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1
Hrbek, Filip. "Metody předvídání volatility." Master's thesis, Vysoká škola ekonomická v Praze, 2015. http://www.nusl.cz/ntk/nusl-264689.
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In this masterthesis I have rewied basic approaches to volatility estimating. These approaches are based on classical and Bayesian statistics. I have applied the volatility models for the purpose of volatility forecasting of a different foreign exchange (EURUSD, GBPUSD and CZKEUR) in the different period (from a second period to a day period). I formulate the models EWMA, GARCH, EGARCH, IGARCH, GJRGARCH, jump diffuison with constant volatility and jump diffusion model with stochastic volatility. I also proposed an MCMC algorithm in order to estimate the Bayesian models. All the models we estimated as univariate models. I compared the models according to Mincer Zarnowitz regression. The most successfull model is the jump diffusion model with a stochastic volatility. On the second place they were the GJR- GARCH model and the jump diffusion model with a constant volatility. But the jump diffusion model with a constat volatilit provided much more overvalued results.The rest of the models were even worse. From the rest the IGARCH model is the best but provided undervalued results. All these findings correspond with R squared coefficient.
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Austad, Haakon Michael. "Parallel Multiple Proposal MCMC Algorithms." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for matematiske fag, 2007. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-12857.
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We explore the variance reduction achievable through parallel implementation of multi-proposal MCMC algorithms and use of control variates. Implemented sequentially multi-proposal MCMC algorithms are of limited value, but they are very well suited for parallelization. Further, discarding the rejected states in an MCMC sampler can intuitively be interpreted as a waste of information. This becomes even more true for a multi-proposal algorithm where we discard several states in each iteration. By creating an alternative estimator consisting of a linear combination of the traditional sample mean and zero mean random variables called control variates we can improve on the traditional estimator. We present a setting for the multi-proposal MCMC algorithm and study it in two examples. The first example considers sampling from a simple Gaussian distribution, while for the second we design the framework for a multi-proposal mode jumping algorithm for sampling from a distribution with several separated modes. We find that the variance reduction achieved from our control variate estimator in general increases as the number of proposals in our sampler increase. For our Gaussian example we find that the benefit from parallelization is small, and that little is gained from increasing the number of proposals. The mode jumping example however is very well suited for parallelization and we get a relative variance reduction pr time of roughly 80% with 16 proposals in each iteration.
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Thiéry, Alexandre H. "Scaling analysis of MCMC algorithms." Thesis, University of Warwick, 2013. http://wrap.warwick.ac.uk/57609/.
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Markov Chain Monte Carlo (MCMC) methods have become a workhorse for modern scientific computations. Practitioners utilize MCMC in many different areas of applied science yet very few rigorous results are available for justifying the use of these methods. The purpose of this dissertation is to analyse random walk type MCMC algorithms in several limiting regimes that frequently occur in applications. Scaling limits arguments are used as a unifying method for studying the asymptotic complexity of these MCMC algorithms. Two distinct strands of research are developed: (a) We analyse and prove diffusion limit results for MCMC algorithms in high or infinite dimensional state spaces. Contrarily to previous results in the literature, the target distributions that we consider do not have a product structure; this leads to Stochastic Partial Differential Equation (SPDE) limits. This proves among other things that optimal proposals results already known for product form target distributions extend to much more general settings. We then show how to use these MCMC algorithms in an infinite dimensional Hilbert space in order to imitate a gradient descent without computing any derivative. (b) We analyse the behaviour of the Random Walk Metropolis (RWM) algorithm when used to explore target distributions concentrating on the neighbourhood of a low dimensional manifold of Rn. We prove that the algorithm behaves, after being suitably rescaled, as a diffusion process evolving on a manifold.
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Melo, Ana Cláudia Oliveira de. "Aspectos Práticos Computacionais dos Algoritmos de Simulação MCMC." Universidade de São Paulo, 1999. http://www.teses.usp.br/teses/disponiveis/55/55134/tde-05032018-163433/.
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Os algoritmos de simulação de Monte Carlo em cadeia de Markov (MCMC) têm aplicações em várias áreas da Estatística, entre elas destacamos os problemas de Inferência Bayesiana. A aplicação destas técnicas no entanto, exige uma análise teórica da distribuição a posteriori para assegurar a convergência. Devido ao alto grau de complexidade de certos problemas, essa análise nem sempre é possível. O objetivo deste estudo é destacar estas dificuldades e apresentar alguns aspectos práticos computacionais que podem auxiliar na solução de problemas de inferência Bayesiana. Entre estes ressaltamos os critérios de seleção de amostras, o uso de técnicas de diagnósticos de convergência e métodos de estimativas.<br>The algorithms of Monte Cano Markov Chain simulation have application in many areas of statistics, among them we highlight the Bayesian inference problem. The application of these technics however, demands a theoretical analysis of the posterior distribution to assure the convergence. Because of the high complexity levei of certain problems, this analysis is not always possible the purpose of this study is to underline this difficulties and present some practical computational aspects that may help in the solution of the Bayesian inference problems. Among them we emphasize sample selection, convergence diagnostics and parameter inference by central limit theorem.
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Altaleb, Anas. "Méthodes d'échantillonnage par mélanges et algorithmes MCMC." Rouen, 1999. http://www.theses.fr/1999ROUES034.
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Nous abordons dans cette thèse, deux aspects distincts : (a) la construction et le test de certaines méthodes de simulation pour l'approximation des intégrales. Nous étudions en particulier les estimateurs de Monte Carlo auxquels il est souvent fait appel dans le traitement de modèles statistiques complexes. Notre apport en ce domaine consiste en l'utilisation des mélanges pour la stabilisation des échantillonnages d'importance. Pour valider l'estimateur pondéré, il est indispensable d'étudier son comportement pour les méthodes MCMC qui permettent la mise en œuvre d'une forme généralisée de l'estimateur pondéré. L'estimateur pondéré obtenu améliore à nouveau l'estimateur standard de Monte Carlo en termes de réduction de la variance et de vitesse de convergence. Cette forme généralisée de l'estimateur pondéré permet d'étendre le domaine d'application de notre estimateur à une grande classe de problèmes d'intégration rencontrés en statistique. (b) l'étude d'un modèle de régression non linéaire généralisée, le modèle Logit, suivant deux méthodes : celle de Damien et Walker (1997) et une technique générique de Hastings-Metropolis. L'ensemble des résultats exposés est illustré par différentes simulations, qui montrent les comportements et les performances de l'algorithme de Hastings-Metropolis en termes de vitesse de convergence vers la loi stationnaire et de rapidité d'exploration de la surface de la loi a posteriori, par rapport à la méthode de Damien et Walker.
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Liu, Shuanglong. "Acceleration of MCMC-based algorithms using reconfigurable logic." Thesis, Imperial College London, 2017. http://hdl.handle.net/10044/1/52431.
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Monte Carlo (MC) methods such as Markov chain Monte Carlo (MCMC) and sequential Monte Carlo (SMC) have emerged as popular tools to sample from high dimensional probability distributions. Because these algorithms can draw samples effectively from arbitrary distributions in Bayesian inference problems, they have been widely used in a range of statistical applications. However, they are often too time consuming due to the prohibitive costly likelihood evaluations, thus they cannot be practically applied to complex models with large-scale datasets. Currently, the lack of sufficiently fast MCMC methods limits their applicability in many modern applications such as genetics and machine learning, and this situation is bound to get worse given the increasing adoption of big data in many fields. The objective of this dissertation is to develop, design and build efficient hardware architectures for MCMC-based algorithms on Field Programmable Gate Arrays (FPGAs), and thereby bring them closer to practical applications. The contributions of this work include: 1) Novel parallel FPGA architectures of the state-of-the-art resampling algorithms for SMC methods. The proposed architectures allow for parallel implementations and thus improve the processing speed. 2) A novel mixed precision MCMC algorithm, along with a tailored FPGA architecture. The proposed design allows for more parallelism and achieves low latency for a given set of hardware resources, while still guaranteeing unbiased estimates. 3) A new variant of subsampling MCMC method based on unequal probability sampling, along with a highly optimized FPGA architecture. The proposed method significantly reduces off-chip memory access and achieves high accuracy in estimates for a given time budget. This work has resulted in the development of hardware accelerators of MCMC and SMC for very large-scale Bayesian tasks by applying the above techniques. Notable speed improvements compared to the respective state-of-the-art CPU and GPU implementations have been achieved in this work.
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Medina, Aguayo Felipe Javier. "Stability and examples of some approximate MCMC algorithms." Thesis, University of Warwick, 2017. http://wrap.warwick.ac.uk/88922/.
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Approximate Monte Carlo algorithms are not uncommon these days, their applicability is related to the possibility of controlling the computational cost by introducing some noise or approximation in the method. We focus on the stability properties of a particular approximate MCMC algorithm, which we term noisy Metropolis-Hastings. Such properties have been studied before in tandem with the pseudo-marginal algorithm, but under fairly strong assumptions. Here, we examine the noisy Metropolis-Hastings algorithm in more detail and explore possible corrective actions for reducing the introduced bias. In this respect, a novel approximate method is presented, motivated by the class of exact algorithms with randomised acceptance. We also discuss some applications and theoretical guarantees of this new approach.
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Mingas, Grigorios. "Algorithms and architectures for MCMC acceleration in FPGAs." Thesis, Imperial College London, 2015. http://hdl.handle.net/10044/1/31572.
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Markov Chain Monte Carlo (MCMC) is a family of stochastic algorithms which are used to draw random samples from arbitrary probability distributions. This task is necessary to solve a variety of problems in Bayesian modelling, e.g. prediction and model comparison, making MCMC a fundamental tool in modern statistics. Nevertheless, due to the increasing complexity of Bayesian models, the explosion in the amount of data they need to handle and the computational intensity of many MCMC algorithms, performing MCMC-based inference is often impractical in real applications. This thesis tackles this computational problem by proposing Field Programmable Gate Array (FPGA) architectures for accelerating MCMC and by designing novel MCMC algorithms and optimization methodologies which are tailored for FPGA implementation. The contributions of this work include: 1) An FPGA architecture for the Population-based MCMC algorithm, along with two modified versions of the algorithm which use custom arithmetic precision in large parts of the implementation without introducing error in the output. Mapping the two modified versions to an FPGA allows for more parallel modules to be instantiated in the same chip area. 2) An FPGA architecture for the Particle MCMC algorithm, along with a novel algorithm which combines Particle MCMC and Population-based MCMC to tackle multi-modal distributions. A proposed FPGA architecture for the new algorithm achieves higher datapath utilization than the Particle MCMC architecture. 3) A generic method to optimize the arithmetic precision of any MCMC algorithm that is implemented on FPGAs. The method selects the minimum precision among a given set of precisions, while guaranteeing a user-defined bound on the output error. By applying the above techniques to large-scale Bayesian problems, it is shown that significant speedups (one or two orders of magnitude) are possible compared to state-of-the-art MCMC algorithms implemented on CPUs and GPUs, opening the way for handling complex statistical analyses in the era of ubiquitous, ever-increasing data.
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Chang, Meng-I. "A Comparison of Two MCMC Algorithms for Estimating the 2PL IRT Models." OpenSIUC, 2017. https://opensiuc.lib.siu.edu/dissertations/1446.
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The fully Bayesian estimation via the use of Markov chain Monte Carlo (MCMC) techniques has become popular for estimating item response theory (IRT) models. The current development of MCMC includes two major algorithms: Gibbs sampling and the No-U-Turn sampler (NUTS). While the former has been used with fitting various IRT models, the latter is relatively new, calling for the research to compare it with other algorithms. The purpose of the present study is to evaluate the performances of these two emerging MCMC algorithms in estimating two two-parameter logistic (2PL) IRT models, namely, the 2PL unidimensional model and the 2PL multi-unidimensional model under various test situations. Through investigating the accuracy and bias in estimating the model parameters given different test lengths, sample sizes, prior specifications, and/or correlations for these models, the key motivation is to provide researchers and practitioners with general guidelines when it comes to estimating a UIRT model and a multi-unidimensional IRT model. The results from the present study suggest that NUTS is equally effective as Gibbs sampling at parameter estimation under most conditions for the 2PL IRT models. Findings also shed light on the use of the two MCMC algorithms with more complex IRT models.
