Deep neural network models have become ubiquitous in recent years, and have been applied to nearly all areas of science, engineering, and industry. These models are particularly useful for data that have strong dependencies in space (e.g., images) and time (e.g., sequences). Indeed, deep models have also been extensively used by the statistical community to model spatial and spatio-temporal data through, for example, the use of multi-level Bayesian hierarchical models and deep Gaussian processes. In this review, we first present an overview of traditional statistical and machine learning perspectives for modeling spatial and spatio-temporal data, and then focus on a variety of hybrid models that have recently been developed for latent process, data, and parameter specifications. These hybrid models integrate statistical modeling ideas with deep neural network models in order to take advantage of the strengths of each modeling paradigm. We conclude by giving an overview of computational technologies that have proven useful for these hybrid models, and with a brief discussion on future research directions.

翻译：近年来,深神经网络模型已变得无处不在,并已应用于几乎所有科学、工程和工业领域。这些模型对于空间(例如图像)和时间(例如序列)高度依赖的数据特别有用。事实上,统计界也广泛使用深模型来模拟空间和时空数据,例如通过使用多层次贝叶斯等级模型和深层高斯进程。在本次审查中,我们首先概述了空间和时空数据建模的传统统计和机器学习视角,然后侧重于最近为潜在过程、数据和参数规格开发的各种混合模型。这些混合模型将统计模型想法与深线性网络模型结合起来,以便利用每个模型的优势。我们最后概述了已证明对这些混合模型有用的计算技术,并简要讨论了未来的研究方向。