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Understanding the stochastic partial differential equation approach to smoothing. (English) Zbl 07225437
J. Agric. Biol. Environ. Stat. 25, No. 1, 1-16 (2020); correction ibid. 25, No. 2, 276 (2020).
Summary: 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 [S. N. Wood, Generalized additive models. An introduction with R. 2nd edition. Boca Raton, FL: CRC Press (2017; Zbl 1368.62004)] and stochastic partial differential equations (SPDEs) [F. Lindgren et al., J. R. Stat. Soc., Ser. B, Stat. Methodol. 73, No. 4, 423–498 (2011; Zbl 1274.62360)]. 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.
Reviewer: Reviewer (Berlin)

MSC:
62P12 Applications of statistics to environmental and related topics
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