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This thesis addresses three interrelated challenges of disease mapping and contributes a new approach for improving visualization of disease burdens to enhance disease surveillance systems. First, it determines an appropriate threshold choice (smoothing parameter) for the adaptive kernel density estimation (KDE) in disease mapping. The results show that the appropriate threshold value depends on the characteristics of data, and bandwidth selector algorithms can be used to guide such decisions about mapping parameters. Similar approaches are recommended for map-makers who are faced with decisions about choosing threshold values for their own data. This can facilitate threshold selection. Second, the study evaluates the relative performance of the adaptive KDE and spatial empirical Bayes for disease mapping. The results reveal that while the estimated rates at the state level computed from both methods are identical, those at the zip code level are slightly different. These findings indicate that using either the adaptive KDE or spatial empirical Bayes method to map disease in urban areas may provide identical rate estimates, but caution is necessary when mapping diseases in non-urban (sparsely populated) areas. This study contributes insights on the relative performance in terms of accuracy of visual representation and associated limitations. Lastly, the study contributes a new approach for delimiting spatial units of disease risk using straightforward statistical and spatial methods and social determinants of health. The results show that the neighborhood risk map not only helps in geographically targeting where but also in tailoring interventions in those areas to those high risk populations. Moreover, when health data is limited, the neighborhood risk map alone is adequate for identifying where and which populations are at risk. These findings will benefit public health tasks of planning and targeting appropriate intervention even in areas with limited and poor-quality health data. This study not only fills the identified gaps of knowledge in disease mapping but also has a wide range of broader impacts. The findings of this study improve and enhance the use of the adaptive KDE method in health research, provide better awareness and understanding of disease mapping methods, and offer an alternative method to identify populations at risk in areas with limited health data. Overall, these findings will benefit public health practitioners and health researchers as well as enhance disease surveillance systems.

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Cette thèse traite de problèmes de dépendance entre processus stochastiques en temps continu. Ces résultats sont appliqués à la modélisation et à la gestion des risques des marchés de l'électricité.Dans une première partie, de nouvelles copules sont établies pour modéliser la dépendance entre deux mouvements Browniens et contrôler la distribution de leur différence. On montre que la classe des copules admissibles pour les Browniens contient des copules asymétriques. Avec ces copules, la fonction de survie de la différence des deux Browniens est plus élevée dans sa partie positive qu'avec une dépendance gaussienne. Les résultats sont appliqués à la modélisation jointe des prix de l'électricité et d'autres commodités énergétiques. Dans une seconde partie, nous considérons un processus stochastique observé de manière discrète et défini par la somme d'une semi-martingale continue et d'un processus de Poisson composé avec retour à la moyenne. Une procédure d'estimation pour le paramètre de retour à la moyenne est proposée lorsque celui-ci est élevé dans un cadre de statistique haute fréquence en horizon fini. Ces résultats sont utilisés pour la modélisation des pics dans les prix de l'électricité.Dans une troisième partie, on considère un processus de Poisson doublement stochastique dont l'intensité stochastique est une fonction d'une semi-martingale continue. Pour estimer cette fonction, un estimateur à polynômes locaux est utilisé et une méthode de sélection de la fenêtre est proposée menant à une inégalité oracle. Un test est proposé pour déterminer si la fonction d'intensité appartient à une certaine famille paramétrique. Grâce à ces résultats, on modélise la dépendance entre l'intensité des pics de prix de l'électricité et de facteurs exogènes tels que la production éolienne. / In this thesis, we study some dependence modeling problems between continuous time stochastic processes. These results are applied to the modeling and risk management of electricity markets. In a first part, we propose new copulae to model the dependence between two Brownian motions and to control the distribution of their difference. We show that the class of admissible copulae for the Brownian motions contains asymmetric copulae. These copulae allow for the survival function of the difference between two Brownian motions to have higher value in the right tail than in the Gaussian copula case. Results are applied to the joint modeling of electricity and other energy commodity prices. In a second part, we consider a stochastic process which is a sum of a continuous semimartingale and a mean reverting compound Poisson process and which is discretely observed. An estimation procedure is proposed for the mean reversion parameter of the Poisson process in a high frequency framework with finite time horizon, assuming this parameter is large. Results are applied to the modeling of the spikes in electricity prices time series. In a third part, we consider a doubly stochastic Poisson process with stochastic intensity function of a continuous semimartingale. A local polynomial estimator is considered in order to infer the intensity function and a method is given to select the optimal bandwidth. An oracle inequality is derived. Furthermore, a test is proposed in order to determine if the intensity function belongs to some parametrical family. Using these results, we model the dependence between the intensity of electricity spikes and exogenous factors such as the wind production.