：
Bardossy, Andras;Li, Jing
通讯作者：
Li, Jing