Abstract

Spatially distributed processes can be modeled as random fields. The complex spatial dependence is then incorporated in the joint probability density function. Knowledge of the joint probability density allows predicting missing data. While environmental data often exhibit significant deviations from Gaussian behavior (rainfall, wind speed, and earthquakes being characteristic examples), only a few non-Gaussian joint probability density functions admit explicit expressions. In addition, random field models are computationally costly for big datasets. We propose an “effective distribution” approach which is based on the product of univariate conditional probability density functions modified by local interactions. The effective densities involve local parameters that are estimated by means of kernel regression. The prediction of missing data is based on the median value from an ensemble of simulated states generated from the effective distribution model. The latter can capture non-Gaussian dependence and is applicable to large spatial datasets, since it does not require the storage and inversion of large covariance matrices. We compare the predictive performance of the effective distribution approach with classical geostatistical methods using Gaussian and non-Gaussian synthetic data. We also apply the effective distribution approach to the reconstruction of gaps in large raster data.

中文翻译：

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重建丢失数据的有效概率分布近似

摘要

空间分布过程可以建模为随机字段。然后将复杂的空间相关性合并到联合概率密度函数中。了解联合概率密度可以预测丢失的数据。尽管环境数据通常显示出与高斯行为的明显偏差（降雨，风速和地震为特征示例），但只有少数非高斯联合概率密度函数允许使用明确的表达式。此外，对于大型数据集，随机字段模型的计算成本很高。我们提出了一种“有效分布”方法，该方法基于通过局部交互作用修改的单变量条件概率密度函数的乘积。有效密度包括通过核回归估计的局部参数。缺失数据的预测基于有效分配模型生成的一组模拟状态的中值。后者可以捕获非高斯依赖关系，并且适用于大型空间数据集，因为它不需要存储和求逆大型协方差矩阵。我们将有效分布方法的预测性能与使用高斯和非高斯综合数据的经典地统计学方法进行比较。我们还将有效的分配方法应用于重建大型栅格数据中的间隙。因为它不需要大协方差矩阵的存储和求逆。我们将有效分布方法的预测性能与使用高斯和非高斯综合数据的经典地统计学方法进行比较。我们还将有效的分配方法应用于重建大型栅格数据中的间隙。因为它不需要大协方差矩阵的存储和求逆。我们将有效分布方法的预测性能与使用高斯和非高斯综合数据的经典地统计学方法进行比较。我们还将有效的分配方法应用于重建大型栅格数据中的间隙。