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Faure, Charly. "Approches bayésiennes appliquées à l’identification d’efforts vibratoires par la méthode de Résolution Inverse." Thesis, Le Mans, 2017. http://www.theses.fr/2017LEMA1002.
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Des modèles de plus en plus précis sont développés pour prédire le comportement vibroacoustique des structures et dimensionner des traitements adaptés. Or, les sources vibratoires, qui servent de données d'entrée à ces modèles, restent assez souvent mal connues. Une erreur sur les sources injectées se traduit donc par un biais sur la prédiction vibroacoustique. En amont des simulations, la caractérisation expérimentale de sources vibratoires en conditions opérationnelles est un moyen de réduire ce biais et fait l'objet de ces travaux de thèse.L'approche proposée utilise une méthode inverse, la Résolution Inverse (RI), permettant l'identification de sources à partir des déplacements de structure. La sensibilité aux perturbations de mesure, commune à la plupart des méthodes inverses, est traitée dans un cadre probabiliste par des méthodes bayésiennes.Ce formalisme bayésien permet : d'améliorer la robustesse de la méthode RI ; la détection automatique de sources sur la distribution spatiale ; l'identification parcimonieuse pour le cas de sources ponctuelles ; l'identification de paramètres de modèle pour les structures homogénéisées ; l'identification de sources instationnaires ; la propagation des incertitudes de mesures sur l'évaluation du spectre d'effort ; l'évaluation de la qualité de la mesure par un indicateur empirique de rapport signal à bruit.Ces deux derniers points sont obtenus avec une unique mesure, là où des approches statistiques plus classiques demandent une campagne de mesures plus conséquente. Ces résultats ont été validés à la fois numériquement et expérimentalement, avec une source maîtrisée mais aussi avec une source industrielle. De plus, la procédure est en grande partie non-supervisée. Il ne reste alors à la charge de l’utilisateur qu’un nombre restreint de paramètres à fixer. Lesapproches proposées peuvent donc être utilisées dans une certaine mesure comme des boites noires<br>Increasingly accurate models are developped to predict the vibroacoustic behavior of structures and to propose adequate treatments.Vibration sources used as input of these models are still broadly unknown. In simulation, an error on vibration sources produces a bias on the vibroacoustic predictions. A way to reduce this bias is to characterize experimentally the vibration sources in operational condition before some simulations. It is therefore the subject of this PhD work.The proposed approach is based on an inverse method, the Force Analysis Technique (FAT), and allows the identification of vibration sources from displacement measurements. The noise sensibility, common to most of inverse methods, is processed in a probabilistic framework using Bayesian methods.This Bayesian framework allows: some improvements of the FAT robustness; an automatic detection of sources; the sparse identification of sources for pointwise sources; the model parameters identification for the purpose of homogenized structures; the identification of unsteady sources; the propagation of uncertainties through force spectrum (with credibility intervals); measurement quality assessment from a empirical signal to noise ratio.These two last points are obtained from a unique scan of the structure, where more traditional statistical methods need multiple scans of the structure. Both numerical and experimental validations have been proposed, with a controled excitation and with an industrial source. Moreover, the procedure is rather unsupervised in this work. Therefore, the user only has a few number of parameters to set by himself. In a certain extent, the proposed approaches can then be applied as black boxes
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Karimi, Belhal. "Non-Convex Optimization for Latent Data Models : Algorithms, Analysis and Applications." Thesis, Université Paris-Saclay (ComUE), 2019. http://www.theses.fr/2019SACLX040/document.
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De nombreux problèmes en Apprentissage Statistique consistent à minimiser une fonction non convexe et non lisse définie sur un espace euclidien. Par exemple, les problèmes de maximisation de la vraisemblance et la minimisation du risque empirique en font partie.Les algorithmes d'optimisation utilisés pour résoudre ce genre de problèmes ont été largement étudié pour des fonctions convexes et grandement utilisés en pratique.Cependant, l'accrudescence du nombre d'observation dans l'évaluation de ce risque empirique ajoutée à l'utilisation de fonctions de perte de plus en plus sophistiquées représentent des obstacles.Ces obstacles requièrent d'améliorer les algorithmes existants avec des mis à jour moins coûteuses, idéalement indépendantes du nombre d'observations, et d'en garantir le comportement théorique sous des hypothèses moins restrictives, telles que la non convexité de la fonction à optimiser.Dans ce manuscrit de thèse, nous nous intéressons à la minimisation de fonctions objectives pour des modèles à données latentes, ie, lorsque les données sont partiellement observées ce qui inclut le sens conventionnel des données manquantes mais est un terme plus général que cela.Dans une première partie, nous considérons la minimisation d'une fonction (possiblement) non convexe et non lisse en utilisant des mises à jour incrémentales et en ligne. Nous proposons et analysons plusieurs algorithmes à travers quelques applications.Dans une seconde partie, nous nous concentrons sur le problème de maximisation de vraisemblance non convexe en ayant recourt à l'algorithme EM et ses variantes stochastiques. Nous en analysons plusieurs versions rapides et moins coûteuses et nous proposons deux nouveaux algorithmes du type EM dans le but d'accélérer la convergence des paramètres estimés<br>Many problems in machine learning pertain to tackling the minimization of a possibly non-convex and non-smooth function defined on a Many problems in machine learning pertain to tackling the minimization of a possibly non-convex and non-smooth function defined on a Euclidean space.Examples include topic models, neural networks or sparse logistic regression.Optimization methods, used to solve those problems, have been widely studied in the literature for convex objective functions and are extensively used in practice.However, recent breakthroughs in statistical modeling, such as deep learning, coupled with an explosion of data samples, require improvements of non-convex optimization procedure for large datasets.This thesis is an attempt to address those two challenges by developing algorithms with cheaper updates, ideally independent of the number of samples, and improving the theoretical understanding of non-convex optimization that remains rather limited.In this manuscript, we are interested in the minimization of such objective functions for latent data models, ie, when the data is partially observed which includes the conventional sense of missing data but is much broader than that.In the first part, we consider the minimization of a (possibly) non-convex and non-smooth objective function using incremental and online updates.To that end, we propose several algorithms exploiting the latent structure to efficiently optimize the objective and illustrate our findings with numerous applications.In the second part, we focus on the maximization of non-convex likelihood using the EM algorithm and its stochastic variants.We analyze several faster and cheaper algorithms and propose two new variants aiming at speeding the convergence of the estimated parameters
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Azevedo, Caio Lucidius Naberezny. "Modelos longitudinais de grupos múltiplos multiníveis na teoria da resposta ao item: métodos de estimação e seleção estrutural sob uma perspectiva bayesiana." Universidade de São Paulo, 2008. http://www.teses.usp.br/teses/disponiveis/45/45133/tde-15042008-165256/.
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No presente trabalho propomos uma estrutura bayesiana, através de um esquema de dados aumentados, para analisar modelos longitudinais com grupos mútiplos (MLGMTRI) na Teoria da Resposta ao Item (TRI). Tal estrutura consiste na tríade : modelagem, métodos de estimação e métodos de diagnóstico para a classe de MLGMTRI. Na parte de modelagem, explorou-se as estruturas multivariada e multinível, com o intuito de representar a hierarquia existente em dados longitudinais com grupos múltiplos. Esta abordagem permite considerar várias classes de submodelos como: modelos de grupos múltiplos e modelos longitudinais de um único grupo. Estudamos alguns aspectos positivos e negativos de cada uma das supracitadas abordagens. A modelagem multivariada permite representar de forma direta estruturas de dependência, além de possibilitar que várias delas sejam facilmente incorporadas no processo de estimação. Isso permite considerar, por exemplo, uma matriz não estruturada e assim, obter indícios da forma mais apropriada para a estrutura de dependência. Por outro lado, a modelagem multinível propicia uma interpretação mais direta, obtenção de condicionais completas univariadas, fácil inclusão de informações adicionais, incorporação de fontes de dependência intra e entre unidades amostrais, dentre outras. Com relação aos métodos de estimação, desenvolvemos um procedimento baseado nas simulações de Monte Carlo via cadeias de Markov (MCMC). Mostramos que as distribuições condicionais completas possuem forma analítica conhecida e, além disso, são fáceis de se amostrar. Tal abordagem, apesar de demandar grande esforço computacional, contorna diversos problemas encontrados em outros procedimentos como: limitação no número de grupos envolvidos, quantidade de condições de avaliação, escolha de estruturas de dependência, assimetria dos traços latentes, imputação de dados, dentre outras. Além disso, através da metodologia MCMC, desenvolvemos uma estrutura de seleção de matrizes de covariâncias, através de um esquema de Monte Carlo via Cadeias de Markov de Saltos Reversíveis (RJMCMC). Estudos de simulação indicam que o modelo, o método de estimação e o método de seleção produzem resultados bastante satisfatórios. Também, robustez à escolha de prioris e valores iniciais foi observada. Os métodos de estimação desenvolvidos podem ser estendidos para diversas situações de interesse de um modo bem direto. Algumas das técnicas de diagnóstico estudadas permitem avaliar a qualidade do ajuste do modelo de um modo global. Outras medidas fornecem indícios de violação de suposições específicas, como ausência de normalidade para os traços latentes. Tal metodologia fornece meios concretos de se avaliar a qualidade do instrumento de medida (prova, questionário etc). Finalmente, a análise de um conjunto de dados real, utilizando-se alguns dos modelos abordados no presente trabalho, ilustra o potencial da tríade desenvolvida além de indicar um ganho na utilização dos modelos longitudinais da TRI na análise de ensaios educacionais com medidas repetidas em deterimento a suposição de independência.<br>In this work we proposed a bayesian framework, by using an augmented data scheme, to analyze longitudinal multiple groups models (LMGMIRT) in the Item Response Theory (IRT). Such framework consists in the following set : modelling, estimation methods and diagnostic tools to the LMGMIRT. Concerning the modelling, we exploited multivariate and multilevel structures in order to represent the hierarchical nature of the longitudinal multiple groupos model. This approach allows to consider several submodels such that: multiple groups and longitudinal one group models. We studied some positive and negative aspects of both above mentioned approches. The multivariate modelling allows to represent, in a straightforward way, many dependence structures. Furthermore it possibilities that many of them can be easily considered in the estimation process. This allows, for example, to consider an unstructured covariance matrix and, then, it allows to obtain information about the most appropritate dependece structure. On the other hand, the multilevel modelling permits to obtain: more straightforward interpretations of the model, the construction of univariate full conditional distributions, an easy way to include auxiliary information, the incorporation of within and between subjects (groups) sources of variability, among others. Concerning the estimation methods, we developed a procedure based on Monte Carlo Markov Chain (MCMC) simulation. We showed that the full conditional distributions are known and easy to sample from. Even though such approach demands a considerable amount of time it circumvents many problems such that: limitation in the number of groups that can be considered, the limitation in the number of instants of observation, the choice of covariance matrices, latent trait asymmetry, data imputation, among others. Furthermore, within the MCMC metodology, we developed a procedure to select covariance matrices, by using the so called Reversible Jump MCMC (RJMCMC). Simulation studies show that the model, the estimation method and the model selection procedure produce reasonable results. Also, the studies indicate that the developed metodology presents robustness concerning prior choice and different initial values choice. It is possible to extent the developed estimation methods to other situations in a straightforward way. Some diagnostics techniques that were studied allow to assess the model fit, in a global sense. Others techniques give directions toward the departing from some specific assumptions as the latent trait normality. Such methodology also provides ways to assess the quality of the test or questionaire used to measure the latent traits. Finally, by analyzing a real data set, using some of the models that were developed, it was possible to verify the potential of the methodology considered in this work. Furthermore, the results of this analysis indicate advantages in using longitudinal IRT models to model educational repeated measurement data instead of to assume independence.
