Cette dissertation de doctorat développe des théories de l'influence sociale dynamique. Dans un cadre dynamique, les individus interagissent à plusieurs reprises avec leur environnement social et échangent leurs croyances et opinions sur différentes questions économiques, politiques et sociales. Dans le Chapitre 2, nous étudions les processus d'influence modélisés par les moyennes ordonnées pondérées. Ces dernières sont anonymes : elles ne dépendent que du nombre d'agents qui partagent la même croyance. Nous exhibons une condition nécessaire et suffisante pour la convergence au consensus et caractérisons les résultats où la société se retrouve polarisée. Enfin, nous appliquons nos résultats aux quantificateurs linguistiques flous. Dans le Chapitre 3, nous introduisons la possibilité de manipulation dans le modèle de DeGroot (1974). Nous montrons que la manipulation peut modifier la structure de confiance et mène à une société connectée. La manipulation promeut le leadership d'opinion, mais même l'agent manipulé peut gagner de l'influence sur les croyances à long terme. Finalement, nous étudions la tension entre l'agrégation d'informations et le déploiement de désinformations. Dans le Chapitre 4, nous introduisons des conflits d'intérêt dans un modèle de dynamique de croyance non-bayésienne. Les agents se rencontrent avec leurs voisins dans le réseau social et échangent des informations stratégiquement. Avec des conflits d'intérêt, la dynamique de croyance ne converge pas en général: la croyance de chaque agent converge vers un certain intervalle et continue à fluctuer sur celui-ci pour toujours. / This Ph.D. dissertation develops theories of dynamic social influence. In a dynamic framework, individuals internet repeatedly with their social environment and exchange beliefs and opinions on various economic, political and social issues. In Chapter 2, we study influence processes modeled by ordered weighted averaging operators. These operators an anonymous: they only depend on how many agents share a belief. We find a necessary and sufficient condition for convergence to consensus and characterize outcomes where the society ends up polarized. Furthermore, we apply our results to fuzzy linguistic quantifiers. ln Chapter 3, we introduce the possibility of manipulation into the model by DeGroot (1974). We show that manipulation can modify the trust structure and lead to a connected society. Manipulation fosters opinion leadership, but the manipulated agent may even gain influence on the long-run beliefs. Finally, we investigate the tension between information aggregation and spread of misinformation. In Chapter 4, we introduce conflicting interests into a model of non-Bayesian belief dynamics. Agents meet with their neighbors in the social network and exchange information strategically. With conflicting interests, the belief dynamics typically fails to converge: each agent's belief converges to some interval and keeps fluctuating on it forever.

Submitted by Johnny Rodrigues (johnnyrodrigues@ufcg.edu.br) on 2018-08-08T21:14:19Z No. of bitstreams: 1 DÉBORA KAROLLYNE XAVIER SILVA - DISSERTAÇÃO PPGMAT 2013..pdf: 5676823 bytes, checksum: 10779ac6b54c624585a998fed783af51 (MD5) / Made available in DSpace on 2018-08-08T21:14:19Z (GMT). No. of bitstreams: 1 DÉBORA KAROLLYNE XAVIER SILVA - DISSERTAÇÃO PPGMAT 2013..pdf: 5676823 bytes, checksum: 10779ac6b54c624585a998fed783af51 (MD5) Previous issue date: 2013-12 / Capes / A distribuição Birnbaum-Saunders surgiu em 1969 com aplicações fortemente ligadas à engenharia e se expandiu nas últimas décadas a diversas áreas. Na literatura, além de tomar um papel de destaque na análise de sobrevivência, podemos destacar o surgimento de várias generalizações. Neste trabalho apresentaremos uma dessas generalizações, a qual foi formulada por Mentainis em 2010. Primeiramente, faremos uma breve explanação sobre a distribuição Birnbaum-Saunders cl´assica e sobre a generaliza¸c˜ao que foi proposta por Mentainis (2010), a qual chamaremos de distribuição Birnbaum-Saunders generalizada. Em seguida, discorreremos sobre a distribuição senh-normal, a qual possui uma importante relação com a distribuição Birnbaum-Saunders. Numa outra etapa, apresentaremos alguns métodos de diagnóstico para o modelo de regressão log-Birnbaum-Saunders generalizado e investigaremos testes de homogeneidade para os correspondentes parˆametros de forma e escala. Por fim, analisamos um conjunto de dados para ilustrar a teoria desenvolvida. / The Birnbaum-Saunders distribution emerged in 1969 motivated by problems in engineering. However, its field of application has been extended beyond the original context of material fatigue and reliability analysis. In the literature, it has made an important role in survival analysis. Moreover, many generalizations of it have been considered. In this work we present one of these generalizations, which was formulated by Mentainis in 2010. First, we provide a brief explanation of the classical Birnbaum-Saunders distribution and its generalization proposed by Mentainis (2010), which we name as the generalized Birnbaum-Saunders distribution. Thereafter, we discuss the sinh-normal distribution, which has an important relationship with the Birnbaum-Saunders distribution. In a further part of this work, we present some diagnostic methods for generalized log-Birnbaum-Saunders regression models and investigate tests of homogeneity for the corresponding shape and scale parameters. Finally, an application with real data is presented.

