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Understanding the Stochastic Partial Differential Equation Approach to Smoothing


  • David L. Miller

    () (University of St Andrews)

  • Richard Glennie

    (University of St Andrews)

  • Andrew E. Seaton

    (University of St Andrews)


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. Supplementary materials accompanying this paper appear online.

Suggested Citation

  • David L. Miller & Richard Glennie & Andrew E. Seaton, 2020. "Understanding the Stochastic Partial Differential Equation Approach to Smoothing," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 25(1), pages 1-16, March.
  • Handle: RePEc:spr:jagbes:v:25:y:2020:i:1:d:10.1007_s13253-019-00377-z
    DOI: 10.1007/s13253-019-00377-z

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    References listed on IDEAS

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