Esta tese tem como objetivo principal a proposição de solução para o problema do encaixe de moldes em tecidos listrados da indústria do vestuário. Os moldes são peças com formato irregular que devem ser dispostos sobre a matéria-prima, neste caso o tecido, para a etapa posterior de corte. No problema específico do encaixe em tecidos listrados, o local em que os moldes são posicionados no tecido deve garantir que, após a confecção da peça, as listras apresentem continuidade. Assim, a fundamentação teórica do trabalho abrange temas relacionados à moda e ao design do vestuário, como os tipos e padronagens de tecidos listrados, e as possibilidades de rotação e colocação dos moldes sobre tecidos listrados. Na fundamentação teórica também são abordados temas da pesquisa em otimização combinatória como: características dos problemas bidimensionais de corte e encaixe e algoritmos utilizados por diversos autores para solucionar o problema. Ainda na parte final da fundamentação teórica são descritos o método Cadeia de Markov Monte Carlo e o algoritmo de Metropolis-Hastings. Com base na pesquisa bibliográfica, foram propostos dois algoritmos distintos para lidar com o problema de encaixe de moldes em tecidos listrados: algoritmo com pré-processamento e algoritmo de busca do melhor encaixe utilizando o algoritmo de Metropolis-Hastings. Ambos foram implementados no software Riscare Listrado, que é uma continuidade do software Riscare para tecidos lisos desenvolvido em Alves (2010). Para testar o desempenho dos dois algoritmos foram utilizados seis problemas benchmarks da literatura e proposto um novo problema denominado de camisa masculina. Os problemas benchmarks da literatura foram propostos para matéria-prima lisa e o problema camisa masculina especificamente para tecidos listrados. Entre os dois algoritmos desenvolvidos, o algoritmo de busca do melhor encaixe apresentou resultados com melhores eficiências de utilização do tecido para todos os problemas propostos. Quando comparado aos melhores resultados publicados na literatura para matéria-prima lisa, o algoritmo de busca do melhor encaixe apresentou encaixes com eficiências inferiores, porém com resultados superiores ao recomendado pela literatura específica da área de moda para tecidos estampados. / This thesis proposes the solution for the packing problem of patterns on striped fabric in clothing industry. The patterns are pieces with irregular form that should be placed on raw material which is, in this case, the fabric. This fabric is cut after packing. In the specific problem of packing on striped fabric, the position that patterns are put in the fabric should ensure that, after the clothing sewing, the stripes should present continuity. Thus, the theoretical foundation of this project includes subjects about fashion and clothing design, such as types and rapports of striped fabric, and the possibilities of rotation and the correct place to put the patterns on striped fabric. In the theoretical foundation, there are also subjects about research in combinatorial optimization as: characteristics about bi-dimensional packing and cutting problems and algorithms used for several authors to solve the problem. In addition, the Markov Chain Monte Carlo method and the Metropolis-Hastings algorithm are described at end of theoretical foundation. Based on the bibliographic research, two different algorithms for the packing problem with striped fabric are proposed: algorithm with pre-processing step and algorithm of searching the best packing using the Metropolis-Hastings algorithm. Both algorithms are implemented in the Striped Riscare software, which is a continuity of Riscare software for clear fabrics developed in the Masters degree of the author. Both algorithms performances are tested with six literature benchmark problems and a new problem called “male shirt” is proposed here. The benchmark problems of literature were iniatially proposed for clear raw material and the male shirt problem, specifically for striped fabrics. Between the two developed algorithms, the algorithm of searching the best packing has shown better results with better efficiencies of the fabric usage for all the problems tested. When compared to the best results published in the literature for clear raw material, the algorithm of searching the best packing has shown packings with lower efficiencies. However, it showed results higher than recommended for the specific literature of fashion design for patterned fabrics.

The main goal of this thesis was to design and implement a tool that would be able to classify the sequences of the 16S rRNA gene into taxonomic categories using the properties of the 16S rRNA gene. The created tool analyzes all input sequences simultaneously, which differs from common classification approaches, which classify input sequences individually. This tool relies on the fact that bacteria contain several copies of the 16S rRNA gene, which may differ in sequence. The main contribution of this work is design, implementation and evaluation of the capabilities of this tool. Experiments have shown that the proposed tool is able to identify the corresponding bacteria for smaller datasets and determine the correct ratios of their abundances. However, with larger datasets, the state space becomes very large and fragmented, which requires further improvements in order for it to search the state space in an efficient way.

