Mountaintop removal mining and valley filling (MTR/VF) is a common form of land conversion in Central Appalachia and threatens the integrity of stream ecosystems. We investigated the effects of MTR/VF on stream salamander occupancy probabilities and community structure by conducting area constrained active searches for stream salamanders within intermittent streams located in mature forest (i.e., control) and those impacted by MTR/VF. During March to June of 2013, we detected five stream salamander species (Desmognathus fuscus, D. monticol, Eurycea cirrigera, Pseudotriton ruber, and Gyrinophilus porphyriticus) and found that the probability of occupancy was greatly reduced in MTR/VF streams compared to control streams. Additionally, the salamander community was greatly reduced in MTR/VF streams; the mean species richness estimate for MTR/VF streams was 2.09 (± 1.30 SD), whereas richness was 4.83 (± 0.58 SD) for control streams. Numerous mechanisms may be responsible for decreased occupancy and diminished salamander communities at MTR/VF streams, although water chemistry of streams may be a particularly important mechanism. Indeed, we detected elevated levels of specific conductivity, pH, total organic carbon, and dissolved ions in MTR/VF streams. Our results indicate that salamander communities, with other invertebrates, fish, and other aquatic and/or semi-aquatic animals, are susceptible to MTR/VF mining practices.

Cette thèse explore l'utilisation des modèles bayésiens dans les IA de jeux vidéo multi-joueurs, particulièrement l'IA des jeux de stratégie en temps réel (STR). Les jeux vidéo se situent entre la robotique et la simulation totale, car les autres joueurs ne sont pas simulés, et l'IA n'a pas de contrôle sur la simulation. Les jeux de STR demandent simultanément d'effectuer des actions reactives (contrôle d'unités) et de prendre des décisions stratégiques (technologiques, économiques) et tactiques (spatiales, temporelles). Nous avons utilisé la modélisation bayésienne comme une alternative à la logique (booléenne), étant capable de travailler avec des informations incomplètes, et donc incertaines. En effet, la spécification incomplète des comportement "scriptés", ou la spécification incomplète des états possibles dans la recherche de plans, demandent une solution qui peut gérer cette incertitude. L'apprentissage artificiel aide à réduire la complexité de spécifier de tels modèles. Nous montrons que la programmation bayésienne peut intégrer toutes sortes de sources d'incertitudes (états cachés, intentions, stochasticité) par la réalisation d'un joueur de StarCraft complètement robotique. Les distributions de probabilité sont un moyen de transporter, sans perte, l'information que l'on a et qui peut représenter au choix: des contraintes, une connaissance partielle, une estimation de l'espace des états et l'incomplétude du modèle lui-même. Dans la première partie de cette thèse, nous détaillons les solutions actuelles aux problèmes qui se posent lors de la réalisation d'une IA de jeu multi-joueur, en donnant un aperçu des caractéristiques calculatoires et cognitives complexes des principaux types de jeux. En partant de ce constat, nous résumons les catégories transversales de problèmes, et nous introduisons comment elles peuvent être résolues par la modélisation bayésienne. Nous expliquons alors comment construire un programme bayésien en partant de connaissances et d'observations du domaine à travers un exemple simple de jeu de rôle. Dans la deuxième partie de la thèse, nous détaillons l'application de cette approche à l'IA de STR, ainsi que les modèles auxquels nous sommes parvenus. Pour le comportement réactif (micro-management), nous présentons un controleur multi-agent décentralisé et temps réel inspiré de la fusion sensori-motrice. Ensuite, nous accomplissons les adaptation dynamiques de nos stratégies et tactiques à celles de l'adversaire en le modélisant à l'aide de l'apprentissage artificiel (supervisé et non supervisé) depuis des traces de joueurs de haut niveau. Ces modèles probabilistes de joueurs peuvent être utilisés à la fois pour la prédiction des décisions/actions de l'adversaire, mais aussi à nous-même pour la prise de décision si on substitue les entrées par les notres. Enfin, nous expliquons l'architecture de notre joueur robotique de StarCraft, et nous précisions quelques détails techniques d'implémentation. Au delà des modèles et de leurs implémentations, il y a trois contributions principales: la reconnaissance de plan et la modélisation de l'adversaire par apprentissage artificiel, en tirant partie de la structure du jeu, la prise de décision multi-échelles en présence d'informations incertaines, et l'intégration des modèles bayésiens au contrôle temps réel d'un joueur artificiel. / This thesis explores the use of Bayesian models in multi-player video games AI, particularly real-time strategy (RTS) games AI. Video games are an in-between of real world robotics and total simulations, as other players are not simulated, nor do we have control over the simulation. RTS games require having strategic (technological, economical), tactical (spatial, temporal) and reactive (units control) actions and decisions on the go. We used Bayesian modeling as an alternative to (boolean valued) logic, able to cope with incompleteness of information and (thus) uncertainty. Indeed, incomplete specification of the possible behaviors in scripting, or incomplete specification of the possible states in planning/search raise the need to deal with uncertainty. Machine learning helps reducing the complexity of fully specifying such models. We show that Bayesian programming can integrate all kinds of sources of uncertainty (hidden state, intention, stochasticity), through the realization of a fully robotic StarCraft player. Probability distributions are a mean to convey the full extent of the information we have and can represent by turns: constraints, partial knowledge, state space estimation and incompleteness in the model itself. In the first part of this thesis, we review the current solutions to problems raised by multi-player game AI, by outlining the types of computational and cognitive complexities in the main gameplay types. From here, we sum up the transversal categories of prob- lems, introducing how Bayesian modeling can deal with all of them. We then explain how to build a Bayesian program from domain knowledge and observations through a toy role-playing game example. In the second part of the thesis, we detail our application of this approach to RTS AI, and the models that we built up. For reactive behavior (micro-management), we present a real-time multi-agent decentralized controller inspired from sensory motor fusion. We then show how to perform strategic and tactical adaptation to a dynamic opponent through opponent modeling and machine learning (both supervised and unsupervised) from highly skilled players' traces. These probabilistic player-based models can be applied both to the opponent for prediction, or to ourselves for decision-making, through different inputs. Finally, we explain our StarCraft robotic player architecture and precise some technical implementation details. Beyond models and their implementations, our contributions are threefolds: machine learning based plan recognition/opponent modeling by using the structure of the domain knowledge, multi-scale decision-making under uncertainty, and integration of Bayesian models with a real-time control program.

No description available.

My dissertation comprises three related topics of evolutionary and computational biology, which correspond to the three Chapters. Chapter 1 focuses on tempo and mode of evolution in visual genes, namely opsins, via duplication events and subsequent molecular adaptation in Odonata (dragonflies and damselflies). Gene duplication plays a central role in adaptation to novel environments by providing new genetic material for functional divergence and evolution of biological complexity. Odonata have the largest opsin repertoire of any insect currently known. In particular our results suggest that both the blue sensitive (BS) and long-wave sensitive (LWS) opsin classes were subjected to strong positive selection that greatly weakens after multiple duplication events, a pattern that is consistent with the permanent heterozygote model. Due to the immense interspecific variation and duplicability potential of opsin genes among odonates, they represent a unique model system to test hypotheses regarding opsin gene duplication and diversification at the molecular level. Chapter 2 primarily focuses on reconstruction of the phylogenetic backbone of Odonata using RNA-seq data. In order to reconstruct the evolutionary history of Odonata, we performed comprehensive phylotranscriptomic analyses of 83 species covering 75% of all extant odonate families. Using maximum likelihood, Bayesian, coalescent-based and alignment free tree inference frameworks we were able to test, refine and resolve previously controversial relationships within the order. In particular, we confirmed the monophyly of Zygoptera, recovered Gomphidae and Petaluridae as sister groups with high confidence and identified Calopterygoidea as monophyletic. Fossil calibration coupled with diversification analyses provided insight into key events that influenced the evolution of Odonata. Specifically, we determined that there was a possible mass extinction of ancient odonate diversity during the P-Tr crisis and a single odonate lineage persisted following this extinction event. Lastly, Chapter 3 focuses on identification of erroneously assigned sequence homology using the intelligent agents of machine learning techniques. Accurate detection of homologous relationships of biological sequences (DNA or amino acid) amongst organisms is an important and often difficult task that is essential to various evolutionary studies, ranging from building phylogenies to predicting functional gene annotations. We developed biologically informative features that can be extracted from multiple sequence alignments of putative homologous genes (orthologs and paralogs) and further utilized in context of guided experimentation to verify false positive outcomes.

