论文标题
大型空间数据集的线性投影的多分辨率近似
A multi-resolution approximation via linear projection for large spatial datasets
论文作者
论文摘要
收集空间数据的最新技术进步一直在增加对分析大空间数据集的方法的需求。这些类型的数据集的统计分析可以在各个领域提供有用的知识。但是，由于必要的矩阵倒置，对于大型空间数据集的常规空间统计方法（例如最大似然估计和KRIGING）在不切实际的时间上耗时。为了解决这个问题，我们通过线性投影（$ M $ -RA-LP）提出了多分辨率近似。每当将空间结构域细分时，$ M $ -RA-LP都会在每个子区域进行线性投影方法，从而导致近似的协方差函数捕获大小空间变化。此外，我们通过通过$ M $ -RA-LP获得的近似协方差函数来快速计算对数可能的函数和预测分布的算法。仿真研究和空气剂量率的真实数据分析表明，我们提出的$ M $ -RA-LP相对于相关的现有方法很好地工作。
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). The $M$-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 the $M$-RA-lp. Simulation studies and a real data analysis for air dose rates demonstrate that our proposed $M$-RA-lp works well relative to the related existing methods.
