, Finite-dimensional approximation of additive Gaussian processes
, 82 6.2.2 Conditioning to interpolation and inequality constraints 83 6.2.3 Numerical illustrations
, Future, p.89
Additivity per blocks in 3D, p.91 ,
,
, Contents
, Covariance parameter estimation under inequality constraints
, Asymptotic consistency of maximum likelihood estimators
,
, Asymptotic normality of maximum likelihood estimators
Variance parameter estimation, p.105 ,
, Microergodic parameter estimation for the isotropic Matérn model
, 5 2D application: nuclear safety criticality, p.110
,
, 120 8.3.1 Approximation of Gaussian processes in 1D
123 8.4.1 Metropolis-Hastings algorithm with truncated Gaussian proposals ,
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, Modélisation par Processus Gaussiens sous Contraintes d'Inégalité Spécialité : Mathématiques Appliquées Mots clefs : Méthodes d'Inférence Bayésienne, Processus Gaussiens, Métamodélisation sous Contraintes d'Inégalité
, Nous remarquons que l'introduction d'un bruit d'observations permet de monterà la dimension cinq. Nous proposons un algorithme d'insertion des noeuds, qui concentre le budget de calcul sur les dimensions les plus actives. Nous explorons aussi la triangulation de Delaunay comme alternativeà la tensorisation. Enfin, nousétudions l'utilisation de modèles additifs dans ce contexte, théoriquement et sur des problèmes de plusieurs centaines de variables. Troisièmement, nous donnons des résultats théoriques sur l'inférence sous contraintes d'inégalité. La consistance et la normalité asymptotique d'estimateurs par maximum de vraisemblance sontétablies. L'ensemble des travaux a fait l'objet d'un développement logiciel en R. Ils sont appliquésà des problèmes de gestion des risques en sûreté nucléaire et inondations côtières, Le conditionnement de Processus Gaussiens (PG) par des contraintes d'inégalité permet d'obtenir des modèles plus réalistes. Cette thèse s'intéresse au modèle de type PG proposé par Maatouk, 2015.