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ÉDITIONS UNIVERSITAIRES EUROPÉENNES Régression bayésienne sous contraintes de régularité et de forme: De la théorie de la régression bayésienne avec B-splines sous contraintes à l’implémentation par les méthodes MCMC (Omn.Univ.Europ.)

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£41.00 £16.74 £22.04 £27.33 £32.62 £37.91 £43.21 25 July 2026 11 August 2026 28 August 2026 14 September 2026 02 October 2026
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Description

Nous étudions la régression bayésienne avec B-splines sous contraintes de régularité et de forme. Nous démontrons que la forme d'une spline engendrée par une base de B-spline est contrôlée par un ensemble de points de contrôle qui ne sont pas situés sur la courbe de la spline. On propose différents types de contraintes de forme (monotonie, unimodalité, convexité, etc). Nous démontrons également que lorsque le nombres de nœuds tend vers l'infini, l'adhérence des contraintes de monotonie, de l'unimodalité et de l'unimodalité concave approche respectivement les fonctions monotone, unimodale et unimodale concave. Ces contraintes sont prises en compte grâce à la loi a priori. Nous estimons la fonction de régression par le mode a posteriori. Un algorithme de type recuit simulé a permis de calculer le mode a posteriori. La convergence des algorithmes de simulations et du calcul de l'estimateur est prouvée. En particulier, quand les nœuds des B-splines sont variables, l'analyse bayésienne de la régression sous contrainte devient complexe. On propose des schémas de simulations originaux permettant de générer suivant la loi a posteriori lorsque le posterior est de dimensions variables.

Product Specifications

Format
paperback
Domain
Amazon UK
Release Date
23 December 2011
Listed Since
24 December 2011

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