Rare events play a crucial role in our society and a great effort has been dedicated to numerically study them in different contexts. This thesis proposes a numerical methodology based on Monte Carlo Metropolis-Hastings algorithm to efficiently sample rare events in chaotic systems. It starts by reviewing the relevance of rare events in chaotic systems, focusing in two types of rare events: states in closed systems with rare chaoticities, characterised by a finite-time Lyapunov exponent on a tail of its distribution, and states in transiently chaotic systems, characterised by a escape time on the tail of its distribution. This thesis argues that these two problems can be interpreted as a traditional problem of statistical physics: sampling exponentially rare states in the phase-space - states in the tail of the density of states - with an increasing parameter - the system size. This is used as the starting point to review Metropolis-Hastings algorithm, a traditional and flexible methodology of importance sampling in statistical physics. By an analytical argument, it is shown that the chaoticity of the system hinders direct application of Metropolis-Hastings techniques to efficiently sample these states because the acceptance is low. It is argued that a crucial step to overcome low acceptance rate is to construct a proposal distribution that uses information about the system to bound the acceptance rate. Using generic properties of chaotic systems, such as exponential divergence of initial conditions and fractals embedded in their phase-spaces, a proposal distribution that guarantees a bounded acceptance rate is derived for each type of rare events. This proposal is numerically tested in simple chaotic systems, and the efficiency of the resulting algorithm is measured in numerous examples in both types of rare events. The results confirm the dramatic improvement of using Monte Carlo importance sampling with the derived proposals against traditional methodologies: the number of samples required to sample an exponentially rare state increases polynomially, as opposed to an exponential increase observed in uniform sampling. This thesis then analyses the sub-optimal (polynomial) efficiency of this algorithm in a simple system and shows analytically how the correlations induced by the proposal distribution can be detrimental to the efficiency of the algorithm. This thesis also analyses the effect of high-dimensional chaos in the proposal distribution and concludes that an anisotropic proposal that takes advantage of the different rates of expansion along the different unstable directions, is able to efficiently find rare states. The applicability of this methodology is also discussed to sample rare states in non-hyperbolic systems, with focus on three systems: the logistic map, the Pomeau-Manneville map, and the standard map. Here, it is argued that the different origins of non-hyperbolicity require different proposal distributions. Overall, the results show that by incorporating specific information about the system in the proposal distribution of Metropolis-Hastings algorithm, it is possible to efficiently find and sample rare events of chaotic systems. This improved methodology should be useful to a large class of problems where the numerical characterisation of rare events is important.

Traditional clinical trials have been inefficient in their methods of dose finding and dose allocation. In this paper a four-parameter logistic equation is used to model the outcome of Bernoulli-response clinical trials. A Bayesian adaptive design is used to fit the logistic equation to the dose-response curve of Phase II and Phase III clinical trials. Because of inherent restrictions in the logistic model, symmetric candidate densities cannot be used, thereby creating asymmetric jumping rules inside the Markov chain Monte Carlo algorithm. An order restricted Metropolis-Hastings algorithm is implemented to account for these limitations. Modeling clinical trials in a Bayesian framework allows the experiment to be adaptive. In this adaptive design batches of subjects are assigned to doses based on the posterior probability of success for each dose, thereby increasing the probability of receiving advantageous doses. Good posterior fitting is demonstrated for typical dose-response curves and the Bayesian design is shown to properly stop drug trials for clinical futility or clinical success. In this paper we demonstrate that an adaptive Bayesian approach to dose-response studies increases both the statistical and medicinal effectiveness of clinical research.

Each year, billions of dollars are spent on missiles and munitions by the United States government. It is therefore vital to have a dependable method to estimate the reliability of these missiles. It is important to take into account the age of the missile, the reliability of different components of the missile, and the impact of different launch phases on missile reliability. Additionally, it is of importance to estimate the missile performance under a variety of test conditions, or modalities. Bayesian logistic regression is utilized to accurately make these estimates. This project presents both previously proposed methods and ways to combine these methods to accurately estimate the reliability of the Cruise Missile.

No description available.

Les méthodes de Monte Carlo par chaîne de Markov (MCMC) sont des outils très populaires pour l’échantillonnage de lois de probabilité complexes et/ou en grandes dimensions. Étant donné leur facilité d’application, ces méthodes sont largement répandues dans plusieurs communautés scientifiques et bien certainement en statistique, particulièrement en analyse bayésienne. Depuis l’apparition de la première méthode MCMC en 1953, le nombre de ces algorithmes a considérablement augmenté et ce sujet continue d’être une aire de recherche active. Un nouvel algorithme MCMC avec ajustement directionnel a été récemment développé par Bédard et al. (IJSS, 9 :2008) et certaines de ses propriétés restent partiellement méconnues. L’objectif de ce mémoire est de tenter d’établir l’impact d’un paramètre clé de cette méthode sur la performance globale de l’approche. Un second objectif est de comparer cet algorithme à d’autres méthodes MCMC plus versatiles afin de juger de sa performance de façon relative. / Markov Chain Monte Carlo algorithms (MCMC) have become popular tools for sampling from complex and/or high dimensional probability distributions. Given their relative ease of implementation, these methods are frequently used in various scientific areas, particularly in Statistics and Bayesian analysis. The volume of such methods has risen considerably since the first MCMC algorithm described in 1953 and this area of research remains extremely active. A new MCMC algorithm using a directional adjustment has recently been described by Bédard et al. (IJSS, 9:2008) and some of its properties remain unknown. The objective of this thesis is to attempt determining the impact of a key parameter on the global performance of the algorithm. Moreover, another aim is to compare this new method to existing MCMC algorithms in order to evaluate its performance in a relative fashion.

