Understanding the stochastic partial differential equation approach to smoothing

David L. Miller; Richard Glennie; Andrew E. Seaton

doi:10.1007/s13253-019-00377-z

Understanding the stochastic partial differential equation approach to smoothing

David L. Miller, Richard Glennie, Andrew E. Seaton

Research output: Contribution to journal › Article › peer-review

Abstract

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 in Texts in statistical science, CRC Press, Boca Raton, 2017) and stochastic partial differential equations (SPDEs) (Lindgren et al. in J R Stat Soc Series B (Stat Methodol) 73(4):423–498, 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.

Original language	English
Pages (from-to)	1-16
Number of pages	16
Journal	Journal of Agricultural, Biological and Environmental Statistics
Volume	25
Issue number	1
Early online date	19 Sept 2019
DOIs	https://doi.org/10.1007/s13253-019-00377-z
Publication status	Published - 1 Mar 2020

Keywords

Smoothing
Stochastic partial differential equations
Generalized additive model
Spatial modelling
Basis-penalty smoothing

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10.1007/s13253-019-00377-zLicence: CC BY

Miller_2019_JABES_smoothing_CC
Copyright © The Author(s) 2019. Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Final published version, 569 KBLicence: CC BY

Cite this

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abstract = "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 in Texts in statistical science, CRC Press, Boca Raton, 2017) and stochastic partial differential equations (SPDEs) (Lindgren et al. in J R Stat Soc Series B (Stat Methodol) 73(4):423–498, 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.",

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Understanding the stochastic partial differential equation approach to smoothing

Abstract

Keywords

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