Bayesian Nonstationary and Nonparametric Covariance Estimation for Large Spatial Data

IF 4.9 2区 数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
Brian Kidd, M. Katzfuss
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引用次数: 8

Abstract

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.
大空间数据的贝叶斯非平稳和非参数协方差估计
在空间统计学中,通常假设感兴趣的空间场是平稳的,其协方差具有简单的参数形式,但这些假设在许多应用中并不合适。给定高斯空间场的重复观测,我们提出了关于空间相关性的非平稳和非参数贝叶斯推断。与其估计协方差矩阵的二次项(在空间位置的数量上),不如推断精度矩阵的稀疏Cholesky因子中的非零项的近似线性数量。我们先前的假设是由最近关于特定排序方案下Matern型协变量的Cholesky因子项的指数衰减的结果所推动的。我们的方法具有高度可扩展性和可并行性。我们进行数值比较,并将我们的方法应用于气候模型输出,从而能够对昂贵的物理模型进行统计模拟。
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来源期刊
Bayesian Analysis
Bayesian Analysis 数学-数学跨学科应用
CiteScore
6.50
自引率
13.60%
发文量
59
审稿时长
>12 weeks
期刊介绍: Bayesian Analysis is an electronic journal of the International Society for Bayesian Analysis. It seeks to publish a wide range of articles that demonstrate or discuss Bayesian methods in some theoretical or applied context. The journal welcomes submissions involving presentation of new computational and statistical methods; critical reviews and discussions of existing approaches; historical perspectives; description of important scientific or policy application areas; case studies; and methods for experimental design, data collection, data sharing, or data mining. Evaluation of submissions is based on importance of content and effectiveness of communication. Discussion papers are typically chosen by the Editor in Chief, or suggested by an Editor, among the regular submissions. In addition, the Journal encourages individual authors to submit manuscripts for consideration as discussion papers.
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