论文标题
使用非平稳光谱模拟的大空间数据推断贝叶斯推断
Bayesian Inference for Big Spatial Data Using Non-stationary Spectral Simulation
论文作者
论文摘要
越来越多地理解，对于许多空间过程，平稳性的假设是不现实的。在本文中，我们将维度扩展与光谱方法结合起来，以计算上有效的方式对大型非平稳空间场进行建模。具体而言，我们使用Mejia和Rodriguez-Iturbe（1974）的光谱仿真方法来模拟具有扩展维度的位置的协同图。我们将贝叶斯分层建模引入尺寸扩展，最初仅使用矩方法方法对其进行建模。特别是，我们使用倒塌的Gibbs采样器从后部分布中模拟。我们的方法既是全等级又是非平稳的，并且可以应用于大空间数据，因为它不涉及存储和反转大协方差矩阵。此外，我们的参数比许多其他非平稳空间模型都少。我们使用仿真研究证明了我们方法的广泛适用性，以及使用从国家航空航天局（NASA）获得的臭氧数据的应用。
It is increasingly understood that the assumption of stationarity is unrealistic for many spatial processes. In this article, we combine dimension expansion with a spectral method to model big non-stationary spatial fields in a computationally efficient manner. Specifically, we use Mejia and Rodriguez-Iturbe (1974)'s spectral simulation approach to simulate a spatial process with a covariogram at locations that have an expanded dimension. We introduce Bayesian hierarchical modelling to dimension expansion, which originally has only been modeled using a method of moments approach. In particular, we simulate from the posterior distribution using a collapsed Gibbs sampler. Our method is both full rank and non-stationary, and can be applied to big spatial data because it does not involve storing and inverting large covariance matrices. Additionally, we have fewer parameters than many other non-stationary spatial models. We demonstrate the wide applicability of our approach using a simulation study, and an application using ozone data obtained from the National Aeronautics and Space Administration (NASA).
