Understanding the Stochastic Partial Differential Equation Approach to Smoothing

David L. Miller (), Richard Glennie and Andrew E. Seaton
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David L. Miller: University of St Andrews
Richard Glennie: University of St Andrews
Andrew E. Seaton: University of St Andrews

Journal of Agricultural, Biological and Environmental Statistics, 2020, vol. 25, issue 1, No 1, 16 pages

Abstract: 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. Supplementary materials accompanying this paper appear online.

Keywords: Smoothing; Stochastic partial differential equations; Generalized additive model; Spatial modelling; Basis-penalty smoothing (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13253-019-00377-z

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