The Mat\'ern model has been a cornerstone of spatial statistics for more than half a century. More recently, the Mat\'ern model has been central to disciplines as diverse as numerical analysis, approximation theory, computational statistics, machine learning, and probability theory. In this article we take a Mat\'ern-based journey across these disciplines. First, we reflect on the importance of the Mat\'ern model for estimation and prediction in spatial statistics, establishing also connections to other disciplines in which the Mat\'ern model has been influential. Then, we position the Mat\'ern model within the literature on big data and scalable computation: the SPDE approach, the Vecchia likelihood approximation, and recent applications in Bayesian computation are all discussed. Finally, we review recent devlopments, including flexible alternatives to the Mat\'ern model, whose performance we compare in terms of estimation, prediction, screening effect, computation, and Sobolev regularity properties.
翻译：半个多世纪以来, Mat\'ern模型一直是空间统计的基石。 最近, Mat\'ern模型一直是数字分析、 近似理论、 计算统计、 机器学习和概率理论等不同学科的核心。 在本篇文章中, 我们从这些学科中进行基于 Mat\'ern 的旅程。 首先, 我们思考了 Mat\'ern 模型对于空间统计中估算和预测的重要性, 也建立了与Mat\'ern 模型具有影响力的其他学科的联系。 然后, 我们把 Mat\'ern 模型放在文献中的大数据和可缩放的计算: SPDE 方法、 Vecchia 概率近似值和Bayesian 计算中最近的应用都得到了讨论。 最后, 我们审视了最近的一些偏差, 包括 Mat\' ern 模型的灵活替代方法, 我们在估算、 预测、 筛选效果、 计算和 Sobolev 常规性方面比较了这些模型的性能。</s>
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