NONSEPARABLE DYNAMIC NEAREST NEIGHBOR GAUSSIAN PROCESS MODELS FOR LARGE SPATIO-TEMPORAL DATA WITH AN APPLICATION TO PARTICULATE MATTER ANALYSIS.
NONSEPARABLE DYNAMIC NEAREST NEIGHBOR GAUSSIAN PROCESS MODELS FOR LARGE SPATIO-TEMPORAL DATA WITH AN APPLICATION TO PARTICULATE MATTER ANALYSIS.
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DOI：
10.1214/16-aoas931
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发表时间：
2016-09
期刊：
影响因子：
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通讯作者：
Schaap M
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文献类型：
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作者：
Datta A;Banerjee S;Finley AO;Hamm NAS;Schaap M
颗粒物（PM）是一类有害的环境污染物，已知对人体健康有害。不同国家旨在控制颗粒物水平的监管工作通常需要高分辨率的时空地图，这些地图能够识别出超过法定浓度限值的危险区域。连续时空高斯过程（GP）模型能够提供描绘预测颗粒物水平的地图，并量化预测的不确定性。然而，基于高斯过程的方法通常会受到大型数据集带来的计算难题的阻碍。我们构建了一类新的可扩展动态最近邻高斯过程（DNNGP）模型，它能够对任何时空高斯过程（例如，具有不可分离协方差结构的）提供一种稀疏近似。我们在此开发的DNNGP可在任何贝叶斯层次模型中用作时空随机效应的诱导稀疏性的先验，以提供完整的后验推断。DNNGP模型的存储和内存需求与数据集大小呈线性关系，从而在不牺牲推断丰富性的情况下实现大规模的可扩展性。大量的数值研究表明，DNNGP对潜在过程的近似比低秩近似要好得多。最后，我们使用DNNGP分析一个大规模的空气质量数据集，结合LOTOS - EUROS化学传输模型（CTMs）大幅提高对欧洲各地颗粒物水平的预测。
Particulate matter (PM) is a class of malicious environmental pollutants known to be detrimental to human health. Regulatory efforts aimed at curbing PM levels in different countries often require high resolution space–time maps that can identify red-flag regions exceeding statutory concentration limits. Continuous spatio-temporal Gaussian Process (GP) models can deliver maps depicting predicted PM levels and quantify predictive uncertainty. However, GP-based approaches are usually thwarted by computational challenges posed by large datasets. We construct a novel class of scalable Dynamic Nearest Neighbor Gaussian Process (DNNGP) models that can provide a sparse approximation to any spatio-temporal GP (e.g., with nonseparable covariance structures). The DNNGP we develop here can be used as a sparsity-inducing prior for spatio-temporal random effects in any Bayesian hierarchical model to deliver full posterior inference. Storage and memory requirements for a DNNGP model are linear in the size of the dataset, thereby delivering massive scalability without sacrificing inferential richness. Extensive numerical studies reveal that the DNNGP provides substantially superior approximations to the underlying process than low-rank approximations. Finally, we use the DNNGP to analyze a massive air quality dataset to substantially improve predictions of PM levels across Europe in conjunction with the LOTOS-EUROS chemistry transport models (CTMs).