Although many genetic factors have been successfully identified for human diseases in genome-wide association studies (GWAS), genes discovered to date only account for a small proportion of overall genetic contributions to many complex traits. Association studies have difficulty in detecting the remaining true genetic variants that are either common variants with weak allelic effects, or rare variants that have strong allelic effects but are weakly associated at the population level. In this work we applied a goodness-of-fit test for detecting sets of common and rare variants associated with quantitative or binary traits by using whole genome sequencing (WGS) data. This test has been proved optimal for detecting weak and sparse signals in the literature, which fits the requirements for targeting the genetic components of missing heritability. Furthermore, this p-value-combining method allows one to incorporate different data and/or research results for meta-analysis. The method was used to simultaneously analyse the WGS and GWAS data of Genetic Analysis Workshop (GAW) 18 for detecting true genetic variants. The results show that goodness-of-fit test is comparable or better than the influential sequence kernel association test in many cases.

Le monde entier est en train de subir le brassage des populations au moins deux fois plus intense qu'il y a cinquante ans. Les gens traversent le globe, menés d'un côté par la curiosité, la volonté de connaître et de comprendre les différentes nations, cultures, religions etc., l'envie d'élargir ses propres horizons, et d'un autre côté par la recherche d'une vie meilleure. Sur ces routes dessinées par les différentes volontés les destins des personnes dissemblables se croisent et c'est à ce moment-là, confrontés à la diversité nationale, culturelle, religieuse, linguistique, … qu'ils choisissent de vivre ou de renoncer à une histoire d'amour avec un ‘étranger' à ses propres valeurs. Je souhaite comprendre cette partie de la population, statistiquement minoritaire, qui décide de braver des interdits et de s'unir avec une personne d'une autre confession, et ceux malgré la société et surtout les représentants religieux qui favorisent les couples homogames. Pourquoi choisir ‘un(e) étranger(ère)' quand la grande majorité préfère de se marier avec une personne qui leurs ressemble de point de vue religieux et culturel? Qu'offre de plus l'union interconfessionnelle pour renoncer aux solutions plus faciles ? Dans quelles conditions est-il possible un tel mariage ? Quelle sont des relations des couples mixtes avec la société ? A travers nos recherches, basées sur la théorie de don de Marcel Mauss : donner, recevoir, rendre, nous souhaitons apporter les réponses à toutes ces questions. / The world is undergoing the mixing of populations at least two times more intense than fifty years ago. People across the globe, led on one side by curiosity, the desire to know and understand the different nations, cultures, religions ..., the desire to broaden its horizons, and on the other hand by the search of a better life. On these routes drawn by different wills destinies intersect dissimilar people and this is then faced with diverse national, cultural, religious, linguistic, they choose to live ... or not a story love with a 'stranger' to its own values. I want to understand this part of the population, statistically minority who decides to defy prohibitions and to live with a person of another faith, and despite those society and especially religious representatives who promote homogamous couples. Why choose a foreign when the vast majority of people prefer to marry someone who theirs resembles (from the point of view of religion and culture)? Under what conditions is it possible such a marriage? What are the relations of mixed couples with society? Through our research, based on the theory of gift Marcel Mauss: giving, receiving, making, we want to give the answers to all these questions.

Cognitive Radio (CR) has received tremendous research attention over the past decade, both in the academia and industry, as it is envisioned as a promising solution to the problem of spectrum scarcity. ACR is a device that senses the spectrum for occupancy by licensed users(also called as primary users), and transmits its data only when the spectrum is sensed to be available. For the efficient utilization of the spectrum while also guaranteeing adequate protection to the licensed user from harmful interference, the CR should be able to sense the spectrum for primary occupancy quickly as well as accurately. This makes Spectrum Sensing(SS) one of the where the goal is to test whether the primary user is inactive(the null or noise-only hypothesis), or not (the alternate or signal-present hypothesis). Computational simplicity, robustness to uncertainties in the knowledge of various noise, signal, and fading parameters, and ability to handle interference or other source of non-Gaussian noise are some of the desirable features of a SS unit in a CR. In many practical applications, CR devices can exploit known structure in the primary signal. IntheIEEE802.22CR standard, the primary signal is a wideband signal, but with a strong narrowband pilot component. In other applications, such as military communications, and blue tooth, the primary signal uses a Frequency Hopping (FH)transmission. These applications can significantly benefit from detection schemes that are tailored for detecting the corresponding primary signals. This thesis develops novel detection schemes and rigorous performance analysis of these primary signals in the presence of fading. For example, in the case of wideband primary signals with a strong narrowband pilot, this thesis answers the further question of whether to use the entire wideband for signal detection, or whether to filter out the pilot signal and use narrowband signal detection. The question is interesting because the fading characteristics of wideband and narrowband signals are fundamentally different. Due to this, it is not obvious which detection scheme will perform better in practical fading environments. At another end of the gamut of SS algorithms, when the CR has no knowledge of the structure or statistics of the primary signal, and when the noise variance is known, Energy Detection (ED) is known to be optimal for SS. However, the performance of the ED is not robust to uncertainties in the noise statistics or under different possible primary signal models. In this case, a natural way to pose the SS problem is as a Goodness-of-Fit Test (GoFT), where the idea is to either accept or reject the noise-only hypothesis. This thesis designs and studies the performance of GoFTs when the noise statistics can even be non-Gaussian, and with heavy tails. Also, the techniques are extended to the cooperative SS scenario where multiple CR nodes record observations using multiple antennas and perform decentralized detection. In this thesis, we study all the issues listed above by considering both single and multiple CR nodes, and evaluating their performance in terms of(a)probability of detection error,(b) sensing-throughput trade off, and(c)probability of rejecting the null-hypothesis. We propose various SS strategies, compare their performance against existing techniques, and discuss their relative advantages and performance tradeoffs. The main contributions of this thesis are as follows: The question of whether to use pilot-based narrowband sensing or wideband sensing is answered using a novel, analytically tractable metric proposed in this thesis called the error exponent with a confidence level. Under a Bayesian framework, obtaining closed form expressions for the optimal detection threshold is difficult. Near-optimal detection thresholds are obtained for most of the commonly encountered fading models. Foran FH primary, using the Fast Fourier Transform (FFT) Averaging Ratio(FAR) algorithm, the sensing-through put trade off are derived in closed form. A GoFT technique based on the statistics of the number of zero-crossings in the observations is proposed, which is robust to uncertainties in the noise statistics, and outperforms existing GoFT-based SS techniques. A multi-dimensional GoFT based on stochastic distances is studied, which pro¬vides better performance compared to some of the existing techniques. A special case, i.e., a test based on the Kullback-Leibler distance is shown to be robust to some uncertainties in the noise process. All of the theoretical results are validated using Monte Carlo simulations. In the case of FH-SS, an implementation of SS using the FAR algorithm on a commercially off-the ¬shelf platform is presented, and the performance recorded using the hardware is shown to corroborate well with the theoretical and simulation-based results. The results in this thesis thus provide a bouquet of SS algorithms that could be useful under different CRSS scenarios.