an:07225437
Zbl 7225437
Miller, David L.; Glennie, Richard; Seaton, Andrew E.
Understanding the stochastic partial differential equation approach to smoothing
EN
J. Agric. Biol. Environ. Stat. 25, No. 1, 1-16 (2020); correction ibid. 25, No. 2, 276 (2020).
1085-7117 1537-2693
2020
j
62P12
smoothing; stochastic partial differential equations; generalized additive model; spatial modelling; basis-penalty smoothing
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 [\textit{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) [\textit{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.
1368.62004; 1274.62360