Functional analyses have gained more interest as we have easier access to massive data sets. However, such data sets often contain large heterogeneities, noise, and dimensionalities. When generalizing the analyses from vectors to functions, classical methods might not work directly. This dissertation considers noisy information reduction in functional analyses from two perspectives: functional variable selection to reduce the dimensionality and functional clustering to group similar observations and thus reduce the sample size. The complicated data structures and relations can be easily modeled by a Bayesian hierarchical model, or developed from a more generic one by changing the prior distributions. Hence, this dissertation focuses on the development of Bayesian approaches for functional analyses due to their flexibilities. A nonparametric Bayesian approach, such as the Dirichlet process mixture (DPM) model, has a nonparametric distribution as the prior. This approach provides flexibility and reduces assumptions, especially for functional clustering, because the DPM model has an automatic clustering property, so the number of clusters does not need to be specified in advance. Furthermore, a weighted Dirichlet process mixture (WDPM) model allows for more heterogeneities from the data by assuming more than one unknown prior distribution. It also gathers more information from the data by introducing a weight function that assigns different candidate priors, such that the less similar observations are more separated. Thus, the WDPM model will improve the clustering and model estimation results. In this dissertation, we used an advanced nonparametric Bayesian approach to study functional variable selection and functional clustering methods. We proposed 1) a stochastic search functional selection method with application to 1-M matched case-crossover studies for aseptic meningitis, to examine the time-varying unknown relationship and find out important covariates affecting disease contractions; 2) a functional clustering method via the WDPM model, with application to three pathways related to genetic diabetes data, to identify essential genes distinguishing between normal and disease groups; and 3) a combined functional clustering, with the WDPM model, and variable selection approach with application to high-frequency spectral data, to select wavelengths associated with breast cancer racial disparities. / Doctor of Philosophy / As we have easier access to massive data sets, functional analyses have gained more interest to analyze data providing information about curves, surfaces, or others varying over a continuum. However, such data sets often contain large heterogeneities and noise. When generalizing the analyses from vectors to functions, classical methods might not work directly. This dissertation considers noisy information reduction in functional analyses from two perspectives: functional variable selection to reduce the dimensionality and functional clustering to group similar observations and thus reduce the sample size. The complicated data structures and relations can be easily modeled by a Bayesian hierarchical model due to its flexibility. Hence, this dissertation focuses on the development of nonparametric Bayesian approaches for functional analyses. Our proposed methods can be applied in various applications: the epidemiological studies on aseptic meningitis with clustered binary data, the genetic diabetes data, and breast cancer racial disparities.

Méthodes et principaux résultats. Dans une revue systématique des études sur les facteurs déclenchants des infarctus cérébraux, nous n’avons identifié qu’une seule étude, négative, consacrée aux événements de vie. Nous avons montré, dans une étude prospective portant sur 247 patients admis pour un infarctus cérébral, qu’une exposition à au moins 1 évènement de vie était plus fréquente dans le mois précédant l’infarctus cérébral que dans les 5 périodes témoins (OR=2,96 ; IC à 95% 2,19-4,00). L’exposition à des évènements de vie était aussi un facteur prédictif des dépressions survenant dans les 6 mois suivant un infarctus cérébral. Les autres facteurs prédictifs de dépression post-AVC étaient un score de Rankin > 2, un antécédent de dépression, une lésion caudée et/ou lenticulaire gauche, le sexe féminin et des pleurs pathologiques. Conclusion et perspectives. Ce travail de thèse apporte des arguments en faveur d’un rôle des évènements de vie d’une part, dans la survenue à court terme d’un infarctus cérébral, d’autre part dans la survenue d’une dépression dans les 6 mois suivant un AVC. Il souligne aussi les difficultés spécifiques de l’étude des événements de vie concernant leur définition, l’évaluation de leur sévérité, les biais de rappel et la définition de la période à risque. Nos résultats doivent être confirmés et précisés avant d’évaluer le bénéfice d’une stratégie préventive. / Methods and main results. In our systematic review of potential triggers of ischemic stroke, the only study that examined stressful life events didn’t show any association with stroke onset. In a prospective study of 247 consecutive patients admitted for ischemic stroke, exposure to at least one stressful life event was significantly more common during the first month preceding stroke onset than during the five control periods (OR=2.96 ; 95% CI 2.19-4.00). Stressful life events exposure also predicted depression occurring within six months after ischemic stroke onset. The other predictors of post-stroke depression were a modified Rankin score > 2, a prior history of depression, a left caudate and/or lenticular lesion, the female sex and pathologic crying.Conclusion and perspectives. Our results support the role of stressful life events as triggers of ischemic stroke and predictors of post-stroke depression. Our research also highlights the difficulty of studying stressful life events, due to potential influence of memory biases and lack of precise definitions of stressful life events, severe vs. minor events and hazard period durations. These preliminary results should be confirmed in order to assess benefits of preventive strategies.