Combining covariance tapering and lasso driven low rank decomposition for the kriging of large spatial datasets
Résumé
Large spatial datasets are becoming ubiquitous in environmental
sciences with the explosion in the amount of data produced by
sensors that monitor and measure the Earth system. Consequently, the
geostatistical analysis of these data requires adequate methods.
Richer datasets lead to more complex modeling but may also prevent
from using classical techniques. Indeed, the kriging predictor is
not straightforwarldly available as it requires the inversion of the
covariance matrix of the data. The challenge of handling such
datasets is therefore to extract the maximum of information they
contain while ensuring the numerical tractability of the associated
inference and prediction algorithms. The different approaches that
have been developed in the literature to address this problem can be
classified into two families, both aiming at making the inversion of
the covariance matrix computationally feasible. The covariance
tapering approach circumvents the problem by enforcing the sparsity
of the covariance matrix, making it invertible in a reasonable
computation time. The second available approach assumes a low rank
representation of the covariance function. While both approaches
have their drawbacks, we propose a way to combine them and benefit
from their advantages. The covariance model is assumed to have the
form low rank plus sparse. The choice of the basis functions
sustaining the low rank component is data driven and is achieved
through a selection procedure, thus alleviating the computational
burden of the low rank part. This model expresses as a spatial
random effects model and the estimation of the parameters is
conducted through a step by step approach treating each scale
separately. The resulting model can account for second order non
stationarity and handle large volumes of data.
Domaines
Statistiques [math.ST]
Origine : Fichiers produits par l'(les) auteur(s)