A Fused Gaussian Process Model for Very Large Spatial Data

With the development of new remote sensing technology, large or even massive spatial datasets covering the globe become available. Statistical analysis of such data is challenging. This article proposes a semiparametric approach to model large or massive spatial datasets. In particular, a Gaussian process with additive components is proposed, with its covariance structure consisting of two components: one component is flexible without assuming a specific parametric covariance function but is able to achieve dimension reduction; the other is parametric and simultaneously induces sparsity. The inference algorithm for parameter estimation and spatial prediction is devised. The resulting spatial prediction methodology that we call fused Gaussian process (FGP), is applied to simulated data and a massive satellite dataset. The results demonstrate the computational and inferential benefits of FGP over competing methods and show that FGP is robust against model misspecification and captures spatial nonstationarity. Supplementary materials for this article are available online.

随着新型遥感技术的发展，覆盖全球的大型乃至超大规模空间数据集已逐步可用。对此类数据开展统计分析颇具挑战。本文提出一种半参数方法，用于对大型乃至超大规模空间数据集进行建模。具体而言，本文提出一种带加性分量的高斯过程（Gaussian Process）模型，其协方差结构包含两个分量：其一具备灵活性，无需预设特定参数化协方差函数，同时可实现维度约简；其二为参数化分量，可同时诱导稀疏性。本文设计了用于参数估计与空间预测的推断算法。本文将所提出的空间预测方法命名为融合高斯过程（Fused Gaussian Process, FGP），并将其应用于模拟数据与超大规模卫星数据集。实验结果表明，相较于同类竞争方法，FGP在计算与推断层面均具备优势；同时FGP对模型误设定具备鲁棒性，且可捕捉空间非平稳性特征。本文的补充材料可在线获取。