The work here presents two main parts. In the first part, chapters 1 – 3 focus on dynamical systems modeling in plant immunity, whereas chapters 4 – 6 describe contributions to computational modeling and analysis of proteomics and genomics data. Chapter 1 investigates dynamical and biochemical patterns of reversibly oxidized cysteines (RevOxCys) during effector-triggered immunity (ETI) in Arabidopsis, examines the regulatory patterns associated with Arabidopsis thimet oligopeptidase 1 and 2’s (TOP1 and TOP2), roles in the RevOxCys events during ETI, and analyzes the redox phenotype of the top1top2 mutant. The second chapter investigates the peptidome dynamics during ETI in wild-type (WT) and top1top2 mutant, introduces a novel method to learn the cleavage motif for TOPs and predicts and validates bioactive peptides association with TOPs activity. The third chapter examines gene expression dynamics during Systemic Acquired Resistance (SAR). Time-series clustering identifies unique oscillatory patterns in gene transcription associated with the early onset of SAR. It then describes a mathematical model using ordinary differential equations to represent WT's transcriptional dynamics. The second part of this dissertation explores imputation and statistical modeling for proteomics data analysis and proposes a network inference methodology for polymorphic cysteines. The fourth chapter analyzes the performance of linear models (limma) and the effect of imputation in proteomics data. It shows the advantage of data imputation over filtering and the benefit of using limma over t-test for the statistical decision of differences in means between conditions for different peptides, PTMs, etc. The fifth chapter proposes a statistical model for proteomics data analysis using mean-variance (M-V) trend modeling. It describes a gamma regression to model the dependency of the variance on the mean of observations. Finally, a Bayesian decision model is proposed; the model shows an improvement over existing methods in statistical decision performance. The sixth and final chapter describes a network inference procedure that identifies genetic dependencies between polymorphic cysteines. It models the interactions between cysteines (nodes) as signed edges for positive or inhibitory relations. It utilizes local network structures for inferences about the relationship between the cysteines. The algorithm exhibits stability and efficiency, converging rapidly to inferred solutions.

Fashion webshops face high return rates, which is both an unsustainable and very costly practice. A significant part of returns is made because of size and fit-related issues. We introduce four models for providing product size recommendations based on cross-merchant sales and return data. This data is typically highly sparse and noisy, making the development of a size recommendation system challenging. Moreover, we do not have access to fit feedback or the reason why a consumer made a return. We assess model performance on both a proprietary data set consisting of shoe purchases and a publicly available data set containing rentals of various categories of women's apparel. Our baseline model predicts the probability of fit for a specific consumer-article combination based on the average catalog size of all articles purchased and kept by that particular consumer. This model outperforms two more advanced models deriving true size variables for consumers and articles on both data sets. The fourth model we develop is a Bayesian size recommendation model, which is fitted with mean-field variational inference. It performs comparably to baseline on unseen data. However, it has the added benefit of being able to filter out low-confidence recommendations, such that higher performance can be achieved at the cost of a lower coverage level. All models show signs of overfitting to training data, and hence we recommend future research to focus on developing a variant of the Bayesian model with fewer degrees of freedom. Results suggest that such a model could be able to provide even better product size recommendations. / E-handlare inom modesegmentet lider av höga nivåer av returer, vilket är både ohållbart och mycket kostsamt. En signifikant del av returer görs på grund av problem relaterat till storlek och passform. Vi presenterar fyra modeller för att ge storleksrekommendationer baserat på försäljningar och returer från flera företag. Sådan data är typiskt mycket gles och brusig, vilket gör utvecklandet av system för storleksrekommendationer utmanande. Utöver detta så har vi inte tillgång till någon återkoppling från kunderna om storleken och passformen, eller anledningen till att produkten returnerats. Vi utvärderar modellernas kvalitet på både ett proprietärt dataset med skoköp, samt ett publikt dataset med hyrkläder av olika sorter. Vår grundläggande model förutsäger sannolikheten för att en artikel passar en viss kund baserat på medelvärdet av storleken för kundens tidigare köp. Denna modell presterar bättre än två av de mer avancerade modellerna som estimerar denna sanna storleken för kunder och artiklar. Den fjärde modellen vi utvecklar är en Bayesiansk modell som tränas med en uppskattningsmetod. Denna modell presterar likvärdigt med den enklaste modellen, men har den extra fördelen att bättre rekommendationer kan fås genom att filtrera baserat på säkerhetsmått. Samtliga modeller har svårt att generalisera på ett önskvärt sätt, och därmed rekommenderar vi framtida forskning som fokuserar på att utveckla den Bayesianska metoden med ett mindre antal frihetsgrader. Resultaten pekar på att en sådan modell skulle kunna bidra med ännu bättre rekommendationer.