Les titres financiers sont souvent modélisés par des équations différentielles stochastiques (ÉDS). Ces équations peuvent décrire le comportement de l'actif, et aussi parfois certains paramètres du modèle. Par exemple, le modèle de Heston (1993), qui s'inscrit dans la catégorie des modèles à volatilité stochastique, décrit le comportement de l'actif et de la variance de ce dernier. Le modèle de Heston est très intéressant puisqu'il admet des formules semi-analytiques pour certains produits dérivés, ainsi qu'un certain réalisme. Cependant, la plupart des algorithmes de simulation pour ce modèle font face à quelques problèmes lorsque la condition de Feller (1951) n'est pas respectée. Dans ce mémoire, nous introduisons trois nouveaux algorithmes de simulation pour le modèle de Heston. Ces nouveaux algorithmes visent à accélérer le célèbre algorithme de Broadie et Kaya (2006); pour ce faire, nous utiliserons, entre autres, des méthodes de Monte Carlo par chaînes de Markov (MCMC) et des approximations. Dans le premier algorithme, nous modifions la seconde étape de la méthode de Broadie et Kaya afin de l'accélérer. Alors, au lieu d'utiliser la méthode de Newton du second ordre et l'approche d'inversion, nous utilisons l'algorithme de Metropolis-Hastings (voir Hastings (1970)). Le second algorithme est une amélioration du premier. Au lieu d'utiliser la vraie densité de la variance intégrée, nous utilisons l'approximation de Smith (2007). Cette amélioration diminue la dimension de l'équation caractéristique et accélère l'algorithme. Notre dernier algorithme n'est pas basé sur une méthode MCMC. Cependant, nous essayons toujours d'accélérer la seconde étape de la méthode de Broadie et Kaya (2006). Afin de réussir ceci, nous utilisons une variable aléatoire gamma dont les moments sont appariés à la vraie variable aléatoire de la variance intégrée par rapport au temps. Selon Stewart et al. (2007), il est possible d'approximer une convolution de variables aléatoires gamma (qui ressemble beaucoup à la représentation donnée par Glasserman et Kim (2008) si le pas de temps est petit) par une simple variable aléatoire gamma. / Financial stocks are often modeled by stochastic differential equations (SDEs). These equations could describe the behavior of the underlying asset as well as some of the model's parameters. For example, the Heston (1993) model, which is a stochastic volatility model, describes the behavior of the stock and the variance of the latter. The Heston model is very interesting since it has semi-closed formulas for some derivatives, and it is quite realistic. However, many simulation schemes for this model have problems when the Feller (1951) condition is violated. In this thesis, we introduce new simulation schemes to simulate price paths using the Heston model. These new algorithms are based on Broadie and Kaya's (2006) method. In order to increase the speed of the exact scheme of Broadie and Kaya, we use, among other things, Markov chains Monte Carlo (MCMC) algorithms and some well-chosen approximations. In our first algorithm, we modify the second step of the Broadie and Kaya's method in order to get faster schemes. Instead of using the second-order Newton method coupled with the inversion approach, we use a Metropolis-Hastings algorithm. The second algorithm is a small improvement of our latter scheme. Instead of using the real integrated variance over time p.d.f., we use Smith's (2007) approximation. This helps us decrease the dimension of our problem (from three to two). Our last algorithm is not based on MCMC methods. However, we still try to speed up the second step of Broadie and Kaya. In order to achieve this, we use a moment-matched gamma random variable. According to Stewart et al. (2007), it is possible to approximate a complex gamma convolution (somewhat near the representation given by Glasserman and Kim (2008) when T-t is close to zero) by a gamma distribution.

