Après une introduction à l’hadronthérapie et à la détection gamma prompts, cette thèse de doctorat comprend deux contributions principales: le développement d'une méthode de simulation des gamma prompt (PG) et son application dans une étude de la détection des changements dans les traitements cliniques. La méthode de réduction de variance (vpgTLE) est une méthode d'estimation de longueur de piste en deux étapes développée pour estimer le rendement en PG dans les volumes voxélisés. Comme les particules primaires se propagent tout au long de la CT du patient, les rendements de PG sont calculés en fonction de l'énergie actuelle du primaire, du matériau du voxel et de la longueur de l'étape. La deuxième étape utilise cette image intermédiaire comme source pour générer et propager le nombre de PG dans le reste de la géométrie de la scène, par exemple Dans un dispositif de détection. Pour un fantôme hétérogéné et un plan de traitement CT complet par rapport à MC analogue, à un niveau de convergence de 2% d'incertitude relative sur le rendement de PG par voxel dans la région de rendement de 90%, un gain d'environ 10^3 A été atteint. La méthode s'accorde avec les simulations analogiques MC de référence à moins de 10^-4 par voxel, avec un biais négligeable. La deuxième étude majeure menée dans portait sur l'estimation PG FOP dans les simulations cliniques. Le nombre de protons (poids spot) requis pour une estimation FOP constante a été étudié pour la première fois pour deux caméras PG optimisées, une fente multi-parallèle (MPS) et une conception de bordure de couteau (KES). Trois points ont été choisis pour une étude approfondie et, au niveau des points prescrits, on a constaté qu'ils produisaient des résultats insuffisants, ce qui rend improbable la production clinique utilisable sur le terrain. Lorsque le poids spot est artificiellement augmenté à 10^9 primaires, la précision sur le FOP atteint une précision millimétrique. Sur le décalage FOP, la caméra MPS fournit entre 0,71 - 1,02 mm (1sigma) de précision pour les trois points à 10 $ 9 $ de protons; Le KES entre 2.10 - 2.66 mm. Le regroupement de couches iso-énergétiques a été utilisé dans la détection par PG de distribution passive pour l'un des prototypes d'appareils PG. Dans le groupement iso-depth, activé par la livraison active, les taches avec des chutes de dose distales similaires sont regroupées de manière à fournir des retombées bien définies comme tentative de mélange de gamme de distance. Il est démontré que le regroupement de taches n'a pas nécessairement une incidence négative sur la précision par rapport à la tache artificiellement accrue, ce qui signifie qu'une certaine forme de groupage de points peut permettre l'utilisation clinique de ces caméras PG. Avec tous les spots ou les groupes spot, le MPS a un meilleur signal par rapport au KES, grâce à une plus grande efficacité de détection et à un niveau de fond inférieur en raison de la sélection du temps de vol. / After an introduction to particle therapy and prompt gamma detection, this doctoral dissertation comprises two main contributions: the development of a fast prompt gammas (PGs) simulation method and its application in a study of change detectability in clinical treatments. The variance reduction method (named vpgTLE) is a two-stage track length estimation method developed to estimate the PG yield in voxelized volumes. As primary particles are propagated throughout the patient CT, the PG yields are computed as function of the current energy of the primary, the material in the voxel and the step length. The second stage uses this intermediate image as a source to generate and propagate the number of PGs throughout the rest of the scene geometry, e.g. into a detection device. For both a geometrical heterogeneous phantom and a complete patient CT treatment plan with respect to analog MC, at a convergence level of 2\% relative uncertainty on the PG yield per voxel in the 90\% yield region, a gain of around $10^3$ was achieved. The method agrees with reference analog MC simulations to within $10^{-4}$ per voxel, with negligible bias. The second major study conducted in this PhD program was on PG FOP estimation in clinical simulations. The number of protons (spot weight) required for a consistent FOP estimate was investigated for the first time for two optimized PG cameras, a multi-parallel slit (MPS) and a knife edge design (KES). Three spots were selected for an in depth study, and at the prescribed spot weights were found to produce results of insufficient precision, rendering usable clinical output on the spot level unlikely. When the spot weight is artificially increased to $10^9$ primaries, the precision on the FOP reaches millimetric precision. On the FOP shift the MPS camera provides between 0.71 - 1.02 mm (1$\upsigma$) precision for the three spots at $10^9$ protons; the KES between 2.10 - 2.66 mm. Grouping iso-energy layers was employed in passive delivery PG detection for one of the PG camera prototypes. In iso-depth grouping, enabled by active delivery, spots with similar distal dose fall-offs are grouped so as to provide well-defined fall-offs as an attempt to sidestep range mixing. It is shown that grouping spots does not necessarily negatively affect the precision compared to the artificially increased spot, which means some form of spot grouping can enable clinical use of these PG cameras. With all spots or spot groups the MPS has a better signal compared to the KES, thanks to a larger detection efficiency and a lower background level due to time of flight selection.

