Conjugate sparse plus low rank models for efficient Bayesian interpolation of large spatial data
Conjugate sparse plus low rank models for efficient Bayesian interpolation of large spatial data
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DOI：
10.1002/env.2748
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发表时间：
2022-08
期刊：
影响因子：
1.7
通讯作者：
Shinichiro Shirota;A. Finley;B. Cook;Sudipto Banerjee
中科院分区：
文献类型：
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作者：
Shinichiro Shirota;A. Finley;B. Cook;Sudipto Banerjee
空间数据科学的一个关键挑战是对大量空间引用数据集的分析。这种分析通常从高斯过程规范出发，它可以产生丰富而稳健的推理，但涉及密集的协方差矩阵，缺乏计算上可利用的结构。空间统计的最新发展提供了各种大规模可扩展的方法。特别是贝叶斯推理和层次模型，由于其在适应空间过程方面的丰富性和灵活性而受到欢迎。我们目前的贡献是为使用可扩展空间过程的大量数据集的空间插值提供计算效率高的精确算法。我们将低秩高斯过程与高效稀疏逼近相结合。根据Zhang等人（2019）最近的工作，我们使用高斯预测过程（GPP）和残差过程作为稀疏性诱导的最近邻高斯过程（NNGP）对低秩过程进行建模。这里的一个关键贡献是使用精确的共轭贝叶斯建模来实现这些模型，以避免昂贵的迭代算法。通过仿真研究，我们评估了该方法的性能和模型的鲁棒性，特别是对于长期预测。我们将我们的方法用于在阿拉斯加内陆偏远地区的美国林务局Tanana库存单元（TIU）收集的遥感光探测和测距（LiDAR）数据。
A key challenge in spatial data science is the analysis for massive spatially‐referenced data sets. Such analyses often proceed from Gaussian process specifications that can produce rich and robust inference, but involve dense covariance matrices that lack computationally exploitable structures. Recent developments in spatial statistics offer a variety of massively scalable approaches. Bayesian inference and hierarchical models, in particular, have gained popularity due to their richness and flexibility in accommodating spatial processes. Our current contribution is to provide computationally efficient exact algorithms for spatial interpolation of massive data sets using scalable spatial processes. We combine low‐rank Gaussian processes with efficient sparse approximations. Following recent work by Zhang et al. (2019), we model the low‐rank process using a Gaussian predictive process (GPP) and the residual process as a sparsity‐inducing nearest‐neighbor Gaussian process (NNGP). A key contribution here is to implement these models using exact conjugate Bayesian modeling to avoid expensive iterative algorithms. Through the simulation studies, we evaluate performance of the proposed approach and the robustness of our models, especially for long range prediction. We implement our approaches for remotely sensed light detection and ranging (LiDAR) data collected over the US Forest Service Tanana Inventory Unit (TIU) in a remote portion of Interior Alaska.