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Understanding the stochastic partial differential equation approach to smoothing

Research output: Contribution to journalArticle

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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Original languageEnglish
Number of pages16
JournalJournal of Agricultural, Biological and Environmental Statistics
VolumeFirst Online
Early online date19 Sep 2019
DOIs
Publication statusE-pub ahead of print - 19 Sep 2019

    Research areas

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

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