Understanding the stochastic partial differential equation approach to smoothing

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

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


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 languageEnglish
Pages (from-to)1-16
Number of pages16
JournalJournal of Agricultural, Biological and Environmental Statistics
Issue number1
Early online date19 Sept 2019
Publication statusPublished - 1 Mar 2020


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


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