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.

Este trabalho tem como objetivo principal apresentar uma abordagem clássica e Bayesiana dos modelos lineares com observações censuradas, que é uma nova área de pesquisa com grandes possibilidades de aplicações. Aqui, substituimos o uso convencional da distribuição normal para os erros por uma família de distribuições mais flexíveis, o que nos permite lidar de forma mais adequada com observações censuradas na presença de outliers. Esta família é obtida através de um mecanismo de fácil construção e possui como casos especiais as distribuições t de Student, Pearson tipo VII, slash, normal contaminada e, obviamente, a normal. Para o caso de respostas correlacionadas e censuradas propomos um modelo de regressão linear robusto baseado na distribuição t de Student, desenvolvendo um algoritmo tipo EM que depende dos dois primeiros momentos da distribuição t de Student truncada. / This work aims to present a classical and Bayesian approach to linear models with censored observations, which is a new area of research with great potential for applications. Here, we replace the conventional use of the normal distribution for the errors of a more flexible family of distributions, which deal in more appropriately with censored observations in the presence of outliers. This family is obtained through a mechanism easy to construct and has as special cases the distributions Student t, Pearson type VII, slash, contaminated normal, and obviously normal. For the case of correlated and censored responses we propose a model of robust linear regression based on Student\'s t distribution and we developed an EM type algorithm based on the first two moments of the truncated Student\'s t distribution.

De nombreuses études de biométrologie sont menées à l’INRS, pour évaluer l’exposition professionnelle à des substances chimiques, en France, et pour compléter les connaissances en proposant des valeurs de références destinées à protéger des salariés exposés à ces substances. Ces études consistent à mesurer simultanément l’imprégnation biologique et l’exposition atmosphérique à une substance, chez des salariés exposés à celle-ci. La relation entre ces mesures biologiques et atmosphériques est ensuite estimée à travers un modèle de régression linéaire. Lorsque que cette relation existe et que la voie d’absorption du toxique est essentiellement inhalatoire, il est ensuite possible de dériver une Valeur Limite Biologique (VLB) à partir de la Valeur Limite d’Exposition Professionnelle (VLEP-8h) du toxique. Deux aspects de ces données ont été identifiés, qui ne sont pas ou seulement partiellement prises en compte dans les modélisations statistiques courantes : la censure due aux limites de détection (LD)/quantification (LQ) des mesures biologiques et atmosphériques et la variabilité inter-individuelle. Ignorer ces deux particularités lors de la modélisation mène à une perte de puissance statistique et à de potentielles conclusions biaisées. Les travaux menés dans le cadre de cette thèse ont permis d’adapter le modèle de régression à ces deux caractéristiques, dans un cadre bayésien. L’approche proposée repose sur la modélisation des mesures atmosphériques à l’aide de modèles à effets aléatoires prenant en compte les valeurs inférieures à la LD/LQ, et sur la modélisation simultanée des mesures biologiques, supposée être linéairement dépendantes sur une échelle logarithmique, de l'exposition atmosphérique, tout en tenant compte de la variabilité inter-individuelle. Ce travail a donné lieu à une publication scientifique dans une revue à comité de lecture. L’application de cette méthodologie a été réalisée sur des jeux d’exposition professionnelle au béryllium et au chrome, après avoir été cependant adaptée aux caractéristiques toxicocinétiques de ces deux substances. Il a ainsi été possible de proposer une VLB pour le béryllium (0,06 µg/g créatinine). L’exploitation de mesures de chrome dans deux secteurs d’activités différents (exposition professionnelle aux peintures de chromates, et exposition professionnelle dans le secteur du chromage électrolytique) a permis de mettre en évidence que le chrome urinaire dépend essentiellement de l’exposition au chrome VI, le chrome non VI ayant moins d’impact. Nous n’avons pas pu montrer de relation entre la solubilité du CrVI et le chrome urinaire. Une VLB de 0,41 µg/g créatinine, de l’ordre de la Valeur Biologique de Référence (VBR) proposée par l’ANSES (0,54 µg/g créatinine), a été estimée pour l’exposition professionnelle aux peintures de chromates, et une VLB de 1,85 µg/g créatinine a été estimée pour l’exposition professionnelle dans le secteur du chromage électrolytique, qui est en cohérence avec la VLB proposée par l’ANSES dans ce secteur, à savoir 1,8 µg/g créatinine / Many biomonitoring studies are conducted at INRS, in order to assess occupational exposure to chemicals in France, and to propose reference values to protect workers exposed to these substances. These studies consist in measuring simultaneously biological and airborne exposure of workers exposed to a toxic substance. The relationship between these biological and airborne measurements is then estimated through a linear regression model. When this relationship exists and the route of absorption of the toxic is essentially inhalatory, it is possible to derive a Biological Limit Value (BLV) from the Occupational Exposure Limit Value (OEL) of the toxic substance. However, two characteristics of these data have been identified, which are not or only partially taken into account in the current statistical modelling: the left-censoring due to limits of detection (LoD)/quantification (LoQ) of biological and airborne measurements, and the between-individual variability. Ignoring both of these features in modelling leads to a loss of statistical power and potentially biased conclusions. The work carried out in this thesis allowed us to adapt the regression model to these two characteristics, in a Bayesian framework. The proposed approach is based on the modelling of airborne measurements using random effects models adapted for values below the LoD / LoQ, and on the simultaneous modelling of biological measurements, assumed to depend linearly on a logarithmic scale, on the airborne exposure, while taking into account between-subject variability. This work resulted in a scientific publication in a peer-reviewed journal. This methodology has been applied on beryllium and chromium occupational exposure datasets, after adaptation to the toxicokinetic characteristics of these two substances. It has thus been possible to propose a BLV for beryllium (0.06 μg / g creatinine). The analysis of chromium measurements in two different sectors of activity (occupational exposure to chromate paints, and occupational exposure in the electroplating sector) made it possible to show that urinary chromium depends mainly on airborne exposure to VI chromium, non-VI chromium having less impact. We were not able to show a relationship between the solubility of airborne VI chromium and urinary chromium. A BLV of 0.41 μg / g creatinine, close to the Biological Guidance Value (BGV) proposed by ANSES (0.54 μg / g creatinine), was estimated for occupational exposure to chromate paints, and a BLV of 1.85 μg/g creatinine was obtained for occupational exposure in the electrolytic chromium plating sector, which is consistent with the ANSES proposed BLV in this sector, i-e 1.8 μg / g creatinine