O conhecimento da base genética dos caracteres é muito importante para orientar os melhoristas quanto às estratégias a serem utilizadas visando uma maior eficiência dos programas de seleção. Para os caracteres quantitativos, o estudo da base genética dos mesmos é geralmente feito através de estimativas de componentes de variância. A maioria dos delineamentos genéticos disponíveis permite estimar a variância genética aditiva e a variância genética dominante. Poucos delineamentos permitem detectar a ocorrência de epistasia e, consequentemente o componente epistático da variância genética. O objetivo deste trabalho foi detectar a ocorrência da epistasia em soja utilizando o Delineamento Trialélico Modificado (\"Modified triple test cross). O material genético utilizado compreendeu uma amostra de 30 linhas puras derivadas do cruzamento entre os genitores PI-123439 e PI-239235. As 30 linhas puras foram cruzadas com dois testadores contrastantes para a produção de grãos, denominados L1 e L2, gerando, portanto, 60 cruzamentos. Os cruzamentos foram autofecundados, a fim de multiplicar as sementes para a realização dos experimentos, obtendo-se, portanto, a geração F2 dos 60 cruzamentos. No ano agrícola de 2003/2004 os tratamentos foram avaliados em um experimento em blocos ao acaso com 15 repetições, contendo 90 tratamentos, isto é, os 60 cruzamentos, e as 30 linhagens. No ano agrícola de 2004/2005 foi feita uma nova avaliação experimental, de maneira semelhante ao ano anterior, utilizando como tratamentos os \"bulks\" de cada tratamento da geração anterior (geração F3). Em todos os casos as parcelas experimentais foram constituídas de uma linha de dois metros, com espaçamento entre linhas de 0,50 metros, contendo 35 plantas no estande ideal. Foram avaliados os seguintes caracteres: produção de grãos (PG), altura da planta no florescimento (AF), altura da planta na maturação (AM), dias para o florescimento (DF) e dias para a maturação (DM). Os dados experimentais foram submetidos às análises de variância e em seguida a uma análise genética, segundo o Delineamento Trialélico Modificado, que foi adaptado para as gerações F2 e F3. Os resultados indicaram a ocorrência de epistasia para PG, DF e DM, mas não para AF. Quanto ao caráter AM, não foi possível tirar conclusões, sendo necessário mais estudos. Estes resultados indicam que as estimativas de variâncias genéticas aditivas e dominantes para caracteres como PG, DF e DM em soja podem ser viesadas, quando não se considera a epistasia no modelo. / The understanding of the nature of genetic traits is very important in guiding plant breeders in designing strategies aiming to increase efficiency of selection programmes. The study of the genetic basis of quantitative traits is generally done through estimates of variance. The majority of genetic tests currently available permit the estimate of both additive and dominant genetic variance. Few tests detect the occurrence of epistasis and consequently the epistatic component of genetic variance. The objective of this work was to detect the occurrence of epistatis in soybean by using the \"Modified triple test cross\". The genetic material utilized consisted of a sample of 30 pure lines derived from a cross between the genitors PI-123439 and PI239235. The 30 pure lines were crossed with two contrasting test individuals to produce seed, which was denominated L1 and L2, generated from a total of 60 crosses. The progeny were self-crossed to multiply the seeds in order to carry out the experiments, producing an F2 generation of the 60 crosses. In the agricultural year 2003-2004 the measurements were carried out in an experiment of random plots with 15 repetitions, totalling 90 sets. In the agricultural year 2004-2005 further experiments were carried out, and measurements were taken using plants from the bulked F3 seed. In all cases the experimental plots consisted of a line of two metres, with a space between lines of 0.5 metres, totalling an average of 35 plants. The following traits were evaluated: grain yield, inflorescence height, plant height at maturation, age at flowering and maturation. The experimental data was subjected to analyses of genetic variance, followed by genetic analysis and the \"Modified triple test cross\" that was adapted for the F2 and F3 generations. The results indicate the occurrence of epistasis for grain yield, age at flowering and maturation, but not for plant height at flowering. It was not possible to determine if the trait for plant height at maturation showed epistasis, further experiments need to be carried out. These results suggest that the estimates of genetic additive and dominant variance for the grain yield, age at flowering and maturation traits in soybean may be incorrect when epistasis is not considered in the model.