There has been tremendous advancement in sequencing technologies; the rate at which sequencing data can be generated has increased multifold while the cost of sequencing continues on a downward descent. Sequencing data provide novel insights into the ecological environment of microbes as well as human health and disease status but challenge investigators with a variety of computational issues. This thesis focuses on three common problems in the analysis of high-throughput data. The goals of the first project are to (1) develop a statistical framework and a complete software pipeline for metagenomics that identifies microbes to the strain level and thus facilitating a personalized drug treatment targeting the strain; and (2) estimate the relative content of microbes in a sample as accurately and as quickly as possible. The second project focuses on the analysis of the microbiome variation across multiple samples. Studying the variation of microbiomes under different conditions within an organism or environment is the key to diagnosing diseases and providing personalized treatments. The goals are to (1) identify various statistical diversity measures; (2) develop confidence regions for the relative abundance estimates; (3) perform multi-dimensional and differential expression analysis; and (4) develop a complete pipeline for multi-sample microbiome analysis. The third project is focused on batch effect analysis. When analyzing high dimensional data, non-biological experimental variation or “batch effects” confound the true associations between the conditions of interest and the outcome variable. Batch effects exist even after normalization. Hence, unless the batch effects are identified and corrected, any attempts for downstream analyses, will likely be error prone and may lead to false positive results. The goals are to (1) analyze the effect of correlation of the batch adjusted data and develop new techniques to account for correlation in two step hypothesis testing approach; (2) develop a software pipeline to identify whether batch effects are present in the data and adjust for batch effects in a suitable way. In summary, we developed software pipelines called PathoScope, PathoStat and BatchQC as part of these projects and validated our techniques using simulation and real data sets.

Cette thèse étudie le traitement statistique des images d’ultrasons de haute fréquence, avec application à l’exploration in-vivo de la peau humaine et l’évaluation non invasive de lésions. Des méthodes Bayésiennes sont considérées pour la segmentation d’images échographiques de la peau. On y établit que les ultrasons rétrodiffusés par la peau convergent vers un processus aléatoire complexe de type Levy-Flight, avec des statistiques non Gaussiennes alpha-stables. L’enveloppe du signal suit une distribution Rayleigh généralisée à queue lourde. A partir de ces résultats, il est proposé de modéliser l’image ultrason de multiples tissus comme un mélange spatialement cohérent de lois Rayleigh à queues lourdes. La cohérence spatiale inhérente aux tissus biologiques est modélisée par un champ aléatoire de Potts-Markov pour représenter la dépendance locale entre les composantes du mélange. Un algorithme Bayésien original combiné à une méthode Monte Carlo par chaine de Markov (MCMC) est proposé pour conjointement estimer les paramètres du modèle et classifier chaque voxel dans un tissu. L’approche proposée est appliquée avec succès à la segmentation de tumeurs de la peau in-vivo dans des images d’ultrasons de haute fréquence en 2D et 3D. Cette méthode est ensuite étendue en incluant l’estimation du paramètre B de régularisation du champ de Potts dans la chaine MCMC. Les méthodes MCMC classiques ne sont pas directement applicables à ce problème car la vraisemblance du champ de Potts ne peut pas être évaluée. Ce problème difficile est traité en adoptant un algorithme Metropolis-Hastings “sans vraisemblance” fondé sur la statistique suffisante du Potts. La méthode de segmentation non supervisée, ainsi développée, est appliquée avec succès à des images échographiques 3D. Finalement, le problème du calcul de la borne de Cramer-Rao (CRB) du paramètre B est étudié. Cette borne dépend des dérivées de la constante de normalisation du modèle de Potts, dont le calcul est infaisable. Ce problème est résolu en proposant un algorithme Monte Carlo original, qui est appliqué avec succès au calcul de la borne CRB des modèles d’Ising et de Potts. / This thesis studies statistical image processing of high frequency ultrasound imaging, with application to in-vivo exploration of human skin and noninvasive lesion assessment. More precisely, Bayesian methods are considered in order to perform tissue segmentation in ultrasound images of skin. It is established that ultrasound signals backscattered from skin tissues converge to a complex Levy Flight random process with non-Gaussian _-stable statistics. The envelope