Understanding the stochastic partial differential equation approach to smoothing

DLM was funded by OPNAV N45 and the SURTASS LFA Settlement Agreement, being managed by the U.S. Navy's Living Marine Resources program under Contract No. N39430-17-C-1982.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.Publisher PDFPeer reviewe