Understanding the stochastic partial differential equation approach to smoothing
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.
Citation
Miller , D L , Glennie , R & Seaton , A E 2020 , ' Understanding the stochastic partial differential equation approach to smoothing ' , Journal of Agricultural, Biological and Environmental Statistics , vol. 25 , no. 1 , pp. 1-16 . https://doi.org/10.1007/s13253-019-00377-z
Publication
Journal of Agricultural, Biological and Environmental Statistics
Status
Peer reviewed
ISSN
1085-7117Type
Journal article
Description
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.Collections
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