Journées MAS de la SMAI
Modèles Spatiaux
Lille, 4 - 6 septembre 2006

Carlo GAETAN

Recent advances in modelling of Spatio-Temporal Processes

In recent years there has been a growth in the statistical models and techniques to analyse spatio-temporal data. Spatio-temporal data arise in many contexts e.g. disease mapping and air-pollution monitoring. One of the primary interests in analysing such data are to smooth and predict time evolution of some response variables over a certain spatial domain. Examples of spatio-temporal data sets are very large and require careful attentions to the computational burden.

This talk provides a review of recent advances in modelling spatio-temporal data. We first describe the primary spatio-temporal data types that arises in different contexts in an attempt to unify the modelling strategies. After that we focus on general models for point reference data and we distinguish two approaches. The geostatistical approach has been developed for random function models in continuous space and time and is based on a limited number of spatially and/or temporally dispersed observations. The approach focus on covariances structures for patio-temporal random functions. In the lecture we review some results about separability and full symmetry.

However, other spatio-temporal domains are also relevant in practise. Monitoring data are frequently observed at fixed temporal lags, and it may suffice to model a random function where the time is considered discrete. We illustrate some promising models in this direction and we discuss the relative merits of a hierarchical Bayesian approach.

Finally we switch on areal or block level data where the region is partitioned into a finite number of areal units with well defined boundaries, e.g. postcodes, counties or districts etc. Here an observation is thought to be associated with an areal unit of non-zero volume rather than a particular location point and we present a spatio-temporal model for epidemic which combines previous ideas.

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