signal follows a generalized (heavy-tailed) Rayleigh distribution. Based on these results, it is proposed to model the distribution of multiple-tissue ultrasound images as a spatially coherent finite mixture of heavy-tailed Rayleigh distributions. Spatial coherence inherent to biological tissues is modeled by a Potts Markov random field. An original Bayesian algorithm combined with a Markov chain Monte Carlo method is then proposed to jointly estimate the mixture parameters and a label-vector associating each voxel to a tissue. The proposed method is successfully applied to the segmentation of in-vivo skin tumors in high frequency 2D and 3D ultrasound images. This method is subsequently extended by including the estimation of the Potts regularization parameter B within the Markov chain Monte Carlo (MCMC) algorithm. Standard MCMC methods cannot be applied to this problem because the likelihood of B is intractable. This difficulty is addressed by using a likelihood-free Metropolis-Hastings algorithm based on the sufficient statistic of the Potts model. The resulting unsupervised segmentation method is successfully applied to tridimensional ultrasound images. Finally, the problem of computing the Cramer-Rao bound (CRB) of B is studied. The CRB depends on the derivatives of the intractable normalizing constant of the Potts model. This is resolved by proposing an original Monte Carlo algorithm, which is successfully applied to compute the CRB of the Ising and Potts models.

Les événements de pluies extrêmes et les inondations qui en résultent constituent une préoccupation majeure en France comme dans le monde. Dans le domaine de l'ingénierie, les méthodes d'analyse probabiliste sont pratiquement utilisées pour prédire les risques, dimensionner des ouvrages hydrauliques et préparer l'atténuation. Ces méthodes sont classiquement basées sur l'hypothèse que les observations sont identiquement distribuées. Il y a aujourd'hui de plus en plus d'éléments montrant que des variabilités climatiques à grande échelle (par exemple les oscillations El Niño – La Niña, cf. indice ENSO) ont une influence significative sur les précipitations dans le monde. Par ailleurs, les effets attendus du changement climatique sur le cycle de l'eau remettent en question l'hypothèse de variables aléatoires "identiquement distribuées" dans le temps. Il est ainsi important de comprendre et de prédire l'impact de la variabilité et du changement climatique sur l'intensité et la fréquence des événements hydrologiques, surtout les extrêmes. Cette thèse propose une étape importante vers cet objectif, en développant un cadre spatio-temporel d'analyse probabiliste régionale qui prend en compte les effets de la variabilité climatique sur les événements hydrologiques. Les données sont supposées suivre une distribution, dont les paramètres sont liés à des variables temporelles et/ou spatiales à l'aide de modèles de régression. Les paramètres sont estimés avec une méthode de Monte-Carlo par Chaînes de Markov dans un cadre Bayésien. La dépendance spatiale des données est modélisée par des copules. Les outils de comparaison de modèles sont aussi intégrés. L'élaboration de ce cadre général de modélisation est complétée par des simulations Monte-Carlo pour évaluer sa fiabilité. Deux études de cas sont effectuées pour confirmer la généralité, la flexibilité et l'utilité du cadre de modélisation pour comprendre et prédire l'impact de la variabilité climatique sur les événements hydrologiques. Ces cas d'études sont réalisés à deux échelles spatiales distinctes: • Echelle régionale: les pluies d'été dans le sud-est du Queensland (Australie). Ce cas d'étude analyse l'impact de l'oscillation ENSO sur la pluie totale et la pluie maximale d'été. En utilisant un modèle régional, l'impact asymétrique de l'ENSO est souligné: une phase La Niña induit une augmentation significative sur la pluie totale et maximale, alors qu'une phase El Niño n'a pas d'influence significative. • Echelle mondiale: une nouvelle base de données mondiale des précipitations extrêmes composée de 11588 stations pluviométriques est utilisée pour analyser l'impact des oscillations ENSO sur les précipitations extrêmes mondiales. Cette analyse permet d'apprécier les secteurs où ENSO a un impact sur les précipitations à l'échelle mondiale et de quantifier son impact sur les estimations de quantiles extrêmes. Par ailleurs, l'asymétrie de l'impact ENSO et son caractère saisonnier sont également évalués. / Extreme precipitations and their consequences (floods) are one of the most threatening natural disasters for human beings. In engineering design, Frequency Analysis (FA) techniques are an integral part of risk assessment and mitigation. FA uses statistical models to estimate the probability of extreme hydrological events which provides information for designing hydraulic structures. However, standard FA methods commonly rely on the assumption that the distribution