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 Mejía and Rodríguez-Iturbe’s (1974) spectral simulation approach to simulate a spatial process with a covariogram at locations that have an expanded dimension. We introduce Bayesian hierarchical modeling to dimension expansion, which originally has only been modeled using a method of moments approach. We consider a novel scheme to re-weight levels in a Bayesian spatial hierarchical model that allows one to use non-stationary spectral simulation within 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. We demonstrate the wide applicability of our approach through simulation studies, and an application using ozone data obtained from the National Aeronautics and Space Administration (NASA).

人们日益理解，平稳性的假设对于许多空间过程而言都是不现实的。在本文中，我们将维数扩展与频谱方法结合起来，以有效的计算方式对大型非平稳空间场进行建模。具体来说，我们使用Mejía和Rodríguez-Iturbe（1974）的光谱模拟方法来模拟具有协方差图的空间过程，该位置具有扩展的维数。我们将贝叶斯层次建模引入维数扩展，该维数扩展最初仅使用矩量法进行建模。我们考虑了一种在Bayes空间层次模型中重新加权级别的新颖方案，该方案允许人们在折叠的Gibbs采样器内使用非平稳频谱模拟。我们的方法是完全固定的和非固定的，并可以应用于大空间数据，因为它不涉及存储和求逆大协方差矩阵。我们通过模拟研究证明了我们的方法的广泛适用性，并使用了从美国国家航空航天局（NASA）获得的臭氧数据进行的应用。