Les titres financiers sont souvent modélisés par des équations différentielles stochastiques (ÉDS). Ces équations peuvent décrire le comportement de l'actif, et aussi parfois certains paramètres du modèle. Par exemple, le modèle de Heston (1993), qui s'inscrit dans la catégorie des modèles à volatilité stochastique, décrit le comportement de l'actif et de la variance de ce dernier. Le modèle de Heston est très intéressant puisqu'il admet des formules semi-analytiques pour certains produits dérivés, ainsi qu'un certain réalisme. Cependant, la plupart des algorithmes de simulation pour ce modèle font face à quelques problèmes lorsque la condition de Feller (1951) n'est pas respectée. Dans ce mémoire, nous introduisons trois nouveaux algorithmes de simulation pour le modèle de Heston. Ces nouveaux algorithmes visent à accélérer le célèbre algorithme de Broadie et Kaya (2006); pour ce faire, nous utiliserons, entre autres, des méthodes de Monte Carlo par chaînes de Markov (MCMC) et des approximations. Dans le premier algorithme, nous modifions la seconde étape de la méthode de Broadie et Kaya afin de l'accélérer. Alors, au lieu d'utiliser la méthode de Newton du second ordre et l'approche d'inversion, nous utilisons l'algorithme de Metropolis-Hastings (voir Hastings (1970)). Le second algorithme est une amélioration du premier. Au lieu d'utiliser la vraie densité de la variance intégrée, nous utilisons l'approximation de Smith (2007). Cette amélioration diminue la dimension de l'équation caractéristique et accélère l'algorithme. Notre dernier algorithme n'est pas basé sur une méthode MCMC. Cependant, nous essayons toujours d'accélérer la seconde étape de la méthode de Broadie et Kaya (2006). Afin de réussir ceci, nous utilisons une variable aléatoire gamma dont les moments sont appariés à la vraie variable aléatoire de la variance intégrée par rapport au temps. Selon Stewart et al. (2007), il est possible d'approximer une convolution de variables aléatoires gamma (qui ressemble beaucoup à la représentation donnée par Glasserman et Kim (2008) si le pas de temps est petit) par une simple variable aléatoire gamma. / Financial stocks are often modeled by stochastic differential equations (SDEs). These equations could describe the behavior of the underlying asset as well as some of the model's parameters. For example, the Heston (1993) model, which is a stochastic volatility model, describes the behavior of the stock and the variance of the latter. The Heston model is very interesting since it has semi-closed formulas for some derivatives, and it is quite realistic. However, many simulation schemes for this model have problems when the Feller (1951) condition is violated. In this thesis, we introduce new simulation schemes to simulate price paths using the Heston model. These new algorithms are based on Broadie and Kaya's (2006) method. In order to increase the speed of the exact scheme of Broadie and Kaya, we use, among other things, Markov chains Monte Carlo (MCMC) algorithms and some well-chosen approximations. In our first algorithm, we modify the second step of the Broadie and Kaya's method in order to get faster schemes. Instead of using the second-order Newton method coupled with the inversion approach, we use a Metropolis-Hastings algorithm. The second algorithm is a small improvement of our latter scheme. Instead of using the real integrated variance over time p.d.f., we use Smith's (2007) approximation. This helps us decrease the dimension of our problem (from three to two). Our last algorithm is not based on MCMC methods. However, we still try to speed up the second step of Broadie and Kaya. In order to achieve this, we use a moment-matched gamma random variable. According to Stewart et al. (2007), it is possible to approximate a complex gamma convolution (somewhat near the representation given by Glasserman and Kim (2008) when T-t is close to zero) by a gamma distribution.

Les méthodes de Monte Carlo par chaîne de Markov (MCMC) sont des outils très populaires pour l’échantillonnage de lois de probabilité complexes et/ou en grandes dimensions. Étant donné leur facilité d’application, ces méthodes sont largement répandues dans plusieurs communautés scientifiques et bien certainement en statistique, particulièrement en analyse bayésienne. Depuis l’apparition de la première méthode MCMC en 1953, le nombre de ces algorithmes a considérablement augmenté et ce sujet continue d’être une aire de recherche active. Un nouvel algorithme MCMC avec ajustement directionnel a été récemment développé par Bédard et al. (IJSS, 9 :2008) et certaines de ses propriétés restent partiellement méconnues. L’objectif de ce mémoire est de tenter d’établir l’impact d’un paramètre clé de cette méthode sur la performance globale de l’approche. Un second objectif est de comparer cet algorithme à d’autres méthodes MCMC plus versatiles afin de juger de sa performance de façon relative. / Markov Chain Monte Carlo algorithms (MCMC) have become popular tools for sampling from complex and/or high dimensional probability distributions. Given their relative ease of implementation, these methods are frequently used in various scientific areas, particularly in Statistics and Bayesian analysis. The volume of such methods has risen considerably since the first MCMC algorithm described in 1953 and this area of research remains extremely active. A new MCMC algorithm using a directional adjustment has recently been described by Bédard et al. (IJSS, 9:2008) and some of its properties remain unknown. The objective of this thesis is to attempt determining the impact of a key parameter on the global performance of the algorithm. Moreover, another aim is to compare this new method to existing MCMC algorithms in order to evaluate its performance in a relative fashion.