of observations is identically distributed. However, there is now a substantial body of evidence that large-scale modes of climate variability (e.g. El-Niño Southern Oscillation, ENSO; Indian Ocean Dipole, IOD; etc.) exert a significant influence on precipitation in various regions worldwide. Furthermore, climate change is likely to have an influence on hydrology, thus further challenging the “identically distributed” assumption. Therefore, FA techniques need to move beyond this assumption. In order to provide a more accurate risk assessment, it is important to understand and predict the impact of climate variability/change on the severity and frequency of hydrological events (especially extremes). This thesis provides an important step towards this goal, by developing a rigorous general climate-informed spatio-temporal regional frequency analysis (RFA) framework for incorporating the effects of climate variability on hydrological events. This framework brings together several components (in particular spatio-temporal regression models, copula-based modeling of spatial dependence, Bayesian inference, model comparison tools) to derive a general and flexible modeling platform. In this framework, data are assumed to follow a distribution, whose parameters are linked to temporal or/and spatial covariates using regression models. Parameters are estimated with a Monte Carlo Markov Chain method under the Bayesian framework. Spatial dependency of data is considered with copulas. Model comparison tools are integrated. The development of this general modeling framework is complemented with various Monte-Carlo experiments aimed at assessing its reliability, along with real data case studies. Two case studies are performed to confirm the generality, flexibility and usefulness of the framework for understanding and predicting the impact of climate variability on hydrological events. These case studies are carried out at two distinct spatial scales: • Regional scale: Summer rainfall in Southeast Queensland (Australia): this case study analyzes the impact of ENSO on the summer rainfall totals and summer rainfall maxima. A regional model allows highlighting the asymmetric impact of ENSO: while La Niña episodes induce a significant increase in both the summer rainfall totals and maxima, the impact of El Niño episodes is found to be not significant. • Global scale: a new global dataset of extreme precipitation including 11588 rainfall stations worldwide is used to describe the impact of ENSO on extreme precipitations in the world. This is achieved by applying the regional modeling framework to 5x5 degrees cells covering all continental areas. This analysis allows describing the pattern of ENSO impact at the global scale and quantifying its impact on extreme quantiles estimates. Moreover, the asymmetry of ENSO impact and its seasonal pattern are also evaluated.

Cette thèse présente des contributions à la littérature des méthodes de Monte Carlo utilisé dans l'analyse des modèles complexes en statistique Bayésienne; l'accent est mis à la fois sur la complexité des modèles et sur les difficultés de calcul.Le premier chapitre élargit Delayed Acceptance, une variante computationellement efficace du Metropolis--Hastings, et agrandit son cadre théorique fournissant une justification adéquate pour la méthode, des limits pour sa variance asymptotique par rapport au Metropolis--Hastings et des idées pour le réglage optimal de sa distribution instrumentale.Nous allons ensuite développer une méthode Bayésienne pour analyser les processus environnementaux non stationnaires, appelées Expansion Dimension, qui considère le processus observé comme une projection depuis une dimension supérieure, où l'hypothèse de stationnarité pourrait etre acceptée. Le dernier chapitre sera finalement consacrée à l'étude des structures de dépendances conditionnelles par une formulation entièrement Bayésienne du modèle de Copule Gaussien graphique. / This thesis presents contributions to the Monte Carlo literature aimed toward the analysis of complex models in Bayesian Statistics; the focus is on both complexity related to complicate models and computational difficulties.We will first expand Delayed Acceptance, a computationally efficient variant ofMetropolis--Hastings, to a multi-step procedure and enlarge its theoretical background, providing proper justification for the method, asymptotic variance bounds relative to its parent MH kernel and optimal tuning for the scale of its proposal.We will then develop a flexible Bayesian method to analyse nonlinear environmentalprocesses, called Dimension Expansion, that essentially consider the observed process as a projection from a higher dimension, where the assumption of stationarity could hold.The last chapter will finally be dedicated to the investigation of conditional (in)dependence structures via a fully Bayesian formulation of the Gaussian Copula graphical model.