Computational advances for spatio-temporal multivariate environmental models

In multivariate Geostatistics, the linear coregionalization model (LCM) has been widely used over the last decades, in order to describe the spatial dependence which characterizes two or more variables of interest. However, in spatio-temporal multiple modeling, the identification of the main elements of a space–time linear coregionalization model (ST-LCM), as well as of the latent structures underlying the analyzed phenomenon, represents a tough task. In this paper, some computational advances which support the selection of an ST-LCM are described, gathering all the necessary steps which allow the analyst to easily and properly detect the basic space–time components for the phenomenon under study. The implemented algorithm is applied on space–time air quality data measured in Scotland in 2017.

[1]  Bert Brunekreef,et al.  Association between mortality and indicators of traffic-related air pollution in the Netherlands: a cohort study , 2002, The Lancet.

[2]  Kazimierz Malanowski,et al.  The Lagrange-Newton method for nonlinear optimal control problems , 1993, Comput. Optim. Appl..

[3]  Bo Li,et al.  Testing the covariance structure of multivariate random fields , 2008 .

[4]  D. E. Myers,et al.  The Linear Coregionalization Model and the Product–Sum Space–Time Variogram , 2003 .

[5]  T. Gneiting,et al.  Matérn Cross-Covariance Functions for Multivariate Random Fields , 2010 .

[6]  Xavier Emery,et al.  Iterative algorithms for fitting a linear model of coregionalization , 2010, Comput. Geosci..

[7]  T. Gneiting.  Nonseparable, Stationary Covariance Functions for Space–Time Data , 2002 .

[8]  On the Flexibility of Multivariate Covariance Models: Comment on the Paper by Genton and Kleiber , 2015, 1507.08386.

[9]  S. De Iaco,et al.  FORTRAN programs for space-time multivariate modeling and prediction , 2010, Comput. Geosci..

[10]  S. De Iaco,et al.  Towards an automatic procedure for modeling multivariate space-time data , 2012, Comput. Geosci..

[11]  D. Harville.  Matrix Algebra From a Statistician's Perspective , 1998 .

[12]  D. Posa,et al.  Testing the type of non-separability and some classes of space-time covariance function models , 2017, Stochastic Environmental Research and Risk Assessment.

[13]  Clayton V. Deutsch,et al.  An intrinsic model of coregionalization that solves variance inflation in collocated cokriging , 2009, Comput. Geosci..

[14]  Donato Posa,et al.  Characteristics of some classes of space–time covariance functions , 2013 .

[15]  D. Myers,et al.  Space–time analysis using a general product–sum model , 2001 .

[16]  Richard A. Davis,et al.  Time Series: Theory and Methods , 2013 .

[17]  Klaus Nordhausen,et al.  Blind Source Separation Based on Joint Diagonalization in R: The Packages JADE and BSSasymp , 2017 .

[18]  D. Posa,et al.  Choosing suitable linear coregionalization models for spatio-temporal data , 2019, Stochastic Environmental Research and Risk Assessment.

[19]  Donato Posa,et al.  Positive and negative non-separability for space–time covariance models , 2013 .

[20]  Michael Sherman,et al.  A Nonparametric Assessment of Properties of Space–Time Covariance Functions , 2007 .

[21]  Antoine Souloumiac,et al.  Jacobi Angles for Simultaneous Diagonalization , 1996, SIAM J. Matrix Anal. Appl..

[22]  Marc G. Genton,et al.  Cross-Covariance Functions for Multivariate Geostatistics , 2015, 1507.08017.

[23]  Claudia Cappello,et al.  covatest: An R Package for Selecting a Class of Space-Time Covariance Functions , 2020, Journal of Statistical Software.

[24]  J. Nath,et al.  Effects of Nitrogen Dioxide on the Expression of Intercellular Adhesion Molecule-1, Neutrophil Adhesion, and Cytotoxicity: Studies in Human Bronchial Epithelial Cells , 2007, Inhalation toxicology.

[25]  S. De Iaco,et al.  Isotropy, symmetry, separability and strict positive definiteness for covariance functions: A critical review , 2019, Spatial Statistics.