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García, González Yaser. "Modelos y Algoritmos para redes neuronales recurrentes basadas en wavelets aplicados a la detección de intrusos." Thesis, Universidad de las Américas Puebla, 2011. http://catarina.udlap.mx/u_dl_a/tales/documentos/mcc/garcia_g_y/.
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A medida que las redes de comunicación crecen y se interconectan con otras redes públicas, estas quedan expuestas a sufrir distintos tipos de ataques que explotan vulnerabilidades en su infraestructura, resultado de la evolución continua de los ataques y la incorporación de nuevos métodos y técnicas. Aún cuando los ataques con frecuencia son iniciados desde el exterior, el aislamiento físico del segmento de red no garantiza la protección contra incidentes originados en el interior, es entonces cuando se hace necesario incorporar distintos niveles de protección para preservar la confidencialidad e integridad de la información de los usuarios. Los sistemas para detección de intrusos representan un componente importante dentro de las herramientas de defensa disponibles, su objetivo principal es detectar actividades no autorizadas e identificar de manera positiva ataques al sistema. A lo largo del desarrollo de estos sistemas se ha experimentado con distintos enfoques en su implementación, para mejorar su efectividad en la detección de ataques y adaptabilidad en la evolución de los mismos, motivando la investigación en distintas áreas como la inteligencia artificial y la estadística. Un enfoque considerado en los sistemas para detección de intrusos es el uso de redes neuronales<br>(cont.) Este modelo está inspirado en el proceso biológico del cerebro humano, considera distintas unidades interconectadas llamadas neurones, organizadas en capas. Cada unidad posee conexiones de entrada mediante las cuales recibe estímulos del medio externo o de otras unidades y conexiones de salida que transmiten el procesamiento de la entrada al aplicar una función de transferencia. Dentro de la implementación de sistemas para detección de intrusos que utilicen redes neuronales, existe una gran variedad de arquitecturas aplicadas, encontrando en cada una distintos resultados en la detección de ataques o conductas intrusivas. En los últimos años distintos modelos de redes neuronales artificiales han sido propuestos, entre estos destaca las redes neuronales artificiales wavelets. Las redes neuronales wavelet implementan el procesamiento wavelet como parte de su funcionamiento a través del cambio de las funciones de transferencia tradicionales como la sigmoide por funciones wavelet. La combinación de ambas teorías busca aprovechar las características de análisis y descomposición del procesamiento wavelet junto con las propiedades de aprendizaje, adaptación y generalización de las redes neuronales<br>(cont.) En esta investigación, el objetivo es mejorar los índices de detección y clasificación de ataques a los sistemas de redes de comunicación a través de un sistema para detección de intrusos que implemente en su funcionamiento una red neuronal recurrente wavelet. La aportación principal de esta investigación consiste en la definición de una nueva arquitectura recurrente con wavelets, dicha arquitectura describe un nuevo esquema de interconexiones entre las unidades de procesamiento, características dinámicas de estas y su distribución entre las distintas capas. Las propiedades recurrentes del modelo se presentan a través de auto conexiones en las unidades de procesamiento, representando de esta manera estados de memoria. A partir de la definición de la arquitectura se propone el algoritmo de aprendizaje para la etapa de entrenamiento, este algoritmo establece la forma en la que se actualizarán los parámetros ajustables en cada ciclo. Los resultados reportados por el modelo propuesto permiten establecer una mayor velocidad de convergencia en la etapa de entrenamiento frente a arquitecturas recurrentes tradicionales y recurrentes con wavelets. También se reconoce su capacidad en la detección de intrusos dando un porcentaje de efectividad de 92.19% y su baja emisión de falsas alarmas con una tasa de 5.43%
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AGUIAR, José Domingos Albuquerque. "MCAC - Monte Carlo Ant Colony: um novo algoritmo estocástico de agrupamento de dados." Universidade Federal Rural de Pernambuco, 2008. http://www.tede2.ufrpe.br:8080/tede2/handle/tede2/5006.
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Previous issue date: 2008-02-29<br>In this work we present a new data cluster algorithm based on social behavior of ants which applies Monte Carlo simulations in selecting the maximum path length of the ants. We compare the performance of the new method with the popular k-means and another algorithm also inspired by the social ant behavior. For the comparative study we employed three data sets from the real world, three deterministic artificial data sets and two random generated data sets, yielding a total of eight data sets. We find that the new algorithm outperforms the others in all studied cases but one. We also address the issue concerning about the right number of groups in a particular data set. Our results show that the proposed algorithm yields a good estimate for the right number of groups present in the data set.<br>Esta dissertação apresenta um algoritmo inédito de agrupamento de dados que têm como fundamentos o método de Monte Carlo e uma heurística que se baseia no comportamento social das formigas, conhecida como Otimização por Colônias de Formigas. Neste trabalho realizou-se um estudo comparativo do novo algoritmo com outros dois algoritmos de agrupamentos de dados. O primeiro algoritmo é o KMédias que é muito conhecido entre os pesquisadores. O segundo é um algoritmo que utiliza a Otimização por Colônias de Formigas juntamente com um híbrido de outros métodos de otimização. Para implementação desse estudo comparativo utilizaram-se oito conjuntos de dados sendo três conjuntos de dados reais, dois artificiais gerados deterministicamente e três artificiais gerados aleatoriamente. Os resultados do estudo comparativo demonstram que o novo algoritmo identifica padrões nas massas de dados, com desempenho igual ou superior aos outros dois algoritmos avaliados. Neste trabalho investigou-se também a capacidade do novo algoritmo em identificar o número de grupos existentes nos conjuntos dados. Os resultados dessa investigação mostram que o novo algoritmo é capaz de identificar o de número provável de grupos existentes dentro do conjunto de dados.
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Du, Yang. "Comparison of change-point detection algorithms for vector time series." Thesis, Linköpings universitet, Statistik, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-59925.
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Change-point detection aims to reveal sudden changes in sequences of data. Special attention has been paid to the detection of abrupt level shifts, and applications of such techniques can be found in a great variety of fields, such as monitoring of climate change, examination of gene expressions and quality control in the manufacturing industry. In this work, we compared the performance of two methods representing frequentist and Bayesian approaches, respectively. The frequentist approach involved a preliminary search for level shifts using a tree algorithm followed by a dynamic programming algorithm for optimizing the locations and sizes of the level shifts. The Bayesian approach involved an MCMC (Markov chain Monte Carlo) implementation of a method originally proposed by Barry and Hartigan. The two approaches were implemented in R and extensive simulations were carried out to assess both their computational efficiency and ability to detect abrupt level shifts. Our study showed that the overall performance regarding the estimated location and size of change-points was comparable for the Bayesian and frequentist approach. However, the Bayesian approach performed better when the number of change-points was small; whereas the frequentist became stronger when the change-point proportion increased. The latter method was also better at detecting simultaneous change-points in vector time series. Theoretically, the Bayesian approach has a lower computational complexity than the frequentist approach, but suitable settings for the combined tree and dynamic programming can greatly reduce the processing time.
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Fort, Gersende. "Contrôle explicite d'ergodicité de chaîne de Markov : applications à l'analyse de convergence de l'algorithme Monte-Carlo EM." Paris 6, 2001. http://www.theses.fr/2001PA066092.
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Biswas, Swati. "On incorporating heterogeneity in linkage analysis." Columbus, Ohio : Ohio State University, 2003. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1070468056.
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Thesis (Ph. D.)--Ohio State University, 2003.<br>Title from first page of PDF file. Document formatted into pages; contains xii, 123 p.; also includes graphics. Includes abstract and vita. Advisor: Shili Lin, Dept. of Statistics. Includes bibliographical references (p. 119-123).
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Rampinelli, Cássio Guilherme. "Modelagem hidrológica sob uma abordagem bayesiana : comparação de algoritmos MCMC e análise da influência da função verossimilhança na estimativa dos parâmetros e descrição das incertezas." reponame:Repositório Institucional da UnB, 2016. http://repositorio.unb.br/handle/10482/22357.
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Dissertação (mestrado)—Universidade de Brasília, Faculdade de Tecnologia, Departamento de Engenharia Civil e Ambiental, 2016.<br>Submitted by Fernanda Percia França (fernandafranca@bce.unb.br) on 2016-11-21T17:02:46Z
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2016_CássioGuilhermeRampinelli.pdf: 17198008 bytes, checksum: d865c15e2b03298454d6e7a91457004e (MD5)<br>Pesquisas realizadas na última década tem mostrado a abordagem bayesiana como uma ferramenta promissora na avaliação de incertezas em modelos hidrológicos e no auxílio à tomada de decisões a partir de prognósticos desses modelos. A abordagem bayesiana com o emprego das denominadas cadeias de Markov via simulação Monte Carlo permite a obtenção das distribuições posteriores completas de todos os parâmetros do modelo e de qualquer função dos mesmos, incluindo a do hidrograma simulado. Contudo, ao se empregar essa abordagem faz-se necessário representar a natureza assumida para os erros do modelo por meio de uma função de verossimilhança. É comum, em diversos casos de simulação, assumir que os resíduos possam ser representados por uma distribuição normal com média zero e desvio padrão conhecido. Entretanto, diversos estudos tem revelado que essa premissa é frequentemente violada para a maioria dos caso sem hidrologia. Este trabalho se insere nesse contexto e apresenta o desenvolvimento e a aplicação dos algoritmos Metropolis Hastings e Adaptive Metropolis para a estimativa das incertezas referentes aos parâmetros do modelo hidrológico do tipo conceitual denominado Soil Moisture Accounting Procedure (SMAP), para passo de tempo mensal. Complementarmente, o algoritmo Differential Evolution Adaptive Metropolis (DREAM), amplamente testado em diversos trabalhos correlatos, é empregado com o propósito de validar os resultados obtidos com os algoritmos implementados, bem como avaliar o comportamento das estimativas dos erros e das distribuições posteriores quando se faz uso de uma função de verossimilhança generalizada, capaz de agregar a não normalidade, a heterocedasticidade e a correlação entre os resíduos. Com o propósito de melhor explorar o comportamento dos parâmetros e contrapor a abordagem bayesiana com os métodos de calibração determinísticos usualmente empregados, os parâmetros são também estimados com o algoritmo de busca global PSO. Os resultados indicam o comportamento adequado dos algoritmos implementados, mostrando o potencial da abordagem bayesiana para a avaliação de incertezas bem como demonstram a influência da função de verossimilhança nas distribuições posteriores dos parâmetros e nas vazões simuladas. Com o intuito de corroborar para disseminação e uso dessa ferramenta os códigos implementados em linguagem R são disponibilizados ao final do trabalho para os principais casos estudados.<br>Researches conducted in the last decade has shown Bayesian approach as a promising tool in exploring uncertainty in hydrologic modeling and as an useful support in decision making process. The application of the Bayesian approach, implemented by Markov chains via Monte Carlo simulation, provides the full posterior distribution of the model parameters and any function of them, including the distribution of the simulated flows. However, when applying Bayesian approach the modeler should make assumptions about the errors nature by implementing an appropriate likelihood function. It is usual, in many cases, assuming that residuals can be described by a normal distribution with zero mean and a given standard deviation. However, several studies have shown that this assumption is often violated for most cases in hydrology. This work corroborates to this context and presents Metropolis Hastings and Adaptive Metropolis algorithms implemented in R programming language in order to assess the uncertainty regarding the Soil Moisture Accounting Procedure (SMAP)parameters, a conceptual Rainfall-Runoff model, to monthly time steps. In addition, DREAM algorithm, widely applied in several related works, is used in order to validate the results obtained with the implemented algorithms. Furthermore, residuals behavior are analyzed by a Generalized Likelihood Function that better address the non-normality, heterocedasticity and correlation between errors. For the sake of comparison, parameters were also estimated with a global optimization procedure and with a Bayesian approach. Results illustrate the potential of the Bayesian approach in exploring the parameters uncertainties, and indicate the influence of the likelihood function in the parameter posterior distributions and simulated flow. In order to corroborate to the use and dissemination of Bayesian analyses in hydrologic modeling, programming codes implemented in R statistical language are available at the end of work for the main case studies.
