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MODELING AND EXPLORING MULTIVARIATE SPACE-TIME VARIATION: A GEOSTATISTICAL APPROACH. IN STATISTICAL MONITORING FOR ENVIRONMENTAL ENGINEERING: MODELS AND APPLICATIONS TO THE PROVINCE OF BERGAMO 

Edited by Roberto Colombi and Alessandro Fassò, Bergamo University Press, Edizioni Sestante, Bergamo, in press (2003).

G. Jona Lasinio (1), A. Orasi (2),

(1) Università di Roma "La Sapienza"
(2) Università di Bologna

Abstract
In this paper we briefly illustrate some exploratory techniques born in the geostatistical setting to model multivariate spatial variation and here extended to the space-time framework. Applications to real data are reported in order to clarify the use of the proposed methods. In particular, we are interested in applying univariate geostatistical tools, like variograms, in order to explore the MSRF (Multivariate Space Random Field). The first step in this direction is to represent our dataset in a dimensionally reduced space, while keeping along the analysis the information on the spatial arrangement of observations As a metric we'll use a "variability measure" that takes into account spatial information: a natural choice is the crossvariogram matrix. Then we'll apply a PCA type procedure to the data. As an example of the use of the above mentioned technique we briefly report an application to oceanographic data. 
In the geostatistical approach it is very easy and useful to extend any technique born in the pure spatial setting to space-time dataset, by simply introducing time as a third dimension and then working in Â3 using, with some caution, the same techniques seen in Â2. We apply the proposed technique to an interesting multivariate dataset of rainfall data (and related variables); this dataset has been recently built to evaluate the experimental results of the "Progetto Pioggia" in the Italian region Puglia.
Keywords: Geostatistics, multivariate space-time variation, PCA