17:00 18:00 
Emilio Porcu University of Newcastle (Upon Tyne, UK) and University Federico Santa Maria Valparaiso (Chile)
Modeling Temporally Evolving and Spatially Globally Dependent Data
Abstract: The last decades have seen an unprecedented increase in the availability of data sets that are inherently global and temporally evolving, from remotely sensed networks to climate model ensembles. This paper provides a view of statistical modeling techniques for spacetime processes, where space is the sphere representing our planet. In particular, we make a distintion between (a) second orderbased, and (b) practical approaches to model temporally evolving global processes. The former are based on the specification of a class of spacetime covariance functions, with space being the twodimensional sphere. The latter are based on explicit description of the dynamics of the spacetime process, i.e., by specifying its evolution as a function of its past history with added spatially dependent noise. We especially focus on approach (a), where the literature has been sparse. We provide new models of spacetime covariance functions for random fields defined on spheres cross time. Practical approaches, (b), are also discussed, with special emphasis on models built directly on the sphere, without projecting the spherical coordinate on the plane. We present a case study focused on the analysis of air pollution from the 2015 wildfires in Equatorial Asia, an event which was classified as the year’s worst environmental disaster. The paper finishes with a list of the main theoretical and applied research problems in the area, where we expect the statistical community to engage over the next decade.