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Pinheiro, Camila Xavier Sá Peixoto, and 92-98825-5055. "Misturas de escala da distribuição normal assimétrica com dados faltantes." Universidade Federal do Amazonas, 2016. http://tede.ufam.edu.br/handle/tede/5987.
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Previous issue date: 2016-05-03<br>CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior<br>No summary<br>Neste trabalho estudamos uma ferramenta de estimação para modelos sob a classe
de misturas de escala da distribuição normal assimétrica multivariada onde valores faltantes
ocorrem nos dados. Desta forma, apresentamos uma proposta utilizando tais modelos
flexíveis e algoritmos computacionais para a análise de dados multivariados com comportamento
que foge do padrão usual da distribuição normal e outras distribuições simétricas
usuais, apresentando forte assimetria e caudas pesadas. Além disso, mostramos a eficiência
da aplicação da modelagem sugerida e do método de estimação proposto, por meio de
estudos de simulação computacional, analisando a qualidade dos estimadores via estudos
de vício e erro quadrático médio e comparando diferentes modelos via critérios de seleção.
A abordagem inferencial utilizada foi a Bayesiana, utilizando os métodos MCMC
tradicionais para obter gerações de amostras da distribuição a posterior.
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Zeppilli, Giulia. "Alcune applicazioni del Metodo Monte Carlo." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2012. http://amslaurea.unibo.it/3091/.
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Chaari, Lotfi. "Parallel magnetic resonance imaging reconstruction problems using wavelet representations." Phd thesis, Université Paris-Est, 2010. http://tel.archives-ouvertes.fr/tel-00587410.
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Pour réduire le temps d'acquisition ou bien améliorer la résolution spatio-temporelle dans certaines application en IRM, de puissantes techniques parallèles utilisant plusieurs antennes réceptrices sont apparues depuis les années 90. Dans ce contexte, les images d'IRM doivent être reconstruites à partir des données sous-échantillonnées acquises dans le " k-space ". Plusieurs approches de reconstruction ont donc été proposées dont la méthode SENSitivity Encoding (SENSE). Cependant, les images reconstruites sont souvent entâchées par des artéfacts dus au bruit affectant les données observées, ou bien à des erreurs d'estimation des profils de sensibilité des antennes. Dans ce travail, nous présentons de nouvelles méthodes de reconstruction basées sur l'algorithme SENSE, qui introduisent une régularisation dans le domaine transformé en ondelettes afin de promouvoir la parcimonie de la solution. Sous des conditions expérimentales dégradées, ces méthodes donnent une bonne qualité de reconstruction contrairement à la méthode SENSE et aux autres techniques de régularisation classique (e.g. Tikhonov). Les méthodes proposées reposent sur des algorithmes parallèles d'optimisation permettant de traiter des critères convexes, mais non nécessairement différentiables contenant des a priori parcimonieux. Contrairement à la plupart des méthodes de reconstruction qui opèrent coupe par coupe, l'une des méthodes proposées permet une reconstruction 4D (3D + temps) en exploitant les corrélations spatiales et temporelles. Le problème d'estimation d'hyperparamètres sous-jacent au processus de régularisation a aussi été traité dans un cadre bayésien en utilisant des techniques MCMC. Une validation sur des données réelles anatomiques et fonctionnelles montre que les méthodes proposées réduisent les artéfacts de reconstruction et améliorent la sensibilité/spécificité statistique en IRM fonctionnelle
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Sedki, Mohammed Amechtoh. "Échantillonnage préférentiel adaptatif et méthodes bayésiennes approchées appliquées à la génétique des populations." Thesis, Montpellier 2, 2012. http://www.theses.fr/2012MON20041/document.
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Dans cette thèse, on propose des techniques d'inférence bayésienne dans les modèles où la vraisemblance possède une composante latente. La vraisemblance d'un jeu de données observé est l'intégrale de la vraisemblance dite complète sur l'espace de la variable latente. On s'intéresse aux cas où l'espace de la variable latente est de très grande dimension et comportes des directions de différentes natures (discrètes et continues), ce qui rend cette intégrale incalculable. Le champs d'application privilégié de cette thèse est l'inférence dans les modèles de génétique des populations. Pour mener leurs études, les généticiens des populations se basent sur l'information génétique extraite des populations du présent et représente la variable observée. L'information incluant l'histoire spatiale et temporelle de l'espèce considérée est inaccessible en général et représente la composante latente. Notre première contribution dans cette thèse suppose que la vraisemblance peut être évaluée via une approximation numériquement coûteuse. Le schéma d'échantillonnage préférentiel adaptatif et multiple (AMIS pour Adaptive Multiple Importance Sampling) de Cornuet et al. [2012] nécessite peu d'appels au calcul de la vraisemblance et recycle ces évaluations. Cet algorithme approche la loi a posteriori par un système de particules pondérées. Cette technique est conçue pour pouvoir recycler les simulations obtenues par le processus itératif (la construction séquentielle d'une suite de lois d'importance). Dans les nombreux tests numériques effectués sur des modèles de génétique des populations, l'algorithme AMIS a montré des performances numériques très prometteuses en terme de stabilité. Ces propriétés numériques sont particulièrement adéquates pour notre contexte. Toutefois, la question de la convergence des estimateurs obtenus parcette technique reste largement ouverte. Dans cette thèse, nous montrons des résultats de convergence d'une version légèrement modifiée de cet algorithme. Sur des simulations, nous montrons que ses qualités numériques sont identiques à celles du schéma original. Dans la deuxième contribution de cette thèse, on renonce à l'approximation de la vraisemblance et onsupposera seulement que la simulation suivant le modèle (suivant la vraisemblance) est possible. Notre apport est un algorithme ABC séquentiel (Approximate Bayesian Computation). Sur les modèles de la génétique des populations, cette méthode peut se révéler lente lorsqu'on vise uneapproximation précise de la loi a posteriori. L'algorithme que nous proposons est une amélioration de l'algorithme ABC-SMC de DelMoral et al. [2012] que nous optimisons en nombre d'appels aux simulations suivant la vraisemblance, et que nous munissons d'un mécanisme de choix de niveauxd'acceptations auto-calibré. Nous implémentons notre algorithme pour inférer les paramètres d'un scénario évolutif réel et complexe de génétique des populations. Nous montrons que pour la même qualité d'approximation, notre algorithme nécessite deux fois moins de simulations par rapport à laméthode ABC avec acceptation couramment utilisée<br>This thesis consists of two parts which can be read independently.The first part is about the Adaptive Multiple Importance Sampling (AMIS) algorithm presented in Cornuet et al.(2012) provides a significant improvement in stability and Effective Sample Size due to the introduction of the recycling procedure. These numerical properties are particularly adapted to the Bayesian paradigm in population genetics where the modelization involves a large number of parameters. However, the consistency of the AMIS estimator remains largely open. In this work, we provide a novel Adaptive Multiple Importance Sampling scheme corresponding to a slight modification of Cornuet et al. (2012) proposition that preserves the above-mentioned improvements. Finally, using limit theorems on triangular arrays of conditionally independant random variables, we give a consistensy result for the final particle system returned by our new scheme.The second part of this thesis lies in ABC paradigm. Approximate Bayesian Computation has been successfully used in population genetics models to bypass the calculation of the likelihood. These algorithms provide an accurate estimator by comparing the observed dataset to a sample of datasets simulated from the model. Although parallelization is easily achieved, computation times for assuring a suitable approximation quality of the posterior distribution are still long. To alleviate this issue, we propose a sequential algorithm adapted fromDel Moral et al. (2012) which runs twice as fast as traditional ABC algorithms. Itsparameters are calibrated to minimize the number of simulations from the model
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Ferreira, Eduardo Vargas 1987. "Modelos da teoria de resposta ao item assimétricos de grupos múltiplos para respostas politômicas nominais e ordinais sob um enfoque bayesiano." [s.n.], 2014. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306788.
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Orientador: Caio Lucidius Naberezny Azevedo<br>Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica<br>Made available in DSpace on 2018-08-24T12:51:18Z (GMT). No. of bitstreams: 1
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Previous issue date: 2014<br>Resumo: No presente trabalho propõem-se novos modelos da Teoria de Resposta ao Item para respostas politômicas nominais e ordinais (graduais), via dados aumentados, para grupos múltiplos. Para a modelagem das distribuições dos traços latentes de cada grupo, considera-se normais assimétricas centradas. Tal abordagem, além de acomodar a característica de assimetria aos dados, ajuda a garantir a identificabilidade dos modelos estudados, a qual é tratada tanto sob a ótica frequentista quanto bayesiana. Com relação aos métodos de estimação, desenvolveu-se procedimentos bayesianos através de algoritmos de Monte Carlo via cadeias de Markov (MCMC), utilizando o algoritmo de Gibbs (DAGS), com a verossimilhança aumentada (dados aumentados) e Metropolis-Hastings, considerando a verossimilhança original. As implementações computacionais foram escritas em linguagem C++, integradas ao ambiente computacional, gráfico e estatístico R, viabilizando rotinas gratuitas, de código aberto e alta velocidade no processamento, essenciais à difusão de tais metodologias. Para a seleção de modelos, utilizou-se o critério de informação deviance (DIC), os valores esperados do critério de informação de Akaike (EAIC) e o critério de informação bayesiano (EBIC). Em relação à verificação da qualidade do ajuste de modelos, explorou-se a checagem preditiva a posteriori, que fornece meios concretos de se avaliar a qualidade do instrumento de medida (prova, questionário etc), qualidade do ajuste do modelo de um modo global, além de indícios de violações de suposições específicas. Estudos de simulação, considerando diversas situações de interesse prático, indicam que os modelos e métodos de estimação produzem resultados bastante satisfatórios, com superioridade dos modelos assimétricos com relação ao simétrico (o qual assume simetria das distribuições das variáveis latentes). A análise de um conjunto de dados reais, referente à primeira fase do vestibular da UNICAMP de 2013, ilustra o potencial da tríade: modelagem, métodos de estimação e ferramentas de diagnósticos, desenvolvida neste trabalho<br>Abstract: In this work, we propose new Item Response Theory models for nominal and ordinal (gradual) polytomous responses through augmented data schemes considering multiple groups. For the distribution of the latent traits of each group, we consider a skew-normal distribution under the centered parametrization. This approach will allow for accommodating a possible skewness of the latent trait distribution, but is also helpful to ensure the identifiability of the models, which is studied under frequentist and Bayesian paradigms. Concerning estimation methods, we developed Bayesian methods through Markov chain Monte Carlo (MCMC) algorithms by using the Gibbs algorithm (DAGS), with augmented likelihood (augmented data) and Metropolis-Hastings algorithms, considering the original
likelihood. The computational environment was written in the C++ language and integrated with the R program (a statistical computational and graphical environment), allowing for free, open source and high-speed routines which, in turn, are essential to the dissemination of the developed methodologies. In terms of model selection, we considered the deviance information criterion (DIC), the expected Akaike information criterion (EAIC) and expected Bayesian information criterion (EBIC). Regarding model-fit assessment tools, we explore the posterior predictive model- checking which allows for assessing the quality of measurement, instruments (tests, questionnaires, and others), the model fit in a global sense,
besides providing directions toward violations of specific assumptions. Simulation studies, considering different situations of practical interest, indicate that the models and estimation methods produced reasonable results, with outperformance of skew models when compared to symmetric ones (which assumes symmetry of the latent trait distribution). Analysis of a data set which corresponds to the first phase of the 2013 written examination of UNICAMP (State University of Campinas), illustrates the potential of the following triad: modelling; estimation methods; and diagnostic tools developed in this work.<br>Mestrado<br>Estatistica<br>Mestre em Estatística
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Carvalho, Silvia Viviane Oliveira. "Um modelo robusto assimétrico de análise fatorial." Universidade Federal do Amazonas, 2014. http://tede.ufam.edu.br/handle/tede/4775.