För att uppskatta influensområdet till följd av skyddsinfiltartion finns ett antal analytiska modeller att tillämpa. Dessa modeller tar hänsyn till parametrar så som hydraulisk konduktivitet och magasinkoefficient, men de följer också med en rad antaganden som i praktiken inte kan uppfyllas. En alternativ tillvägagång för att bestämma influensområdet är därför med hjälp av numeriska modeller, som i större grad kan göras platsspecifika. Numeriska modeller är till följd av detta mer tidskrävande och behöver mer indata. I denna studie undersöktes vilken metod som är bäst lämpad för att bestämma skyddsinfiltrationens influensområden för en fallstudie i Bromstens industriområde, belägen cirka 15 km nordväst om Stockholm centrum. Två numeriska modeller med varierande underlag av platsspecifika data utvecklades över områdets geologi och grundvattenmagasin för att kunna simulera grundvattennivåer med och utan infiltration. Utöver detta beräknades influensområdet med fyra analytiska modeller. Modellerna testades sedan utifrån olika scenarion, där såväl dataupplösning som den platsspecifika kännedomen över området stegvis ökades. Platsspecifika data tillkom till följd av geotekniska undersökningar och hydrogeologiska tester. Studien ämnar även att besvara vilken data som är av störst vikt för att bestämma influensområdet med de analytiska respektive numeriska modellerna samt vilka skillnader som uppstår mellan analytiskt beräknade influensområden och numeriskt simulerade influensområden. Resultaten visar att de numeriska modellerna i huvudsak är känsligast med avseende på den hydrauliska konduktiviteten, samt att den enklare numeriska modellen är känslig för magasinkoefficienten, något som indikerar att denna modell inte uppnår jämvikt i enlighet med vad som observerats i fält. Utöver detta stod det klart att vattenavgivningstalet inte hade någon nämnvärd inverkan på resultaten. Bland de analytiska modellerna råder den största känsligheten i magasinkoefficienten, följt av konduktiviteten. För Sichardts formel, som inte tar hänsyn till magasinkoefficienten var konduktiviteten den känsligaste parametern. Akvifärens mäktighet, vilken reviderades mellan scenario 2 och 3, hade ingen betydande inverkan på de analytiska modellerna. Vidare visade infiltrationstestet på stora skillnader i skyddsinfiltrationens influensområde med avseende på de olika modellerna och dataunderlaget. Den minsta avvikelsen mätt i residualer observerades för den komplexa numeriska modellen under scenario 4, vilket motsvarar det scenario då dataunderlaget var som störst. Trots att detta scenario tillsammans med modell anses vara det dyraste fallet, anses detta vara det bästa och samtidigt mest tillförlitligt metoden för att uppskatta skyddsinfiltrationens influensområde. / To evaluate the area of influence due to artificial infiltration several analytical models are available. Some of the parameters taken into account by these models are the hydraulic conductivity and storage coefficient, but with these models some assumptions, which in reality cannot be fulfilled, are made. An alternative approach to evaluate the area of influence is therefore with numerical models, which in a greater extent account for the site-specific conditions. Due to this, numerical models are more time consuming and require more input data. This project aims to investigate the most effective approaches to evaluate the area of influence due to artificial infiltration for a case study in Bromsten, located 15 kilometers northwest of Stockholm. Two numerical models, with different background data due to the extent of site knowledge, were developed to represent the site's geological settings and groundwater properties to simulate the groundwaterlevels with and without infiltration. Moreover the area of influence were calculated with four analytical models. All of the models were then applied on four different scenarios, in which the data resolution and the site knowledge increased. Site-specific data was added as a result of geological surveys and hydrogeological tests. The study also aims to answer which data is most important in order to determine the area of influence with analytical and numerical models and what differences there are between the analytical solutions compared with the numerical solutions. Among the methods investigated, constructing a more complex model with data from scenario 4, the scenario with the greatest data supply, resulted in the most reliable results and was therefore the best method and the method to choose for this case-study. Other results indicated that the numerical models first of all are sensitive to the conductivity and that the more simpel numerical model is sensitive to the storage coefficient as well. The last result shows that this model does not reach the steady state conditions as observed in field, which highlights the importance of goetechnical investigation for the numerical models. Moreover none of the numerical models were sensitive to the specific yield. Among the analytical models the storage coefficient was the most important followed by the conductivity. For one of the analytical models (Sichardts formula) the conductivity was the most sensitive parameter. The thickness of the aquifer had no significant impact on the analytical models.

