Flexible Spatio-Temporal Smoothing with Array Methods
Dae-Jin Lee
Department of Statistics, Universidad Carlos III de Madrid, Leganes, Madrid, Spain

In recent years, spatio-temporal modelling has become a challenging area of research in many fields (e.g. epidemiology, environmental studies, and disease mapping). However, most of the models developed are constrained by the large amoun of data available. Smoothing methods present very attractive and flexible modelling tools for this type of data set.

In the context of environmental studies, where data often present a strong seasonal trend, and the interaction of spatial and temporal processes may be strong, the size of the regression basis needed to capture the temporal trend is large and, as a consequence, the estimation of the spatio-temporal interaction is computationally intensive.

We propose the use of Penalized Splines as mixed models for smoothing spatio-temporal data. The array properties of the regression bases allow us to fit Smooth-ANOVA-type models, imposing identifiability constraints over the coefficients. These models are fitted taking advantage of the array structure of the space-time interaction and the use of the GLAM (generalized linear array methods) algorithms. We illustrate the methodology with the analysis of real environmental problems.

Keywords: Spatio-temporal data; Penalized splines; Mixed models; GLAM

Biography: Dae-Jin Lee obtained his PhD. degree in the Department of Statistics of University Carlos III de Madrid in 2010. His research topics are: multidimensional smoothing methods, spatial statistics, spatio-temporal modelling and mixed models, with applications in environmental problems, disease mapping and mortality. Since 2011, he holds a postdoctoral position at CSIRO (Commonwealth Scientific and Research Organization) at the Division of Mathemathics, Informatics and Statistics.