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Previous issue date: 2014-05-07<br>Não informada<br>In this work we develop an extension of the classic factor analysis model, by relaxing
the assumption of normality of the factors. Instead, we suppose that the joint distribution
of the factors and observational errors is a scale mixture of skew-normal distributions,
allowing us to model data following a nonstandard pattern, presenting skewness and heavy
tails at the same time. A relevant feature of the model is the parametrization used for the
scale mixture, defined in such a way that all the elements of the shape vector but the first
are guaranteed to be zero.<br>Apresenta-se, nesta dissertação, uma extensão do modelo de análise fatorial, através
da flexibilização da suposição de normalidade dos fatores e dos erros de observação.
Assume-se que a distribuição conjunta do vetor de erros de observação e do vetor de
fatores é uma mistura de escala da distribuição normal assimétrica, o que possibilita a
modelagem de dados que seguem um padrão não usual, apresentado assimetria e caudas
pesadas ao mesmo tempo, por exemplo. Uma característica relevante do modelo é a parametrização utilizada para a mistura de escala, definida de tal maneira que os elementos
do parâmetro vetor de forma, com exceção de um, sejam todos iguais a zero.
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Garay, Aldo William Medina. "Modelos de regressão para dados censurados sob distribuições simétricas." Universidade de São Paulo, 2014. http://www.teses.usp.br/teses/disponiveis/45/45133/tde-15062014-000915/.
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Este trabalho tem como objetivo principal apresentar uma abordagem clássica e Bayesiana dos modelos lineares com observações censuradas, que é uma nova área de pesquisa com grandes possibilidades de aplicações. Aqui, substituimos o uso convencional da distribuição normal para os erros por uma família de distribuições mais flexíveis, o que nos permite lidar de forma mais adequada com observações censuradas na presença de outliers. Esta família é obtida através de um mecanismo de fácil construção e possui como casos especiais as distribuições t de Student, Pearson tipo VII, slash, normal contaminada e, obviamente, a normal. Para o caso de respostas correlacionadas e censuradas propomos um modelo de regressão linear robusto baseado na distribuição t de Student, desenvolvendo um algoritmo tipo EM que depende dos dois primeiros momentos da distribuição t de Student truncada.<br>This work aims to present a classical and Bayesian approach to linear models with censored observations, which is a new area of research with great potential for applications. Here, we replace the conventional use of the normal distribution for the errors of a more flexible family of distributions, which deal in more appropriately with censored observations in the presence of outliers. This family is obtained through a mechanism easy to construct and has as special cases the distributions Student t, Pearson type VII, slash, contaminated normal, and obviously normal. For the case of correlated and censored responses we propose a model of robust linear regression based on Student\'s t distribution and we developed an EM type algorithm based on the first two moments of the truncated Student\'s t distribution.
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Rigouste, Loïs. "Méthodes probabilistes pour l'analyse exploratoire de données textuelles." Phd thesis, Télécom ParisTech, 2006. http://pastel.archives-ouvertes.fr/pastel-00002424.
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Nous abordons le problème de la classification non supervisée de documents par des méthodes probabilistes. Notre étude se concentre sur le modèle de mélange de lois multinomiales avec variables latentes thématiques au niveau des documents. La construction de groupes de documents thématiquement homogènes est une des technologies de base de la fouille de texte, et trouve de multiples applications, aussi bien en recherche documentaire qu'en catégorisation de documents, ou encore pour le suivi de thèmes et la construction de résumés. Diverses propositions récentes ont été faites de modèles probabilistes permettant de déterminer de tels regroupements. Les modèles de classification probabilistes peuvent également être vus comme des outils de construction de représentations numériques synthétiques d'informations contenues dans le document. Ces modèles, qui offrent des facilités pour la généralisation et l'interprétation des résultats, posent toutefois des problèmes d'estimation difficiles, dûs en particulier à la très grande dimensionnalité du vocabulaire. Notre contribution à cette famille de travaux est double: nous présentons d'une part plusieurs algorithmes d'inférence, certains originaux, pour l'estimation du modèle de mélange de multinomiales; nous présentons également une étude systématique des performances de ces algorithmes, fournissant ainsi de nouveaux outils méthodologiques pour mesurer les performances des outils de classification non supervisée. Les bons résultats obtenus par rapport à d'autres algorithmes classiques illustrent, à notre avis, la pertinence de ce modèle de mélange simple pour les corpus regroupant essentiellement des documents monothématiques.
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Uêda, Shirley Tieko. "Uso do processo gama para dados de sobrevivência." Universidade Federal de São Carlos, 2005. https://repositorio.ufscar.br/handle/ufscar/4580.
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Previous issue date: 2005-01-20<br>Financiadora de Estudos e Projetos<br>In this dissertation, we introduce classical and Bayesian approaches to get inferences
on the parameters of interest, considering exponential and Weibull distributions for the
lifetimes. For a Bayesian analysis, we assume a gamma process for the individual rates
considering type II censoring data and the presence of covariates. We also consider ac-
celerated life tests assuming an inverse power law model and an exponential distribution
for the lifetimes.
The proposed methodology in illustrated in three examples.<br>Nesta dissertação, apresentamos uma análise clássica e uma abordagem Bayesiana para
obter inferências dos parâmetros de interesse, considerando as distribuições exponencial e
de Weibull para os tempos de sobrevivência. Assumimos um processo gama para as taxas
indivíduais e a presença de covariadas relacionadas com os tempos de sobrevivência com
censuras do tipo II.
Alguns conceitos e resultados de análise estatística de testes de vida acelerados são
apresentados, em particular, um estudo sobre o Modelo de Lei de Potência Inversa, con-
siderando que os tempos de sobrevivência são ajustados por uma distribuição exponencial.
A metodologia proposta neste trabalho está ilustrada a três conjuntos de dados, onde
dois são referentes à análise de sobrevivência com dados médicos e o outro a dados de
confiabilidade.
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Cosma, Ioana Ada. "Dimension reduction of streaming data via random projections." Thesis, University of Oxford, 2009. http://ora.ox.ac.uk/objects/uuid:09eafd84-8cb3-4e54-8daf-18db7832bcfc.
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A data stream is a transiently observed sequence of data elements that arrive unordered, with repetitions, and at very high rate of transmission. Examples include Internet traffic data, networks of banking and credit transactions, and radar derived meteorological data. Computer science and engineering communities have developed randomised, probabilistic algorithms to estimate statistics of interest over streaming data on the fly, with small computational complexity and storage requirements, by constructing low dimensional representations of the stream known as data sketches. This thesis combines techniques of statistical inference with algorithmic approaches, such as hashing and random projections, to derive efficient estimators for cardinality, l_{alpha} distance and quasi-distance, and entropy over streaming data. I demonstrate an unexpected connection between two approaches to cardinality estimation that involve indirect record keeping: the first using pseudo-random variates and storing selected order statistics, and the second using random projections. I show that l_{alpha} distances and quasi-distances between data streams, and entropy, can be recovered from random projections that exploit properties of alpha-stable distributions with full statistical efficiency. This is achieved by the method of L-estimation in a single-pass algorithm with modest computational requirements. The proposed estimators have good small sample performance, improved by the methods of trimming and winsorising; in other words, the value of these summary statistics can be approximated with high accuracy from data sketches of low dimension. Finally, I consider the problem of convergence assessment of Markov Chain Monte Carlo methods for simulating from complex, high dimensional, discrete distributions. I argue that online, fast, and efficient computation of summary statistics such as cardinality, entropy, and l_{alpha} distances may be a useful qualitative tool for detecting lack of convergence, and illustrate this with simulations of the posterior distribution of a decomposable Gaussian graphical model via the Metropolis-Hastings algorithm.
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Viallefont, Valérie. "Analyses bayesiennes du choix de modèles en épidémiologie : sélection de variables et modélisation de l'hétérogénéité pour des évènements." Paris 11, 2000. http://www.theses.fr/2000PA11T023.
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Cette thèse se décompose en deux parties qui traitent la question du choix modèles dans deux problématiques différentes. Dans la première partie, on s'intéresse, pour les modèles de régression logis multivariée, à différentes stratégies de sélection de variables associées à l'apparition d'une maladie. Les méthodes les plus fréquemment mises en œuvre à l'heure actuelle consistent à sélectionner certaines variables dans un modèle final unique, modèle dans lequel sont ensuite estimés les paramètres et leur variance. Différents critères de sélection existent et la plupart d'entre eux reposent sur une comparaison du degré de signification de tests à une valeur seuil. On s'intéresse aux performances auc performances de ces approches par rapport à celles d'une méthode bayésienne dans laquelle on considère tout un ensemble de modèles. A chaque modèle est associé sa probabilité a posteriori. Cette approche permet d'estimer la probabilité de l'existence d'une association entre chaque variable et l'apparition de la maladie, et de calculer des estimations globale des paramètres. Deux schémas de simulations sont envisagés pour cette comparaison : l'un évoque un cas d'école où l'on s'intéresse à un facteur de risque en présence d'un unique facteur de confusion potentiel, l'autre caractérise une enquête épidémiologique avec un grand nombre de facteurs de risque possibles. Les critères de comparaison portent sur le biais moyen dans l'estimation des coefficients, les pourcentages d’erreurs de première et seconde espèces ou leur équivalent bayésien, et l'expression du degré d'incertitude. La méthode bayésienne fournit notamment une appréciation plus explicite de l'incertitude sur les conclusions. Dans la deuxième partie, on s'intéresse au cas où des données relatives à des événements rares présentent une trop forte hétérogénéité pour être modélisées par une seule distribution de Poisson. On fait alors l'hypothèse qu'elles sont issues de mélange de distributions de Poisson. On propose d'estimer conjointement, dans un modèle hiérarchique bayésien, le nombre de composantes du mélange et les proportions et paramètres de chacune, par les méthodes de Monte Carlo par Chaîne de Markov (MCMC). L'estimation du nombre de composantes nécessite que la dimension de l'espace des paramètres puisse varier : pour ceci on utilise le principe du "Saut Reversible". On illustre la difficulté de trouver une loi a priori faiblement informative pour les paramètres de Poisson en étudiant la sensibilité des résultats au choix de cette loi a priori et de ses paramètres. On propose différentes transformations lors du changement de dimension de l'espace des paramètres et on s'intéresse à leur influence sur les performances de l'algorithme, notamment son caractère mélangeant. Enfin on écrit deux modèles, de prise en compte de covariables, dont l'effet est soit homogène soit hétérogène sur les composantes du mélange. Les comparaisons sont menées sur des jeux de données simulés, et le modèle est finalement illustré sur des données réelles de nature épidémiologique concernant des cas de cancers digestifs en France, puis des données d'accidents de la route<br>This dissertation has two separated parts. In the first part, we compare different strategies for variable selection in a multivariate logistic regression model. Covariate and confounder selection in case-control studies is often carried out using either a two-step method or a stepwise variable selection method. Inference is then carried out conditionally on the selected model, but this ignores the madel uncertainty implicit in the variable selection process, and so underestimates uncertainty about relative risks. It is well known, and showed again in our study, that the ρ-values computed after variable selection can greatly overstate the strength of conclusions. We propose Bayesian Model Averaging as a formal way of taking account of madel uncertainty in a logistic regression context. The BMA methods, that allows to take into account several models, each being associated with its posterior probability, yields an easily interpreted summary, the posterior probability that a variable is a risk factor, and its estimate averaged over the set of models. We conduct two comparative simulations studies : the first one has a simple design including only one risk factor and one confounder, the second one mimics a epidemiological cohort study dataset, with a large number of potential risk factors. Our criteria are the mean bias, the rate of type I and type II errors, and the assessment of uncertainty in the results, which is bath more accurate and explicit under the BMA analysis. The methods are applied and compared in the context of a previously published case-control study of cervical cancer. The choice of the prior distributions are discussed. In the second part, we focus on the modelling of rare events via a Poisson distribution, that sometimes reveals substantial over-dispersion, indicating that sorme un explained discontinuity arises in the data. We suggest to madel this over-dispersion by a Poisson mixture. In a hierarchical Bayesian model, the posterior distributions of he unknown quantities in the mixture (number of components, weights, and Poisson parameters) can be estimated by MCMC algorithms, including reversible jump algothms which allows to vary the dimension of the mixture. We focus on the difficulty of finding a weakly informative prior for the Poisson parameters : different priors are detailed and compared. Then, the performances of different maves created for changing dimension are investigated. The model is extended by the introduction of covariates, with homogeneous or heterogeneous effect. Simulated data sets are designed for the different comparisons, and the model is finally illustrated in two different contexts : an ecological analysis of digestive cancer mortality along the coasts of France, and a dataset concerning counts of accidents in road-junctions
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Arribas, Gil Ana. "Estimation dans des modèles à variables cachées : alignement des séquences biologiques et modèles d'évolution." Paris 11, 2007. http://www.theses.fr/2007PA112054.