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Les familles exponentielles de lois de probabilité offrent une panoplie de modèles très utiles en statistique ainsi qu'en probabilités. Les travaux résumés dans ce mémoire s'intéressent à leurs caractérisations et interprétations probabilistes, ainsi que leurs applications en statistique. Dans la première partie, une nouvelle classe de familles exponentielles naturelles (FEN) est introduite puis décrite complétement. Elle s'appuie sur une transformation dite de Lindsay des FEN de fonctions variance cubiques. Des interprétations probabilistes par les lois de temps de frappe des processus stochastiques sont données. Enfin, à travers une notion de d-pseudo-orthogonalité des polynômes associés à une densité de FEN, plusieurs caractérisations des FEN de fonctions variance polynomiales de degré 2d-1 sont données pour d=2,3,... . La deuxième partie est consacrée au déterminant des matrices de moments des lois multidimensionnelles. Deux aspects sont principalement explorés : le premier a trait à une caractérisation du déterminant de la hessienne d'une transformée de Laplace et ses conséquences ; le second concerne de meilleurs estimateurs de la variance généralisée ou du déterminant de la matrice de variance-covariance. Une nouvelle caractérisation des FEN Poisson-gaussiennes moyennant la variance généralisée est alors donnée. La troisième partie étudie des modèles exponentiels, de plus en plus appropriés et complémentaires, pour l'analyse statistique des données de comptage qui révèle une variabilité plus grande que la moyenne prédite. Ce phénomène dit de surdispersion par rapport à la loi de Poisson est examiné à travers des FEN binomiale négative généralisée et arcsinus stricte ainsi que d'une grande classe des FEN dite de Hinde-Demétrio, laquelle englobe la binomiale négative et l'arcsinus stricte. Des estimations et test d'hypothèses sur certains paramètres des modèles surdispersés sont proposés et appliquées sur des données réelles. Dans la dernière partie, deux techniques d'estimation sont présentées. La première est relative à une loi implicite ou conditionnelle d'un paramètre connaissant les observations. La seconde est une approche pour montrer l'unimodalité de la vraisemblance dans un modèle de capture séquentielle. Cette dernière est appliquée à l'estimation de la biomasse des saumons dans le bassin de l'Adour.

This thesis develops and evaluates statistical methods for different types of genetic analyses, including quantitative trait loci (QTL) analysis, genome-wide association study (GWAS), and genomic evaluation. The main contribution of the thesis is to provide novel insights in modeling genetic variance, especially via random effects models. In variance component QTL analysis, a full likelihood model accounting for uncertainty in the identity-by-descent (IBD) matrix was developed. It was found to be able to correctly adjust the bias in genetic variance component estimation and gain power in QTL mapping in terms of precision.  Double hierarchical generalized linear models, and a non-iterative simplified version, were implemented and applied to fit data of an entire genome. These whole genome models were shown to have good performance in both QTL mapping and genomic prediction. A re-analysis of a publicly available GWAS data set identified significant loci in Arabidopsis that control phenotypic variance instead of mean, which validated the idea of variance-controlling genes.  The works in the thesis are accompanied by R packages available online, including a general statistical tool for fitting random effects models (hglm), an efficient generalized ridge regression for high-dimensional data (bigRR), a double-layer mixed model for genomic data analysis (iQTL), a stochastic IBD matrix calculator (MCIBD), a computational interface for QTL mapping (qtl.outbred), and a GWAS analysis tool for mapping variance-controlling loci (vGWAS).