Submitted by Rafael Santana (rafael.silvasantana@ufpe.br) on 2017-04-26T17:07:37Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Carolina Marchant.pdf: 5792192 bytes, checksum: adbd82c79b286d2fe2470b7955e6a9ed (MD5) / Made available in DSpace on 2017-04-26T17:07:38Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Carolina Marchant.pdf: 5792192 bytes, checksum: adbd82c79b286d2fe2470b7955e6a9ed (MD5) Previous issue date: 2016-10-31 / CAPES; BOLSA DO CHILE. / In the last decades, univariate Birnbaum-Saunders models have received considerable attention in the literature. These models have been widely studied and applied to fatigue, but they have also been applied to other areas of the knowledge. In such areas, it is often necessary to model several variables simultaneously. If these variables are correlated, individual analyses for each variable can lead to erroneous results. Multivariate regression models are a useful tool of the multivariate analysis, which takes into account the correlation between variables. In addition, diagnostic analysis is an important aspect to be considered in the statistical modeling. Furthermore, multivariate quality control charts are powerful and simple visual tools to determine whether a multivariate process is in control or out of control. A multivariate control chart shows how several variables jointly affect a process. First, we propose, derive and characterize multivariate generalized logarithmic Birnbaum-Saunders distributions. Also, we propose new multivariate generalized Birnbaum-Saunders regression models. We use the method of maximum likelihood estimation to estimate their parameters through the expectation-maximization algorithm. We carry out a simulation study to evaluate the performance of the corresponding estimators based on the Monte Carlo method. We validate the proposed models with a regression analysis of real-world multivariate fatigue data. Second, we conduct a diagnostic analysis for multivariate generalized Birnbaum-Saunders regression models. We consider the Mahalanobis distance as a global influence measure to detect multivariate outliers and use it for evaluating the adequacy of the distributional assumption. Moreover, we consider the local influence method and study how a perturbation may impact on the estimation of model parameters. We implement the obtained results in the R software, which are illustrated with real-world multivariate biomaterials data. Third and finally, we develop a robust methodology based on multivariate quality control charts for generalized Birnbaum-Saunders distributions with the Hotelling statistic. We use the parametric bootstrap method to obtain the distribution of this statistic. A Monte Carlo simulation study is conducted to evaluate the proposed methodology, which reports its performance to provide earlier alerts of out-of-control conditions. An illustration with air quality real-world data of Santiago-Chile is provided. This illustration shows that the proposed methodology can be useful for alerting episodes of extreme air pollution. / Nas últimas décadas, o modelo Birnbaum-Saunders univariado recebeu considerável atenção na literatura. Esse modelo tem sido amplamente estudado e aplicado inicialmente à modelagem de fadiga de materiais. Com o passar dos anos surgiram trabalhos com aplicações em outras áreas do conhecimento. Em muitas das aplicações é necessário modelar diversas variáveis simultaneamente incorporando a correlação entre elas. Os modelos de regressão multivariados são uma ferramenta útil de análise multivariada, que leva em conta a correlação entre as variáveis de resposta. A análise de diagnóstico é um aspecto importante a ser considerado no modelo estatístico e verifica as suposições adotadas como também sua sensibilidade. Além disso, os gráficos de controle de qualidade multivariados são ferramentas visuais eficientes e simples para determinar se um processo multivariado está ou não fora de controle. Este gráfico mostra como diversas variáveis afetam conjuntamente um processo. Primeiro, propomos, derivamos e caracterizamos as distribuições Birnbaum-Saunders generalizadas logarítmicas multivariadas. Em seguida, propomos um modelo de regressão Birnbaum-Saunders generalizado multivariado. Métodos para estimação dos parâmetros do modelo, tal como o método de máxima verossimilhança baseado no algoritmo EM, foram desenvolvidos. Estudos de simulação de Monte Carlo foram realizados para avaliar o desempenho dos estimadores propostos. Segundo, realizamos uma análise de diagnóstico para modelos de regressão Birnbaum-Saunders generalizados multivariados. Consideramos a distância de Mahalanobis como medida de influência global de detecção de outliers multivariados utilizando-a para avaliar a adequacidade do modelo. Além disso, desenvolvemos medidas de diagnósticos baseadas em influência local sob alguns esquemas de perturbações. Implementamos a metodologia apresentada no software R, e ilustramos com dados reais multivariados de biomateriais. Terceiro, e finalmente, desenvolvemos uma metodologia robusta baseada em gráficos de controle de qualidade multivariados para a distribuição Birnbaum-Saunders generalizada usando a estatística de Hotelling. Baseado no método bootstrap paramétrico encontramos aproximações da distribuição desta estatística e obtivemos limites de controle para o gráfico proposto. Realizamos um estudo de simulação de Monte Carlo para avaliar a metodologia proposta indicando seu bom desempenho para fornecer alertas precoces de processos fora de controle. Uma ilustração com dados reais de qualidade do ar de Santiago-Chile é fornecida. Essa ilustração mostra que a metodologia proposta pode ser útil para alertar sobre episódios de poluição extrema do ar, evitando efeitos adversos na saúde humana.