Reich Brian J, Fuentes Montserrat
Department of Statistics, North Carolina State University.
Stat Methodol. 2012;9(1-2):265-274. doi: 10.1016/j.stamet.2011.01.007.
A crucial step in the analysis of spatial data is to estimate the spatial correlation function that determines the relationship between a spatial process at two locations. The standard approach to selecting the appropriate correlation function is to use prior knowledge or exploratory analysis, such as a variogram analysis, to select the correct parametric correlation function. Rather that selecting a particular parametric correlation function, we treat the covariance function as an unknown function to be estimated from the data. We propose a flexible prior for the correlation function to provide robustness to the choice of correlation function. We specify the prior for the correlation function using spectral methods and the Dirichlet process prior, which is a common prior for an unknown distribution function. Our model does not require Gaussian data or spatial locations on a regular grid. The approach is demonstrated using a simulation study as well as an analysis of California air pollution data.
空间数据分析中的一个关键步骤是估计空间相关函数，该函数决定了两个位置处空间过程之间的关系。选择合适相关函数的标准方法是使用先验知识或探索性分析，如变差函数分析，来选择正确的参数化相关函数。我们不是选择特定的参数化相关函数，而是将协方差函数视为一个有待从数据中估计的未知函数。我们为相关函数提出了一种灵活的先验，以增强相关函数选择的稳健性。我们使用谱方法和狄利克雷过程先验（这是未知分布函数的一种常见先验）来指定相关函数的先验。我们的模型不需要高斯数据或规则网格上的空间位置。通过模拟研究以及对加利福尼亚空气污染数据的分析对该方法进行了演示。
