论文标题
了解平滑的随机部分微分方程方法
Understanding the stochastic partial differential equation approach to smoothing
论文作者
论文摘要
相关性和平滑度用于描述各种随机数量。在及时，空间和许多其他领域，它们都暗示着相同的想法：近距离发生的数量比进一步分开的数量更相似。代表这一想法的两个流行统计模型是基础弱小的Smoothers（Wood，2017）和随机部分微分方程（SPDE）（Lindgren等，2011）。在本文中，我们讨论了如何将SPDE解释为平滑惩罚，并可以使用R软件包MGCV安装，从而使具有平滑惩罚知识的实践者可以更好地了解SPDE方法背后的实现和理论。
Correlation and smoothness are terms used to describe a wide variety of random quantities. In time, space, and many other domains, they both imply the same idea: quantities that occur closer together are more similar than those further apart. Two popular statistical models that represent this idea are basis-penalty smoothers (Wood, 2017) and stochastic partial differential equations (SPDE) (Lindgren et al., 2011). In this paper, we discuss how the SPDE can be interpreted as a smoothing penalty and can be fitted using the R package mgcv, allowing practitioners with existing knowledge of smoothing penalties to better understand the implementation and theory behind the SPDE approach.
