A multi-resolution approximation via linear projection for large spatial datasets
A multi-resolution approximation via linear projection for large spatial datasets
复制标题
通过线性投影对大型空间数据集进行多分辨率近似
DOI：
10.1007/s42081-020-00092-x
复制
发表时间：
2020
影响因子：
1.3
通讯作者：
Hirano Toshihiro
中科院分区：
文献类型：
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作者：
Hirano Toshihiro
最近在收集空间数据方面的技术进步增加了对分析大型空间数据集的方法的需求。对这些类型的数据集进行统计分析可以提供各个领域的有用知识。然而，传统的空间统计方法，如最大似然估计和克里格，是不切实际的时间消耗大空间数据集，由于必要的矩阵求逆。为了科普这个问题，我们提出了一种通过线性投影的多分辨率逼近（M-RA-lp）。TheM-RA-lp进行线性投影方法对每个子区域每当一个空间域被细分，这导致一个近似的协方差函数捕捉大尺度和小尺度的空间变化。此外，我们还导出了利用M-RA-lp得到的近似协方差函数快速计算对数似然函数和预测分布的算法。空气剂量率的模拟研究和真实的数据分析表明，我们提出的M-RA-lp相对于相关的现有方法工作得很好。
Recent technical advances in collecting spatial data have been increasing the demand for methods to analyze large spatial datasets. The statistical analysis for these types of datasets can provide useful knowledge in various fields. However, conventional spatial statistical methods, such as maximum-likelihood estimation and kriging, are impractically time-consuming for large spatial datasets due to the necessary matrix inversions. To cope with this problem, we propose a multi-resolution approximation via linear projection (M-RA-lp). TheM-RA-lp conducts a linear projection approach on each subregion whenever a spatial domain is subdivided, which leads to an approximated covariance function capturing both the large- and small-scale spatial variations. Moreover, we elicit the algorithms for fast computation of the log-likelihood function and predictive distribution with the approximated covariance function obtained by theM-RA-lp. Simulation studies and a real data analysis for air dose rates demonstrate that our proposedM-RA-lp works well relative to the related existing methods.