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Cette thèse est consacrée à l'estimation paramétrique dans certains modèles d'alignement de séquences biologiques. Ce sont des modèles construits à partir des considérations sur le processus d'évolution des séquences. Dans le cas de deux séquences, le processus d'évolution classique résulte dans un modèle d'alignement appelé pair-Hidden Markov Model (pair-HMM). Dans le pair-HMM les observations sont formées par le couple de séquences à aligner et l'alignement caché est une chaîne de Markov. D'un point de vue théorique nous donnons un cadre rigoureux pour ce modèle et étudions la consistance des estimateurs bayésien et par maximum de vraisemblance. D'un point de vue appliqué nous nous intéressons à la détection de motifs conservés dans les séquences à travers de l'alignement. Pour cela nous introduisons un processus d'évolution permettant différents comportements évolutifs à différents endroits de la séquence et pour lequel le modèle d'alignement est toujours un pair-HMM. Nous proposons des algorithmes d'estimation d'alignements et paramètres d'évolution adaptés à la complexité du modèle. Finalement, nous nous intéressons à l'alignement multiple (plus de deux séquences). Le processus d'évolution classique résulte dans ce cas dans un modèle d'alignement à variables cachées plus complexe et dans lequel il faut prendre en compte les relations phylogénétiques entre les séquences. Nous donnons le cadre théorique pour ce modèle et étudions, comme dans le cas de deux séquences, la propriété de consistance des estimateurs<br>This thesis is devoted to parameter estimation in models for biological sequence alignment. These are models constructed considering an evolution process on the sequences. In the case of two sequences evolving under the classical evolution process, the alignment model is called a pair-Hidden Markov Model (pair-HMM). Observations in a pair-HMM are formed by the couple of sequences to be aligned and the hidden alignment is a Markov chain. From a theoretical point of view, we provide a rigorous formalism for these models and study consistency of maximum likelihood and bayesian estimators. From the point of view of applications, we are interested in detection of conserved motifs in the sequences. To do this we present an evolution process that allows heterogeneity along the sequence. The alignment under this process still fits the pair-HMM. We propose efficient estimation algorithms for alignments and evolution parameters. Finally we are interested in multiple alignment (more than two sequences). The classical evolution process for the sequences provides a complex hidden variable model for the alignment in which the phylogenetic relationships between the sequences must be taken into account. We provide a theoretical framework for this model and study, as for the pairwise alignment, the consistency of estimators
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Monteiro, Renata Evangelista, and 92-99124-4468. "Misturas de modelos de regressão linear com erros nas variáveis usando misturas de escala da normal assimétrica." Universidade Federal do Amazonas, 2018. https://tede.ufam.edu.br/handle/tede/6417.
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Previous issue date: 2018-03-12<br>CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior<br>The traditional estimation of mixture regression models is based on the assumption
of normality of component errors and thus is sensitive to outliers, heavy-tailed and/or
asymmetric errors. Another drawback is that, in general, the analysis is restricted to
directly observed predictors.
We present a proposal to deal with these issues simultaneously in the context of
mixture regression by extending the classic normal model by assuming that, for each
mixture component, the random errors and the covariates jointly follow a scale mixture of
skew-normal distributions. It is also assumed that the covariates are observed with error.
An MCMC-type algorithm to perform Bayesian inference is developed and, in
order to show the efficacy of the proposed methods, simulated and real data sets are
analyzed.<br>A estimação tradicional em mistura de modelos de regressão é baseada na suposição
de normalidade para os erros aleatórios, sendo assim, sensível a outliers, caudas
pesadas e erros assimétricos. Outra desvantagem é que, em geral, a análise é restrita a
preditores que são observados diretamente.
Apresentamos uma proposta para lidar com estas questões simultaneamente no
contexto de mistura de regressões estendendo o modelo normal clássico. Assumimos
que, conjuntamente e em cada componente da mistura, os erros aleatórios e as covariáveis
seguem uma mistura de escala da distribuição normal assimétrica. Além disso, é feita a
suposição de que as covariáveis são observadas com erro aditivo.
Um algorítmo do tipo MCMC foi desenvolvido para realizar inferência Bayesiana.
A eficácia do modelo proposto é verificada via análises de dados simulados e reais.
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Donnet, Sophie. "Inversion de données IRMf : estimation et sélection de modèles." Paris 11, 2006. http://www.theses.fr/2006PA112193.
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Cette thèse est consacrée à l'analyse de données d'Imagerie par Résonance Magnétique fonctionnelle (IRMf). Dans le cadre du modèle classique de convolution, nous testons l'hypothèse de variabilité inter-occurrences des amplitudes des réponses hémodynamiques. L'estimation des paramètres de ce nouveau modèle requiert le recours à l'algorithme Expectation-Maximisation. Nous comparons ce modèle au modèle sans variabilité inter-occurrences par un test du rapport des vraisemblances, sur un grand nombre de jeu de données réelles. Le modèle linéaire souffrant d'un manque de fondement biologique, nous considérons un modèle physiologique aboutissant à l'écriture du signal IRMf comme la somme d'un terme de régression, solution d'une équation différentielle ordinaire (EDO), sans solution analytique dépendant d'un paramètre aléatoire, et d'un bruit de mesure gaussien. Nous proposons une méthode générale d'estimation paramétrique des modèles définis par EDO à données non-observées, intégrant une méthode de résolution numérique du système dynamique et reposant sur une version stochastique de l'algorithme EM. Nous montrons la convergence des estimateurs des paramètres produits par cet algorithme, et contrôlons l'erreur induite par l'approximation de la solution du système différentiel sur l'estimation des paramètres. Nous appliquons cette méthode à la fois sur données d'IRMf simulées et réelles. Enfin, nous considérons des modèles définis par équations différentielles stochastiques (EDS) dépendant d'un paramètre aléatoire. En approchant la diffusion par un schéma numérique, nous proposons une méthode d'estimation des paramètres du modèle. La précision de cette méthode est illustrée sur une étude sur données simulées dans le cadre d'un modèle à effets mixtes, issus de la pharmacocinétique. Une étude sur données réelle démontre la pertinence de l'approche stochastique. Finalement, nous nous intéressons à l'identifiabilité des modèles définis par EDS dépendant de paramètres aléatoires<br>This thesis is devoted to the analysis of functional Magnetic Resonance Imaging data (fMRI). In the framework of standard convolution models, we test a model that allows for the variation of the magnitudes of the hemodynamic reponse. To estimate the parameters of this model, we have to resort to the Expectation-Maximisation algorithm. We test this model against the standard one --withconstant magnitudes-- on several real data, set by a likelihood ratio test. The linear model suffers from a lack of biological basis, hence we consider a physiological model. In this framework, we describe the data as the sum of a regression term, defined as the non-analytical solution of an ordinary differentiel equation (ODE) depending on random parameters, and a gaussian observation noise. We develop a general method to estimate the parameters of a statistical model defined by ODE with non-observed parameters. This method, integrating a numerical resolution of the ODE, relies on a stochastic version of the EM algorithm. The convergence of the algorithm is proved and the error induced by the numerical solving method is controlled. We apply this method on simulated and real data sets. Subsequently, we consider statistical models defined by stochastic differential equations (SDE) depending on random parameters. We approximate the diffusion process by a numerical scheme and propose a general estimation method. Results of a pharmacokineticmixed model study (on simulated and real data set) illustrate the accuracy of the estimation and the relevance of the SDE approach. Finally, the identifiability of statistical models defined by SDE with random parameters is studied
33
Ancelet, Sophie. "Exploiter l'approche hiérarchique bayésienne pour la modélisation statistique de structures spatiales: application en écologie des populations." Phd thesis, AgroParisTech, 2008. http://pastel.archives-ouvertes.fr/pastel-00004396.
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Dans la plupart des questions écologiques, les phénomènes aléatoires d'intérêt sont spatialement structurés et issus de l'effet combiné de multiples variables aléatoires, observées ou non, et inter-agissant à diverses échelles. En pratique, dès lors que les données de terrain ne peuvent être directement traitées avec des structures spatiales standards, les observations sont généralement considérées indépendantes. Par ailleurs, les modèles utilisés sont souvent basés sur des hypothèses simplificatrices trop fortes par rapport à la complexité des phénomènes étudiés. Dans ce travail, la démarche de modélisation hiérarchique est combinée à certains outils de la statistique spatiale afin de construire des structures aléatoires fonctionnelles "sur-mesure" permettant de représenter des phénomènes spatiaux complexes en écologie des populations. L'inférence de ces différents modèles est menée dans le cadre bayésien avec des algorithmes MCMC. Dans un premier temps, un modèle hiérarchique spatial (Geneclust) est développé pour identifier des populations génétiquement homogènes quand la diversité génétique varie continûment dans l'espace. Un champ de Markov caché, qui modélise la structure spatiale de la diversité génétique, est couplé à un modèle bivarié d'occurrence de génotypes permettant de tenir compte de l'existence d'unions consanguines chez certaines populations naturelles. Dans un deuxième temps, un processus de Poisson composé particulier,appelé loi des fuites, est présenté sous l'angle de vue hiérarchique pour décrire le processus d'échantillonnage d'organismes vivants. Il permet de traiter le délicat problème de données continues présentant une forte proportion de zéros et issues d'échantillonnages à efforts variables. Ce modèle est également couplé à différents modèles sur grille (spatiaux, régionalisés) afin d'introduire des dépendances spatiales entre unités géographiques voisines puis, à un champ géostatistique bivarié construit par convolution sur grille discrète afin de modéliser la répartition spatiale conjointe de deux espèces. Les capacités d'ajustement et de prédiction des différents modèles hiérarchiques proposés sont comparées aux modèles traditionnellement utilisés à partir de simulations et de jeux de données réelles (ours bruns de Suède, invertébrés épibenthiques du Golfe-du-Saint-Laurent (Canada)).
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Diabaté, Modibo. "Modélisation stochastique et estimation de la croissance tumorale." Thesis, Université Grenoble Alpes (ComUE), 2019. http://www.theses.fr/2019GREAM040.
