Latent variables and space-time models for environmental problems

Abstract

During the conference of the Italian Statistical Society on ‘‘Advances in Latent Variables’’ held in Brescia, Italy, June 19–21, 2013, the working group on environmental statistics, named GRASPA (http://www.graspa.org), organized the special track on ‘‘Space and space-time models: methods and environmental applications’’. This scientific activity was intended to celebrate the new condition as a permanent group of the Italian statistical society and renew GRASPA’s long life, which dates back to 1989. The idea of a special issue on the track main theme arose considering not only the number and scientific quality of the track contributions, but also the general interest of the topic, which exceeds the conference coverage. The result, raising from both track attendance and space-time statistical scientific community, is an interesting blend of various topics, which amounts at fourteen papers covering various environmental problems. To a large extent climate problems are considered, including upper atmosphere monitoring, rain simulation, air and water temperature and sea currents. Moreover, applications considered water body ecology, seismology and radon emissions. From the methodological point of view, areas covered by the special issue are scalar and vector-valued stochastic processes with continuous index over space or over spacetime. Moreover, functional data, point processes and time series methods are taken into account. Latent variables enter in a natural way in many of these papers either as spatial or temporal components. This methodological key is loosely used in the rest of this editorial to briefly review the special issue contributions. As for spatial processes methods, the work by RuizMedina and Porcu (2014) puts the theoretical basis for understanding the equivalence of Gaussian measures that index multivariate Gaussian fields. Their work will open the lines for research in estimation of Gaussian fields through tapering techniques as well as for assessing the properties of estimators of spatial dependence under infill asymptotics. For binary spatial data, which are built on the basis of a truncated latent Gaussian model, Bevilacqua et al. (2014) explore the possibility of building Euclidean likelihoods, obtaining high computational benefits and ensuring a reasonable level of statistical efficiency. In the same framework of spatial data, Verdin et al. (2014) introduce a stochastic weather generator for the variables of minimum and maximum temperature, as well as precipitation occurrence. In particular, temperature variables are modeled in a vector autoregressive framework, conditional on precipitation occurrence, whilst this last arises via a probit model. Both temperature and occurrence are spatially correlated using spatial Gaussian processes. Fontanella et al. (2014) consider a generalized latent-spatialquantile regression (GLSQR) model for the understanding of indoor radon gas monitoring in central Italy. Vallejo et al. (2014) consider a method for image landscape classification based on the assumption that the vector of image bands is a spatial multivariate process. They build such classification using the divergence of a modified Mahalanobis distance, given by the codispersion matrix. Methods for space-time processes are faced with great detail in this issue. If spatial design represents a critical issue, the paper by Stehlik et al. (2014) gives a clear picture A. Fasso (&) University of Bergamo, Viale Marconi 5, 24044 Dalmine BG, Italy e-mail: alessandro.fasso@unibg.it