Dans le contexte de la théorie bayésienne et de théorie de la décision, l'estimation d'une densité prédictive d'une variable aléatoire occupe une place importante. Typiquement, dans un cadre paramétrique, il y a présence d’information additionnelle pouvant être interprétée sous forme d’une contrainte. Cette thèse porte sur des stratégies et des améliorations, tenant compte de l’information additionnelle, pour obtenir des densités prédictives efficaces et parfois plus performantes que d’autres données dans la littérature. Les résultats s’appliquent pour des modèles avec données gaussiennes avec ou sans une variance connue. Nous décrivons des densités prédictives bayésiennes pour les coûts Kullback-Leibler, Hellinger, Kullback-Leibler inversé, ainsi que pour des coûts du type $\alpha-$divergence et établissons des liens avec les familles de lois de probabilité du type \textit{skew--normal}. Nous obtenons des résultats de dominance faisant intervenir plusieurs techniques, dont l’expansion de la variance, les fonctions de coût duaux en estimation ponctuelle, l’estimation sous contraintes et l’estimation de Stein. Enfin, nous obtenons un résultat général pour l’estimation bayésienne d’un rapport de deux densités provenant de familles exponentielles. / Abstract: In the context of Bayesian theory and decision theory, the estimation of a predictive density of a random variable represents an important and challenging problem. Typically, in a parametric framework, usually there exists some additional information that can be interpreted as constraints. This thesis deals with strategies and improvements that take into account the additional information, in order to obtain effective and sometimes better performing predictive densities than others in the literature. The results apply to normal models with a known or unknown variance. We describe Bayesian predictive densities for Kullback--Leibler, Hellinger, reverse Kullback-Leibler losses as well as for α--divergence losses and establish links with skew--normal densities. We obtain dominance results using several techniques, including expansion of variance, dual loss functions in point estimation, restricted parameter space estimation, and Stein estimation. Finally, we obtain a general result for the Bayesian estimator of a ratio of two exponential family densities.

Made available in DSpace on 2016-06-02T20:05:58Z (GMT). No. of bitstreams: 1 DissLGGBL.pdf: 694668 bytes, checksum: fbe25c1e4093e12425b0a024c8a95456 (MD5) Previous issue date: 2007-01-11 / Financiadora de Estudos e Projetos / We present a general introduction in the construction of experimental design, spe- cially a general factorial design and factorial design 2k and some Bayesian criteria in the construction of experimental design. In practice, usually the researcher can have a priori knowledge of specialists for estimated quantities from an experiment. The use of Bayesian methods can take on best results with low costs. Many Bayesian criteria in- troduced in literature are presented. One of the main applications in the experimental design construction involve the existance of linear trends with objective of verifying the best sequence of runs, specially the factorial designs with eight runs. In this disertation, we introduce some basic concepts in design of experiments and the use of the Bayesian approach to have more e¢ cient and less cost experiments. The main goal of the work, is to consider a special case of great importance in applied indistrial work: the presence of linear trend. In this case, we present a comparative study in design of experiments under the classical and Bayesian approaches. / Inicialmente apresentamos uma introdução geral sobre planejamentos de experimen- tos, em especial, o planejamento fatorial geral e o planejamento fatorial 2k, e alguns critérios Bayesianos na construção de planejamentos de experimentos. Na prática, usual- mente o pesquisador pode ter conhecimento a priori de especialistas das quantidades a serem estimadas, a partir de um experimento. O uso de métodos Bayesianos pode levar à melhores resultados com menores custos. Vários critérios Bayesianos introduzidos na liter- atura são apresentados. Algumas aplicações são consideradas para ilustrar a metodologia proposta. Uma das principais aplicações na construção de um planejamento de exper- imentos envolve a presença de tendências lineares com o objetivo de verificar a melhor seqüência possível de ensaios, em especial o planejamento fatorial com oito ensaios. Nesta dissertação, pretendemos introduzir alguns conceitos básicos em planejamen- tos de experimentos e o uso do enfoque Bayesiano que leva à experimentos com melhor eficiência e menores custos. Como objetivo principal de trabalho, vamos considerar um caso especial de grande importância nas aplicações industriais: a presença de tendên- cias lineares. Neste caso, vamos apresentar um estudo comparativo em planejamento de experimentos clássicos e planejamento de experimentos Bayesianos.