FORTRAN programs for space–time multivariate modeling and prediction

Advances in Spatio-Temporal Modeling and Prediction for Environmental Risk Assessment

“…In other words, for each coregionalized variable Z i ,withi = 1,...,p,a STIRF I i can be appropriately defined. Then the linear spatio-temporal predictor (27) can be easily written in terms of the indicator random variables I i , i = 1,...,p. If the spatio-temporal correlation structure of a MSTIRF is modelled by using the spatio-temporal LCM,b a s e d on the product-sum, the new GSLib routine "COK2ST" [12] can be used to produce risk assessment maps, for one or all the variables under study. If p = 1, the dependence of the indicator variable is characterized by the corresponding indicator variogram of I:…”

“…The new GSLib routine "COK2ST" [12] produces multivariate predictions in space-time, for one or all the variables under study, using the spatio-temporal LCM (20) where the basic spatio-temporal variograms are modelled as generalized product-sum variograms. An application is also given in [11].…”

“…In the last years, a new GSLib routine, called "COK2ST", can be used to make predictions in the domain under study, utilizing the spatio-temporal LCM, based on the generalized product-sum model [12]. This routine could be merged with the automatic procedure for fitting the spatio-temporal LCM using the product-sum variogram model, presented in [15], in order to provide a complete and helpful package for the analyst who needs to obtain predictions in a spatio-temporal multivariate context.…”

“…By using a recent fitting procedure [16], based on the simultaneous diagonalization of several symmetric real-valued matrix variograms, the basic structures of the spatio-temporal LCM which describes the spatio-temporal correlation among the variables, have been easily detected. Predictions of the primary variable (PM 10 ) are obtained by using a modified GSLib program, called "COK2ST" [12]. Then, risk maps showing the probability that the particle pollution exceeds the national law limit have been associated to predition maps and the estimation of the probability distributions for two sites of interest have been produced.…”

“…The maximum likelihood estimation of heterotopic spatio-temporal models with spatial LCM components and temporal dynamics was developed by [22]. A GSLib [19] routine for cokriging was properly modified in [12] to incorporate the spatio-temporal LCM, previously developed using the generalized product-sum variogram model [10]. Recently, in [15] an automatic procedure for fitting the spatio-temporal LCM using the product-sum variogram model has been presented and some computational aspects, analytically described by a main flow-chart, have been discussed.…”