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 spatiotemporal data through, for example, the use of multilevel 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 spatiotemporal 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.

中文翻译：

---

空间和时空数据的统计深度学习


近年来，深度神经网络模型变得无处不在，并已应用于科学、工程和工业的几乎所有领域。这些模型对于在空间（例如图像）和时间（例如序列）方面具有很强依赖性的数据特别有用。事实上，深度模型也被统计界广泛用于对空间和时空数据进行建模，例如，通过使用多级贝叶斯分层模型和深度高斯过程。在这篇综述中，我们首先概述了用于空间和时空数据建模的传统统计和机器学习视角，然后重点介绍了最近为潜在过程、数据和参数规范开发的各种混合模型。这些混合模型将统计建模思想与深度神经网络模型集成在一起，以利用每种建模范例的优势。最后，我们概述了已被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。