论文标题
大空间数据的贝叶斯非平稳和非参数协方差估计
Bayesian nonstationary and nonparametric covariance estimation for large spatial data
论文作者
论文摘要
在空间统计中，通常假定感兴趣的空间领域是固定的，其协方差具有简单的参数形式，但是这些假设在许多应用中都不适合。给定对高斯空间场的复制观察结果，我们提出了对空间依赖性的非统一和非参数贝叶斯的推断。该想法不是估计协方差矩阵的二次（在空间位置的数量）条目，而是在精密矩阵的稀疏chelesky因子中推断出接近线性的非零条目。我们先前的假设是由在特定订购方案下对这个cholesky因子的条目的指数衰减的最新结果。我们的方法高度可扩展且可行。我们进行数值比较，并将方法应用于气候模型输出，从而实现昂贵的物理模型的统计模拟。
In spatial statistics, it is often assumed that the spatial field of interest is stationary and its covariance has a simple parametric form, but these assumptions are not appropriate in many applications. Given replicate observations of a Gaussian spatial field, we propose nonstationary and nonparametric Bayesian inference on the spatial dependence. Instead of estimating the quadratic (in the number of spatial locations) entries of the covariance matrix, the idea is to infer a near-linear number of nonzero entries in a sparse Cholesky factor of the precision matrix. Our prior assumptions are motivated by recent results on the exponential decay of the entries of this Cholesky factor for Matern-type covariances under a specific ordering scheme. Our methods are highly scalable and parallelizable. We conduct numerical comparisons and apply our methodology to climate-model output, enabling statistical emulation of an expensive physical model.