Este trabalho tem como objetivo principal apresentar uma abordagem clássica e Bayesiana dos modelos lineares com observações censuradas, que é uma nova área de pesquisa com grandes possibilidades de aplicações. Aqui, substituimos o uso convencional da distribuição normal para os erros por uma família de distribuições mais flexíveis, o que nos permite lidar de forma mais adequada com observações censuradas na presença de outliers. Esta família é obtida através de um mecanismo de fácil construção e possui como casos especiais as distribuições t de Student, Pearson tipo VII, slash, normal contaminada e, obviamente, a normal. Para o caso de respostas correlacionadas e censuradas propomos um modelo de regressão linear robusto baseado na distribuição t de Student, desenvolvendo um algoritmo tipo EM que depende dos dois primeiros momentos da distribuição t de Student truncada. / This work aims to present a classical and Bayesian approach to linear models with censored observations, which is a new area of research with great potential for applications. Here, we replace the conventional use of the normal distribution for the errors of a more flexible family of distributions, which deal in more appropriately with censored observations in the presence of outliers. This family is obtained through a mechanism easy to construct and has as special cases the distributions Student t, Pearson type VII, slash, contaminated normal, and obviously normal. For the case of correlated and censored responses we propose a model of robust linear regression based on Student\'s t distribution and we developed an EM type algorithm based on the first two moments of the truncated Student\'s t distribution.

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Evaluer, maintenir et restaurer les conditions écologiques des rivières nécessitent des mesures du fonctionnement de leurs écosystèmes. De par leur complexité, notre compréhension de ces systèmes est imparfaite. La prise en compte des incertitudes et variabilités liées à leur évaluation est donc indispensable à la prise de décision des gestionnaires. En analysant des données nationales (~ 1654 sites), les objectifs principaux de cette thèse étaient de (1) tester certaines hypothèses intrinsèques aux bio-indicateurs et (2) d'étudier les incertitudes de l'évaluation écologique associées à la variabilité temporelle des bio-indicateurs et à la prédiction des conditions de référence. (1) Ce travail met en évidence (i) le rôle prépondérant des facteurs environnementaux naturels dans la structuration des communautés aquatiques en comparaison des facteurs anthropiques (définis à l'échelle du bassin versant, du corridor riparien et du tronçon), (ii) les réponses contrastées des communautés aquatiques aux pressions humaines (dégradations hydro-morphologiques et de la qualité de l'eau) et (iii) plus généralement, les forts impacts des barrages et de l'altération de la qualité de l'eau sur les communautés aquatiques. (2) Une méthode Bayésienne a été développée pour estimer les incertitudes liées à la prédiction des conditions de référence d'un indice piscicole (IPR+). Les incertitudes prédictives de l'IPR+ dépendent du site considéré mais aucune tendance claire n'a été observée. Par comparaison, la variabilité temporelle de l'IPR+ est plus faible et semble augmenter avec l'intensité des perturbations anthropiques. Les résultats de ce travail confirment l'avantage d'indices multi-métriques basés sur des traits fonctionnels par rapport à ceux relatifs à la composition taxonomique. Les sensibilités différentes des macrophytes, poissons, diatomées et macro-invertébrés aux pressions humaines soulignent leur complémentarité pour l'évaluation des écosystèmes fluviaux. Néanmoins, de futures recherches sont nécessaires à une meilleure compréhension des effets d'interactions entre types de pressions et entre pressions humaines et environnement. / Sensitive biological measures of ecosystem quality are needed to assess, maintain or restore the ecological conditions of rivers. Since our understanding of these complex systems is imperfect, river management requires recognizing variability and uncertainty of bio-assessment for decision-making. Based on the analysis of national data sets (~ 1654 sites), the main goals of this work were (1) to test some of the assumptions that shape bio-indicators and (2) address the temporal variability and the uncertainty associated to prediction of reference conditions.(1) This thesis highlights (i) the predominant role of physiographic factors in shaping biological communities in comparison to human pressures (defined at catchment, riparian corridor and reach scales), (ii) the differences in the responses of biological indicators to the different types of human pressures (water quality, hydrological, morphological degradations) and (iii) more generally, the greatest biological impacts of water quality alterations and impoundments. (2) A Bayesian method was developed to estimate the uncertainty associated with reference condition predictions of a fish-based bio-indicator (IPR+). IPR+ predictive uncertainty was site-dependent but showed no clear trend related to the environmental gradient. By comparison, IPR+ temporal variability was lower and sensitive to an increase of human pressure intensity. This work confirmed the advantages of multi-metric indexes based on functional metrics in comparison to compositional metrics. The different sensitivities of macrophytes, fish, diatoms and macroinvertebrates to human pressures emphasize their complementarity in assessing river ecosystems. Nevertheless, future research is needed to better understand the effects of interactions between pressures and between pressures and the environment.

