Precision medicine provides targeted treatment for an individual patient based on disease mechanisms, promoting health care. Matched transcriptomes derived from a single subject enable uncovering patient-specific dynamic changes associated with disease status. Yet, conventional statistical methodologies remain largely unavailable for single-subject transcriptome analysis due to the "single-observation" challenge. We hypothesize that, with statistical learning approaches and large-scale inferences, one can learn useful information from single-subject transcriptome data by identifying differentially expressed genes (DEG) / pathways (DEP) between two transcriptomes of an individual. This dissertation is an ensemble of my research work in single-subject transcriptome analytics, including three projects with varying focuses. The first project describes a two-step approach to identify DEPs by employing a parametric Gaussian mixture model followed by Fisher's exact tests. The second project relaxes the parametric assumption and develops a nonparametric algorithm based on k-means, which is more flexible and robust. The third project proposes a novel variance stabilizing framework to transform raw gene counts before identifying DEGs, and the transformation strategically by-passes the challenge of variance estimation in single-subject transcriptome analysis. In this dissertation, I present the main statistical methods and computational algorithms for all the three projects, as well as their real-data applications to personalized treatments.

<p>This thesis investigates frequentist properties of Bayesian multiple testing procedures in a variety of scenarios and depicts the asymptotic behaviors of Bayesian methods. Both Bayesian and frequentist approaches to multiplicity control are studied and compared, with special focus on understanding the multiplicity control behavior in situations of dependence between test statistics.</p><p>Chapter 2 examines a problem of testing mutually exclusive hypotheses with dependent data. The Bayesian approach is shown to have excellent frequentist properties and is argued to be the most effective way of obtaining frequentist multiplicity control without sacrificing power. Chapter 3 further generalizes the model such that multiple signals are acceptable, and depicts the asymptotic behavior of false positives rates and the expected number of false positives. Chapter 4 considers the problem of dealing with a sequence of different trials concerning some medical or scientific issue, and discusses the possibilities for multiplicity control of the sequence. Chapter 5 addresses issues and efforts in reconciling frequentist and Bayesian approaches in sequential endpoint testing. We consider the conditional frequentist approach in sequential endpoint testing and show several examples in which Bayesian and frequentist methodologies cannot be made to match.</p> / Dissertation

Ces travaux se placent dans le contexte de l'étude des champs profonds hyperspectraux produits par l'instrument d'observation céleste MUSE. Ces données permettent de sonder l'Univers lointain et d'étudier les propriétés physiques et chimiques des premières structures galactiques et extra-galactiques. La première problématique abordée dans cette thèse est l'attribution d'une signature spectrale pour chaque source galactique. MUSE étant un instrument au sol, la turbulence atmosphérique dégrade fortement le pouvoir de résolution spatiale de l'instrument, ce qui génère des situations de mélange spectral pour un grand nombre de sources. Pour lever cette limitation, des approches de fusion de données, s'appuyant sur les données complémentaires du télescope spatial Hubble et d'un modèle de mélange linéaire, sont proposées, permettant la séparation spectrale des sources du champ. Le second objectif de cette thèse est la détection du Circum-Galactic Medium (CGM). Le CGM, milieu gazeux s'étendant autour de certaines galaxies, se caractérise par une signature spatialement diffuse et de faible intensité spectrale. Une méthode de détection de cette signature par test d'hypothèses est développée, basée sur une stratégie de max-test sur un dictionnaire et un apprentissage des statistiques de test sur les données. Cette méthode est ensuite étendue pour prendre en compte la structure spatiale des sources et ainsi améliorer la puissance de détection tout en conservant un contrôle global des erreurs. Les codes développés sont intégrés dans la bibliothèque logicielle du consortium MUSE afin d'être utilisables par l'ensemble de la communauté. De plus, si ces travaux sont particulièrement adaptés aux données MUSE, ils peuvent être étendus à d'autres applications dans les domaines de la séparation de sources et de la détection de sources faibles et étendues. / This work takes place in the context of the study of hyperspectral deep fields produced by the European 3D spectrograph MUSE. These fields allow to explore the young remote Universe and to study the physical and chemical properties of the first galactical and extra-galactical structures.The first part of the thesis deals with the estimation of a spectral signature for each galaxy. As MUSE is a terrestrial instrument, the atmospheric turbulences strongly degrades the spatial resolution power of the instrument thus generating spectral mixing of multiple sources. To remove this issue, data fusion approaches, based on a linear mixing model and complementary data from the Hubble Space Telescope are proposed, allowing the spectral separation of the sources.The second goal of this thesis is to detect the Circum-Galactic Medium (CGM). This CGM, which is formed of clouds of gas surrounding some galaxies, is characterized by a spatially extended faint spectral signature. To detect this kind of signal, an hypothesis testing approach is proposed, based on a max-test strategy on a dictionary. The test statistics is learned on the data. This method is then extended to better take into account the spatial structure of the targets, thus improving the detection power, while still ensuring global error control.All these developments are integrated in the software library of the MUSE consortium in order to be used by the astrophysical community.Moreover, these works can easily be extended beyond MUSE data to other application fields that need faint extended source detection and source separation methods.