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Cette thèse porte sur la modélisation mathématique de la dynamique du cancer ; elle se divise en deux projets de recherche.Dans le premier projet, nous estimons les paramètres de la limite déterministe d'un processus stochastique modélisant la dynamique du mélanome (cancer de la peau) traité par immunothérapie. L'estimation est réalisée à l'aide d'un modèle statistique non-linéaire à effets mixtes et l'algorithme SAEM, à partir des données réelles de taille tumorale mesurée au cours du temps chez plusieurs patients. Avec ce modèle mathématique qui ajuste bien les données, nous évaluons la probabilité de rechute du mélanome (à l'aide de l'algorithme Importance Splitting), et proposons une optimisation du protocole de traitement (doses et instants du traitement).Nous proposons dans le second projet, une méthode d'approximation de vraisemblance basée sur une approximation de l'algorithme Belief Propagation à l'aide de l'algorithme Expectation-Propagation, pour une approximation diffusion du modèle stochastique de mélanome observée chez un seul individu avec du bruit gaussien. Cette approximation diffusion (définie par une équation différentielle stochastique) n'ayant pas de solution analytique, nous faisons recours à une méthode d'Euler pour approcher sa solution (après avoir testé la méthode d'Euler sur le processus de diffusion d'Ornstein Uhlenbeck). Par ailleurs, nous utilisons une méthode d'approximation de moments pour faire face à la multidimensionnalité et la non-linéarité de notre modèle. A l'aide de la méthode d'approximation de vraisemblance, nous abordons l'estimation de paramètres dans des Modèles de Markov Cachés<br>This thesis is about mathematical modeling of cancer dynamics ; it is divided into two research projects.In the first project, we estimate the parameters of the deterministic limit of a stochastic process modeling the dynamics of melanoma (skin cancer) treated by immunotherapy. The estimation is carried out with a nonlinear mixed-effect statistical model and the SAEM algorithm, using real data of tumor size. With this mathematical model that fits the data well, we evaluate the relapse probability of melanoma (using the Importance Splitting algorithm), and we optimize the treatment protocol (doses and injection times).We propose in the second project, a likelihood approximation method based on an approximation of the Belief Propagation algorithm by the Expectation-Propagation algorithm, for a diffusion approximation of the melanoma stochastic model, noisily observed in a single individual. This diffusion approximation (defined by a stochastic differential equation) having no analytical solution, we approximate its solution by using an Euler method (after testing the Euler method on the Ornstein Uhlenbeck diffusion process). Moreover, a moment approximation method is used to manage the multidimensionality and the non-linearity of the melanoma mathematical model. With the likelihood approximation method, we tackle the problem of parameter estimation in Hidden Markov Models
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Bhering, Felipe Lunardi. "Confiabilidade em sistemas coerentes: um modelo bayesiano Weibull." Universidade de São Paulo, 2013. http://www.teses.usp.br/teses/disponiveis/45/45133/tde-01122013-155316/.
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O principal objetivo desse trabalho é introduzir um modelo geral bayesiano Weibull hierárquico para dados censurados que estima a função de confiabilidade de cada componente para sistemas de confiabilidade coerentes. São introduzidos formas de estimação mais sólidas, sem a inserção de estimativas médias nas funções de confiabilidade (estimador plug-in). Através desse modelo, são expostos e solucionados exemplos na área de confiabilidade como sistemas em série, sistemas em paralelo, sistemas k-de-n, sistemas bridge e um estudo clínico com dados censurados intervalares. As soluções consideram que as componentes tem diferentes distribuições, e nesse caso, o sistema bridge ainda não havia solução na literatura. O modelo construído é geral e pode ser utilizado para qualquer sistema coerente e não apenas para dados da área de confiabilidade, como também na área de sobrevivência, dentre outros. Diversas simulações com componentes com diferentes proporções de censura, distintas médias, três tipos de distribuições e tamanhos de amostra foram feitas em todos os sistemas para avaliar a eficácia do modelo.<br>The main purpose of this work is to introduce a general bayesian Weibull hierarchical model for censored data which estimates each reliability components function from coherent systems. Its introduced estimation procedures which do not consider plug-in estimators. Also, its exposed and solved with this model examples in reliability area such as series systems, parallel systems, k-out-of-n systems, bridge systems and a clinical study with interval censoring data. The problem of bridge system hadnt a solution before for the case of each component with different distribution. Actually, this model is general and can be used to analyse any kind of coherent system and censored data, not only reliability ones, but also survival data and others. Several components simulations with different censored proportions, distinct means, three kinds of distributions and sample size were made in all systems to evaluate model efficiency.
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Paraiba, Carolina Costa Mota. "Modelos não lineares truncados mistos para locação e escala." Universidade Federal de São Carlos, 2015. https://repositorio.ufscar.br/handle/ufscar/4497.
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Previous issue date: 2015-01-14<br>Financiadora de Estudos e Projetos<br>We present a class of nonlinear truncated mixed-effects models where the truncation nature of the data is incorporated into the statistical model by assuming that the variable of interest, namely the truncated variable, follows a truncated distribution which, in turn, corresponds to a conditional distribution obtained by restricting the support of a given probability distribution function. The family of nonlinear truncated mixed-effects models for location and scale is constructed based on the perspective of nonlinear generalized mixed-effects models and by assuming that the distribution of response variable belongs to a truncated class of distributions indexed by a location and a scale parameter. The location parameter of the response variable is assumed to be associated with a continuous nonlinear function of covariates and unknown parameters and with unobserved random effects, and the scale parameter of the responses is assumed to be characterized by a continuous function of the covariates and unknown parameters. The proposed truncated nonlinear mixed-effects models are constructed assuming both random truncation limits; however, truncated nonlinear mixed-effects models with fixed known limits are readily obtained as particular cases of these models. For models constructed under the assumption of random truncation limits, the likelihood function of the observed data shall be a function both of the parameters of the truncated distribution of the truncated variable and of the parameters of the distribution of the truncation variables. For the particular case of fixed known truncation limits, the likelihood function of the observed data is a function only of the parameters of the truncated distribution assumed for the variable of interest. The likelihood equation resulting from the proposed truncated nonlinear regression models do not have analytical solutions and thus, under the frequentist inferential perspective, the model parameters are estimated by direct maximization of the log-likelihood using an iterative procedure. We also consider diagnostic analysis to check for model misspecification, outliers and influential observations using standardized residuals, and global and local influence metrics. Under the Bayesian perspective of statistical inference, parameter estimates are computed based on draws from the posterior distribution of parameters obtained using an Markov Chain Monte Carlo procedure. Posterior predictive checks, Bayesian standardized residuals and a Bayesian influence measures are considered to check for model adequacy, outliers and influential observations. As Bayesian model selection criteria, we consider the sum of log -CPO and a Bayesian model selection procedure using a Bayesian mixture model framework. To illustrate the proposed methodology, we analyze soil-water retention, which are used to construct soil-water characteristic curves and which are subject to truncation since soil-water content (the proportion of water in soil samples) is limited by the residual soil-water content and the saturated soil-water content.<br>Neste trabalho, apresentamos uma classe de modelos não lineares truncados mistos onde a característica de truncamento dos dados é incorporada ao modelo estatístico assumindo-se que a variável de interesse, isto é, a variável truncada, possui uma função de distribuição truncada que, por sua vez, corresponde a uma função de distribuição condicional obtida ao se restringir o suporte de alguma função de distribuição de probabilidade. A família de modelos não lineares truncados mistos para locação e escala é construída sob a perspectiva de modelos não lineares generalizados mistos e considerando uma classe de distribuições indexadas por parâmetros de locação e escala. Assumimos que o parâmetro de locação da variável resposta é associado a uma função não linear contínua de um conjunto de covariáveis e parâmetros desconhecidos e a efeitos aleatórios não observáveis, e que o parâmetro de escala das respostas pode ser caracterizado por uma função contínua das covariáveis e de parâmetros desconhecidos. Os modelos não lineares truncados mistos para locação e escala, aqui apresentados, são construídos supondo limites de truncamento aleatórios, porém, modelos não lineares truncados mistos com limites fixos e conhecidos são prontamente obtidos como casos particulares desses modelos. Nos modelos construídos sob a suposição de limites de truncamentos aleatórios, a função de verossimilhança é escrita em função dos parâmetros da distribuição da variável resposta truncada e dos parâmetros das distribuições das variáveis de truncamento. Para o caso particular de limites fixos e conhecidos, a função de verossimilhança será apenas uma função dos parâmetros da distribuição truncada assumida para a variável resposta de interesse. As equações de verossimilhança dos modelos, aqui propostos, não possuem soluções analíticas e, sob a perspectiva frequentista de inferência estatística, os parâmetros do modelo são estimados pela maximização direta da função de log-verossimilhança via um procedimento iterativo. Consideramos, também, uma análise de diagnóstico para verificar a adequação do modelo, observações discrepantes e/ou influentes, usando resíduos padronizados e medidas de influência global e influência local. Sob a perspectiva Bayesiana de inferência estatística, as estimativas dos parâmetros dos modelos propostos são definidas como as médias a posteriori de amostras obtidas via um algoritmo do tipo cadeia de Markov Monte Carlo das distribuições a posteriori dos parâmetros. Para a análise de diagnóstico Bayesiano do modelo, consideramos métricas de avaliação preditiva a posteriori, resíduos Bayesianos padronizados e a calibração de casos para diagnóstico de influência. Como critérios Bayesianos de seleção de modelos, consideramos a soma de log -CPO e um critério de seleção de modelos baseada na abordagem Bayesiana de mistura de modelos. Para ilustrar a metodologia proposta, analisamos dados de retenção de água em solo, que são usados para construir curvas de retenção de água em solo e que estão sujeitos a truncamento pois as medições de umidade de água (a proporção de água presente em amostras de solos) são limitadas pela umidade residual e pela umidade saturada do solo amostrado.
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Gonzalez, Jhonny. "Modelling and controlling risk in energy systems." Thesis, University of Manchester, 2015. https://www.research.manchester.ac.uk/portal/en/theses/modelling-and-controlling-risk-in-energy-systems(b575d2c7-154f-4aca-b15e-4b99e0b3c661).html.
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The Autonomic Power System (APS) grand challenge was a multi-disciplinary EPSRC-funded research project that examined novel techniques that would enable the transition between today's and 2050's highly uncertain and complex energy network. Being part of the APS, this thesis reports on the sub-project 'RR2: Avoiding High-Impact Low Probability events'. The goal of RR2 is to develop new algorithms for controlling risk exposure to high-impact low probability (Hi-Lo) events through the provision of appropriate risk-sensitive control strategies. Additionally, RR2 is concerned with new techniques for identifying and modelling risk in future energy networks, in particular, the risk of Hi-Lo events. In this context, this thesis investigates two distinct problems arising from energy risk management. On the one hand, we examine the problem of finding managerial strategies for exercising the operational flexibility of energy assets. We look at this problem from a risk perspective taking into account non-linear risk preferences of energy asset managers. Our main contribution is the development of a risk-sensitive approach to the class of optimal switching problems. By recasting the problem as an iterative optimal stopping problem, we are able to characterise the optimal risk-sensitive switching strategies. As byproduct, we obtain a multiplicative dynamic programming equation for the value function, upon which we propose a numerical algorithm based on least squares Monte Carlo regression. On the other hand, we develop tools to identify and model the risk factors faced by energy asset managers. For this, we consider a class of models consisting of superposition of Gaussian and non-Gaussian Ornstein-Uhlenbeck processes. Our main contribution is the development of a Bayesian methodology based on Markov chain Monte Carlo (MCMC) algorithms to make inference into this class of models. On extensive simulations, we demonstrate the robustness and efficiency of the algorithms to different data features. Furthermore, we construct a diagnostic tool based on Bayesian p-values to check goodness-of-fit of the models on a Bayesian framework. We apply this tool to MCMC results from fitting historical electricity and gas spot price data- sets corresponding to the UK and German energy markets. Our analysis demonstrates that the MCMC-estimated models are able to capture not only long- and short-lived positive price spikes, but also short-lived negative price spikes which are typical of UK gas prices and German electricity prices. Combining together the solutions to the two problems above, we strive to capture the interplay between risk, uncertainty, flexibility and performance in various applications to energy systems. In these applications, which include power stations, energy storage and district energy systems, we consistently show that our risk management methodology offers a tradeoff between maximising average performance and minimising risk, while accounting for the jump dynamics of energy prices. Moreover, the tradeoff is achieved in such way that the benefits in terms of risk reduction outweigh the loss in average performance.
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Alata, Olivier. "Contributions à la description de signaux, d'images et de volumes par l'approche probabiliste et statistique." Habilitation à diriger des recherches, Université de Poitiers, 2010. http://tel.archives-ouvertes.fr/tel-00573224.
