This paper focuses on statistical modelling using additive Gaussian process (GP) models and their efficient implementation for large-scale spatio-temporal data with a multi-dimensional grid structure. To achieve this, we exploit the Kronecker product structures of the covariance kernel. While this method has gained popularity in the GP literature, the existing approach is limited to covariance kernels with a tensor product structure and does not allow flexible modelling and selection of interaction effects. This is considered an important component in spatio-temporal analysis. We extend the method to a more general class of additive GP models that accounts for main effects and selected interaction effects. Our approach allows for easy identification and interpretation of interaction effects. The proposed model is applied to the analysis of NO$_2$ concentrations during the COVID-19 lockdown in London. Our scalable method enables analysis of large-scale, hourly-recorded data collected from 59 different stations across the city, providing additional insights to findings from previous research using daily or weekly averaged data.

翻译：本文聚焦于利用加法高斯过程（GP）模型进行统计建模，并针对具有多维网格结构的大规模时空数据实现高效计算方法。为此，我们利用了协方差核的Kronecker乘积结构。尽管该方法在GP文献中已受到广泛关注，但现有方法仅限于具有张量积结构的协方差核，无法灵活建模和选择交互效应，而这在时空分析中被视为重要组成部分。我们将该方法推广至更广泛的加法GP模型类别，该模型涵盖主效应和选定的交互效应。我们所提出的方法能够轻松识别和解释交互效应。该模型被应用于伦敦COVID-19封锁期间NO$_2$浓度的分析。我们的可扩展方法能够对全市59个不同站点收集的大规模每小时记录数据进行分析，从而为先前基于日平均或周平均数据的研究发现提供更多洞见。