Orientador: Caio Lucidius Naberezny Azevedo / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-24T12:51:18Z (GMT). No. of bitstreams: 1 Ferreira_EduardoVargas_M.pdf: 8131052 bytes, checksum: f344cd1f11e8d818f3aac90f48396cbc (MD5) Previous issue date: 2014 / 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 / 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. / Mestrado / Estatistica / Mestre em Estatística

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. / 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.

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

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. / 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.

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. / 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.

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. / 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.

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.