In this study, we show that realized bipower variation which is an extension of realized power variation is an alternative method that estimates integrated variance like realized variance. It is seen that realized bipower variation is robust to rare jumps. Robustness means that if we add rare jumps to a stochastic volatility process, realized bipower variation process continues to estimate integrated variance although realized variance estimates integrated variance plus the quadratic variation of the jump component. This robustness is crucial since it separates the discontinuous component of quadratic variation which comes from the jump part of the logarithmic price process. Thus, we demonstrate that if the logarithmic price process is in the class of stochastic volatility plus rare jumps processes then the difference between realized variance and realized bipower variation process estimates the discontinuous component of the quadratic variation. So, quadratic variation of the jump component can be estimated and jump detection can be achieved.

This thesis develops and evaluates statistical methods for different types of genetic analyses, including quantitative trait loci (QTL) analysis, genome-wide association study (GWAS), and genomic evaluation. The main contribution of the thesis is to provide novel insights in modeling genetic variance, especially via random effects models. In variance component QTL analysis, a full likelihood model accounting for uncertainty in the identity-by-descent (IBD) matrix was developed. It was found to be able to correctly adjust the bias in genetic variance component estimation and gain power in QTL mapping in terms of precision.  Double hierarchical generalized linear models, and a non-iterative simplified version, were implemented and applied to fit data of an entire genome. These whole genome models were shown to have good performance in both QTL mapping and genomic prediction. A re-analysis of a publicly available GWAS data set identified significant loci in Arabidopsis that control phenotypic variance instead of mean, which validated the idea of variance-controlling genes.  The works in the thesis are accompanied by R packages available online, including a general statistical tool for fitting random effects models (hglm), an efficient generalized ridge regression for high-dimensional data (bigRR), a double-layer mixed model for genomic data analysis (iQTL), a stochastic IBD matrix calculator (MCIBD), a computational interface for QTL mapping (qtl.outbred), and a GWAS analysis tool for mapping variance-controlling loci (vGWAS).

Bioequivalence determines if two drugs are alike. The three kinds of bioequivalence are Average, Population, and Individual Bioequivalence. These Bioequivalence criteria can be evaluated using aggregate and disaggregate methods. Considerable work assessing bioequivalence in a frequentist method exists, but the advantages of Bayesian methods for Bioequivalence have been recently explored. Variance parameters are essential to any of theses existing Bayesian Bioequivalence metrics. Usually, the prior distributions for model parameters use either informative priors or vague priors. The Bioequivalence inference may be sensitive to the prior distribution on the variances. Recently, there have been questions about the routine use of inverse gamma priors for variance parameters. In this paper we examine the effect that changing the prior distribution of the variance parameters has on Bayesian models for assessing Bioequivalence and the carry-over effect. We explore our method with some real data sets from the FDA.

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal

本論文在Li(2000)的Gaussian Copula的背景之下，將資產價值服從常態分配的假設改為服從Variance Gamma分配，利用Copula模型模擬債權群組內各個標的資產的違約時點，並利用蒙地卡羅抽取亂數的方法，取平均之後求得信用連結債券所連結的資產債權組合價值。除此之外，本論文比較假設資產價值服從常態分配、Student t分配和Variance Gamma分配下，計算求得的資產池價值。實證結果顯示，假設服從Variance Gamma分配最接近市場的真實違約資料。這是由於Variance Gamma分配具備Student t分配的厚尾性質，能有效捕捉常態分配缺少的尾端損失機率，並可調整偏態係數和峰態係數，可以求出更接近市場價值的評價結果。最後，在敏感度分析方面，改變影響資產池價值的兩大因子：平均違約回收率和資產間相關係數。結果顯示，當平均違約回收率高於0.7時，相關係數越高的債權群組，其資產池價值亦越高。若平均違約回收率越低且資產間相關係數越高的話，越容易出現一起違約的現象，因此資產池價值會下降。因此投資人在挑選信用連結債券時，應注意所連結的標的資產群組內資產報酬的相關性，最好避免相關性高的資產群組，以免金融海嘯來臨的時候，多個資產同時違約的情形發生。