L'esca de la vigne fait partie des maladies de dépérissement incurables dont l'étiologie n'est pas complément élucidée. Elle représente un des problèmes majeurs en viticulture. L'objectif général de cette thèse est d'améliorer la compréhension des processus épidémiques et des facteurs de risque. Pour ce faire, nous avons mené une étude quantitative du développement spatio-temporel de l'esca à l'échelle de la parcelle. Dans un premier temps, pour détecter d'éventuelles corrélations spatiales entre les cas de maladie, des tests statistiques non paramétriques sont appliqués aux données spatio-temporelles d'expression foliaires de l'esca pour 15 parcelles du bordelais. Une diversité de profils spatiaux, allant d'une distribution aléatoire à fortement structurée est trouvée. Dans le cas de structures très agrégées, les tests n'ont pas montré d'augmentation significative de la taille des foyers, ni de propagation secondaire locale à partir de ceps symptomatiques, suggérant un effet de l'environnement dans l'explication de cette agrégation. Dans le but de modéliser l'occurrence des symptômes foliaires, nous avons développé des modèles logistiques hiérarchiques intégrant à la fois des covariables exogènes liées à l'environnement et des covariables de voisinage de ceps déjà malades mais aussi un processus latent pour l'auto-corrélation spatio-temporelle. Les inférences bayésiennes sont réalisées en utilisant la méthode INLA (Inverse Nested Laplace Approximation). Les résultats permettent de conforter l'hypothèse du rôle significatif des facteurs environnementaux dans l'augmentation du risque d'occurrence des symptômes. L'effet de propagation de l'esca à petite échelle à partir de ceps déjà atteints situés sur le rang ou hors rang n'est pas montré. Un modèle autologistique de régression, deux fois centré, qui prend en compte de façon plus explicite la structure spatio-temporelle de voisinage, est également développé. Enfin, une méthode géostatistique d'interpolation de données de nature anisotropique atypique est proposée. Elle permet d'interpoler la variable auxiliaire de résistivité électrique du sol pour estimer à l'échelle de chaque plante de la parcelle, la réserve en eau du sol disponible pour la vigne. Les méthodes géostatistique et spatio-temporelles développées dans cette thèse ouvrent des perspectives pour identifier les facteurs de risques et prédire le développement de l'esca de la vigne dans des contextes agronomiques variés. / Esca grapevine disease is one of the incurable dieback disease with the etiology not completely elucidated. It represents one of the major threats for viticulture around the world. To better understand the underlying process of esca spread and the risk factors of this disease, we carried out quantitative analyses of the spatio-temporal development of esca at vineyard scale. In order to detect the spatial correlation among the diseased vines, the non-parametric statistical tests were applied to the spatio-temporal data of esca foliar symptom expression for 15 vineyards in Bordeaux region. Among vineyards, a large range of spatial patterns, from random to strongly structured, were found. In the vineyards with strongly aggregated patterns, no significant increase in the size of cluster and local spread from symptomatic vines was shown, suggesting an effect of the environment in the explanation of this aggregation. To model the foliar symptom occurrence, we developed hierarchical logistic regression models by integrating exogenous covariates, covariates of neighboring symptomatic vines already diseased, and also a latent process with spatio-temporal auto-correlation. The Bayesian inferences of these models were performed by INLA (Inverse Nested Laplace Approximation) approach. The results confirmed the effect of environmental factors on the occurrence risk of esca symptom. The secondary locally spread of esca from symptomatic vines located on the same row or out of row was not shown. A two-step centered auto-logistic regression model, which explicitly integrated the spatio-temporal neighboring structure, was also developed. At last, a geostatistical method was proposed to interpolate data with a particular anisotropic structure. It allowed interpolating the ancillary variable, electrical resistivity of soil, which were used to estimate the available soil water content at vine-scale. These geostatistical methods and spatio-temporal statistical methods developed in this thesis offered outlook to identify risk factors, and thereafter to predict the development of esca grapevine disease in different agronomical contexts.

In this thesis we develop several kinds of latent variable models in order to address three types of bio-statistical problem. The three problems are the treatment effect of carcinogens on tumour development, spatial interactions between plant species and motor unit number estimation (MUNE). The three types of data looked at are: highly heterogeneous longitudinal count data, quadrat counts of species on a rectangular lattice and lastly, electrophysiological data consisting of measurements of compound muscle action potential (CMAP) area and amplitude. Chapter 1 sets out the structure and the development of ideas presented in this thesis from the point of view of: model structure, model selection, and efficiency of estimation. Chapter 2 is an introduction to the relevant literature that has in influenced the development of this thesis. In Chapter 3 we use the EM algorithm for an application of an autoregressive hidden Markov model to describe longitudinal counts. The data is collected from experiments to test the effect of carcinogens on tumour growth in mice. Here we develop forward and backward recursions for calculating the likelihood and for estimation. Chapter 4 is the analysis of a similar kind of data using a more sophisticated model, incorporating random effects, but estimation this time is conducted from the Bayesian perspective. Bayesian model selection is also explored. In Chapter 5 we move to the two dimensional lattice and construct a model for describing the spatial interaction of tree types. We also compare the merits of directed and undirected graphical models for describing the hidden lattice. Chapter 6 is the application of a Bayesian hierarchical model (MUNE), where the latent variable this time is multivariate Gaussian and dependent on a covariate, the stimulus. Model selection is carried out using the Bayes Information Criterion (BIC). In Chapter 7 we approach the same problem by using the reversible jump methodology (Green, 1995) where this time we use a dual Gaussian-Binary representation of the latent data. We conclude in Chapter 8 with suggestions for the direction of new work. In this thesis, all of the estimation carried out on real data has only been performed once we have been satisfied that estimation is able to retrieve the parameters from simulated data. Keywords: Amyotrophic lateral sclerosis (ALS), carcinogens, hidden Markov models (HMM), latent variable models, longitudinal data analysis, motor unit disease (MND), partially ordered Markov models (POMMs), the pseudo auto- logistic model, reversible jump, spatial interactions.