Une question fondamentale en écologie des populations est l’identification des facteurs influençant la dynamique d’une population. L’objectif principal de cette thèse est de déterminer quelles sont les réponses démographiques et populationnelles de prédateurs marins supérieurs face aux fluctuations d’abondance de leurs proies, aux variations climatiques, à la densité-dépendance tout en tenant compte de l’hétérogénéité inter et intra-individuelle (âge, expérience, sexe, qualité ou stratégie). Pour ce faire, nous nous baserons sur l’analyse de suivis à long-terme individuels et populationnels d’oiseaux marins longévifs et prédateurs apicaux phylogénétiquement très proches dans deux biomes contrastés : le labbe de McCormick Catharacta maccormicki sur l’archipel de Pointe Géologie en Antarctique et le labbe subantarctique Catharacta lonnbergi sur l’archipel des Kerguelen en milieu subantarctique. Nous tirerons parti d’estimations d’abondances de leurs proies respectives : le manchot Adélie Pygoscelis adeliae et le manchot empereur Aptenodytes forsteri en Antarctique, et le pétrel bleu Halobaena caerulea et le prion de Belcher Pachyptila belcheri à Kerguelen. Ces jeux de données offrent une opportunité unique de pouvoir déterminer et quantifier simultanément les différentes sources de variabilité dans les changements de taille de populations naturelles occupant l’un des niveaux trophiques les plus élevés des réseaux alimentaires antarctiques et subantarctiques. Nous avons mis en évidence de la variation dans plusieurs traits vitaux des deux populations influencées par les performances des individus et de l’hétérogénéité individuelle latente. Nous discutons des mécanismes par lesquels la variabilité climatique, l’abondance de proie et la densité de population peuvent affecter différentiellement les différentes classes d’âges de chaque trait vital, et les conséquences potentielles de futurs changements environnementaux. / A fundamental endeavor in population ecology is to identify the drivers of population dynamics. The main objective of this thesis is to determine what are the demographic and population responses of superior marine predators to the fluctuations of their prey abundance, to climatic variations, to density-dependence while taking into account inter and intra individual heterogeneity (age, experience, sex, quality or strategy). To do this, we analysed long-term individual and population-based monitoring of long-lived seabirds and phylogenetically close apical predators in two contrasting biomes: the south polar skua Catharacta maccormicki at Pointe Géologie archipelago, Antarctica, and the brown skua Catharacta lonnbergi on the sub-Antarctic Kerguelen Archipelago. We will use direct abundance of their respective prey: Adélie penguin Pygoscelis adeliae and emperor penguin Aptenodytes forsteri in Antarctica, and the blue petrel Halobaena caerulea and the thin-billed prion Pachyptila belcheri prion in Kerguelen islands. These datasets provide a unique opportunity to simultaneously disentangle and quantify the different sources of variability driving variation in natural populations occupying one of the highest trophic levels of the Antarctic and sub-Antarctic food webs. We found variation in several vital traits of both populations influenced by individual performance and latent individual heterogeneity. We discuss the mechanisms by which climatic variability, prey abundance, and population density can differentially affect the different age classes of each age class, and the potential consequences of future environmental changes.