Contributions à la modélisation et à l'inférence des fonctions aléatoires non-stationnaires de second ordre

Abstract : Stationary Random Functions have been sucessfully applied in geostatistical applications for decades. The underlying spatial dependence structure of the Random Function is represented by a stationary variogram or covariance. However, in some instances, there is little reason to expect the spatial dependence structure to be stationary over the whole region of interest. In this manuscript, two non-stationary modelling approaches for Random Functions are considered: space deformation and stochastic convolution. For each of them, we develop a statistical methodology for estimating the non-stationary spatial dependence structure, in the context of a single realization. Moreover, we also show how spatial predictions and conditional simulations can be carried out in this non-stationary framework. The developed inference methods allow to capture varying spatial structures while guaranteeing the global consistency of the final model. The assessment of their performance on both synthetic and real datasets show that they outperform stationary method, according to several criteria. Beyond the prediction, they can also serve as a tool for exploratory analysis of the non-stationarity.
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Migraine Francky Fouedjio Kameni. Contributions à la modélisation et à l'inférence des fonctions aléatoires non-stationnaires de second ordre. Méthodologie [stat.ME]. Ecole Nationale Supérieure des Mines de Paris, 2014. Français. ⟨NNT : 2014ENMP0040⟩. ⟨tel-01139460⟩

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