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Les éléments principaux apparaissant dans ce document de synthèse sont les suivants : - La mise en exergue de la pertinence du critère d'information $\phi_\beta$ qui offre la possibilité d'être ``réglé'' par apprentissage de $\beta$ et cela quelque soit le problème de sélection de modèles pour lequel il est possible d'écrire un critère d'information, possibilité qui a été illustrée dans divers contextes applicatifs (supports de prédiction linéaire et dimension du modèle utilisé pour les cinétiques de $\dot VO_2$). - Une méthode d'estimation d'histogrammes pour décrire de manière non-paramé-trique la distribution d'échantillons et son utilisation en reconnaissance de lois supervisée dans un contexte de canaux de transmission. \item Une méthode dite ``comparative descendante'' permettant de trouver la meilleure combinaison des paramètres pour décrire les données étudiées sans avoir à tester toutes les combinaisons, illustrée sur l'obtention de supports de prédiction linéaire 1-d et 2-d. - La mise en place de stratégies de choix de modèles par rapport à des contextes variés comme l'imagerie TEP et les lois de mélange de Gauss et de Poisson ou les espaces couleur et les lois de mélange gaussiennes multidimensionnelles. - L'exploration des modèles de prédiction linéaire vectorielle complexe sur les images représentées dans des espaces couleur séparant l'intensité lumineuse de la partie chromatique et l'usage qui peut en être fait en caractérisation de textures afin de les classifier ou de segmenter les images texturées couleur. \item Des apports en segmentation : optimisation d'une méthode de segmentation non-supervisée d'images texturées en niveaux de gris ; une nouvelle méthode supervisée de segmentation d'images texturées couleur exploitant les espaces couleur psychovisuels et les erreurs de prédiction linéaire vectorielle complexe ; prise en compte dans des distributions de Gibbs d'informations géométriques et topologiques sur le champ des régions afin de réaliser de la segmentation 3-d ``haut-niveau'' exploitant le formalisme des processus ponctuels. - L'illustration des méthodes MCMC dans des contextes divers comme l'estimation de paramètres, l'obtention de segmentations 2-d ou 3-d ou la simulation de processus. Et beaucoup d'autres éléments se révèleront à sa lecture ...
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Grenon-Godbout, Nicolas. "Partition adaptative de l’espace dans un algorithme MCMC avec adaptation régionale." Thèse, 2018. http://hdl.handle.net/1866/21288.
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Holotňáková, Dominika. "Pokročilé metody kalibrace modelů úrokových sazeb." Master's thesis, 2013. http://www.nusl.cz/ntk/nusl-321342.
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This thesis is focused on the study of advanced methods of interest rate mo- dels calibration. The theoretical part provides introduction to basic terminology of financial mathematics, financial, concretely interest rate derivatives. It presents interest rate models, it is mainly aimed at HJM approach and describes in detail the Libor market model, then introduces the use of Bayesian principle in calcula- ting the probability of MCMC methods. At the end of this section the methods of calibration of volatility to market data are described. The last chapter consists of the practical application of different methods of calibration Libor market model and consequently pricing od interest rate swaption. The introduction describes procedure of arrangement of input data and process of pricing of interest rate derivatives. It is consequently used for the valuation of derivative contract accor- ding to mentioned methods. 1
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CHEN, CHIN-YU, and 陳金佑. "A COMPARATIVE ANALYSIS OF EM AND MCMC ALGORITHMS FOR MULTI–SOURCE INCOMPLETE TIME SERIES DATA." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/87035082898519417862.
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碩士<br>國立臺北大學<br>統計學系<br>96<br>Incomplete data are pervasive in scientific investigations and can occur for a variety of reasons. Moreover, data from different sources may not be consistent. This thesis aims to deal with the multi-source incomplete time series problems under a state-space model. Two methods, EM algorithm and Markov Chain Monte Carlo (MCMC) algorithms are used and compared to merge multiple sources incomplete time series data into a complete time series data. EM algorithm is used in conjunction with the conventional Kalman smoothed estimators to derive a simple recursive procedure for estimating the parameters by maximum likelihood method, while MCMC algorithm is associated with Gibbs Sampling and Metropolis-Hastings algorithm to perform a Bayesian analysis for estimating parameters. A Monte Carlo simulation is used to compare estimation performance of the two methods for multi-source time series with missing data. The simulation results show that EM algorithm has a better estimation performance.
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Neves, Bruno Miguel Bandarra das. "Desenvolvimento das técnicas de análise de espectros 3D de MCC-IMS." Master's thesis, 2013. http://hdl.handle.net/10362/18335.
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Recentemente, a técnica de Espectrometria de Mobilidade Iónica associada a uma coluna multicapilar (MCC-IMS) tem sido aplicada à análise do ar exalado dos seres humanos. O ar que é expelido na respiração contém compostos orgânicos voláteis (VOCs) que possuem informação importante relativa ao estado metabólico do sujeito. Existem inúmeras vantagens na utilização desta tecnologia relativamente às técnicas de rastreio através do sangue, designadamente o facto de ser um processo não doloroso, não invasivo e a recolha de amostras não necessita de ser efectuada por pessoal médico especializado. Esta técnica está a ser desenvolvida com progressos no diagnóstico precoce do cancro do pulmão (entre outros) ou da doença pulmonar obstrutiva crónica (DPOC), e também para controlo da medicação ou na fase terapêutica. Esta técnica é utilizada para detetar analitos em matrizes voláteis através da sua mobilidade iónica e combina alta sensibilidade através de um limite de deteção da ordem dos baixos ppbv [ng/L], com baixos custos de manutenção.
O principal objectivo do trabalho desenvolvido nesta dissertação foi a projecção e implementação de uma interface gráfica que permita a detecção automática dos picos presentes nos espectros 3D de MCC-IMS. Para esta finalidade foi implementado um algoritmo que permite obter a informação acerca da posição e intensidade dos máximos de cada pico. A identificação automática de compostos relativos a cada pico detectado foi igualmente implementada através da ligação à base de dados existente, passível de ser aumentada no decorrer das medições experimentais. Além disso, foi desenvolvida uma ferramenta que permite eliminar influências da matriz, seja do ar ambiente, do sistema ou outro, por meio da subtracção dos espectros de background aos espectros experimentais.
A interface desenvolvida foi testada para diferentes medições experimentais de aquisição dos espectros de ar exalado com a tecnologia de MCC-IMS e os resultados obtidos foram apresentados como comunicação científica de painel na Conferência iMed 4.0 em 2012 na FCM-UNL e na Conferência Internacional Breath Analysis Summit, na Alemanha em Junho de 2013.
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(9158723), Supriyo Maji. "Efficient Minimum Cycle Mean Algorithms And Their Applications." Thesis, 2020.
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<p>Minimum cycle mean (MCM) is an important concept in directed graphs. From clock period optimization, timing analysis to layout optimization, minimum cycle mean algorithms have found widespread use in VLSI system design optimization. With transistor size scaling to 10nm and below, complexities and size of the systems have grown rapidly over the last decade. Scalability of the algorithms both in terms of their runtime and memory usage is therefore important. </p>
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<p>Among the few classical MCM algorithms, the algorithm by Young, Tarjan, and Orlin (YTO), has been particularly popular. When implemented with a binary heap, the YTO algorithm has the best runtime performance although it has higher asymptotic time complexity than Karp's algorithm. However, as an efficient implementation of YTO relies on data redundancy, its memory usage is higher and could be a prohibitive factor in large size problems. On the other hand, a typical implementation of Karp's algorithm can also be memory hungry. An early termination technique from Hartmann and Orlin (HO) can be directly applied to Karp's algorithm to improve its runtime performance and memory usage. Although not as efficient as YTO in runtime, HO algorithm has much less memory usage than YTO. We propose several improvements to HO algorithm. The proposed algorithm has comparable runtime performance to YTO for circuit graphs and dense random graphs while being better than HO algorithm in memory usage. </p>
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<p>Minimum balancing of a directed graph is an application of the minimum cycle mean algorithm. Minimum balance algorithms have been used to optimally distribute slack for mitigating process variation induced timing violation issues in clock network. In a conventional minimum balance algorithm, the principal subroutine is that of finding MCM in a graph. In particular, the minimum balance algorithm iteratively finds the minimum cycle mean and the corresponding minimum-mean cycle, and uses the mean and cycle to update the graph by changing edge weights and reducing the graph size. The iterations terminate when the updated graph is a single node. Studies have shown that the bottleneck of the iterative process is the graph update operation as previous approaches involved updating the entire graph. We propose an improvement to the minimum balance algorithm by performing fewer changes to the edge weights in each iteration, resulting in better efficiency.</p>
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<p>We also apply the minimum cycle mean algorithm in latency insensitive system design. Timing violations can occur in high performance communication links in system-on-chips (SoCs) in the late stages of the physical design process. To address the issues, latency insensitive systems (LISs) employ pipelining in the communication channels through insertion of the relay stations. Although the functionality of a LIS is robust with respect to the communication latencies, such insertion can degrade system throughput performance. Earlier studies have shown that the proper sizing of buffer queues after relay station insertion could eliminate such performance loss. However, solving the problem of maximum performance buffer queue sizing requires use of mixed integer linear programming (MILP) of which runtime is not scalable. We formulate the problem as a parameterized graph optimization problem where for every communication channel there is a parameterized edge with buffer counts as the edge weight. We then use minimum cycle mean algorithm to determine from which edges buffers can be removed safely without creating negative cycles. This is done iteratively in the similar style as the minimum balance algorithm. Experimental results suggest that the proposed approach is scalable. Moreover, quality of the solution is observed to be as good as that of the MILP based approach.</p><p><br></p>
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Jung, Maarten Lars. "Reaction Time Modeling in Bayesian Cognitive Models of Sequential Decision-Making Using Markov Chain Monte Carlo Sampling." 2020. https://tud.qucosa.de/id/qucosa%3A74048.
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In this thesis, a new approach for generating reaction time predictions for Bayesian cognitive models of sequential decision-making is proposed. The method is based on a Markov chain Monte Carlo algorithm that, by utilizing prior distributions and likelihood functions of possible action sequences, generates predictions about the time needed to choose one of these sequences. The plausibility of the reaction time predictions produced by this algorithm was investigated for simple exemplary distributions as well as for prior distributions and likelihood functions of a Bayesian model of habit learning. Simulations showed that the reaction time distributions generated by the Markov chain Monte Carlo sampler exhibit key characteristics of reaction time distributions typically observed in decision-making tasks. The introduced method can be easily applied to various Bayesian models for decision-making tasks with any number of choice alternatives. It thus provides the means to derive reaction time predictions for models where this has not been possible before.<br>In dieser Arbeit wird ein neuer Ansatz zum Generieren von Reaktionszeitvorhersagen für bayesianische Modelle sequenzieller Entscheidungsprozesse vorgestellt. Der Ansatz basiert auf einem Markov-Chain-Monte-Carlo-Algorithmus, der anhand von gegebenen A-priori-Verteilungen und Likelihood-Funktionen von möglichen Handlungssequenzen Vorhersagen über die Dauer einer Entscheidung für eine dieser Handlungssequenzen erstellt. Die Plausibilität der mit diesem Algorithmus generierten Reaktionszeitvorhersagen wurde für einfache Beispielverteilungen sowie für A-priori-Verteilungen und Likelihood-Funktionen eines bayesianischen Modells zur Beschreibung von Gewohnheitslernen untersucht. Simulationen zeigten, dass die vom Markov-Chain-Monte-Carlo-Sampler erzeugten Reaktionszeitverteilungen charakteristische Eigenschaften von typischen Reaktionszeitverteilungen im Kontext sequenzieller Entscheidungsprozesse aufweisen. Das Verfahren lässt sich problemlos auf verschiedene bayesianische Modelle für Entscheidungsparadigmen mit beliebig vielen Handlungsalternativen anwenden und eröffnet damit die Möglichkeit, Reaktionszeitvorhersagen für Modelle abzuleiten, für die dies bislang nicht möglich war.
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Bégin, Jean-François. "New simulation schemes for the Heston model." Thèse, 2012. http://hdl.handle.net/1866/8752.
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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.<br>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.