Η παρούσα εργασία διαπραγματεύεται την επεξεργασία ετήσιων και εποχικών χρονοσειρών βροχόπτωσης από 12 σταθμούς της Δυτικής Ελλάδας για την περίοδο 1975-2004. Επιπλέον για τους 8 από τους συνολικά 12 σταθμούς όπου υπήρχε η δυνατότητα, η επεξεργασία αφορά μια περίοδο 50 ετών (1956-2005). Χρησιμοποιώντας ως κλιματικό δείκτη το ετήσιο βροχομετρικό ύψος προκύπτει ότι το σύνολο των 12 σταθμών χαρακτηρίζεται εν γένει από έναν συνδυασμό ημίυγρου ή υγρού κλιματικού τύπου. Χρησιμοποιώντας τον μη-παραμετρικό έλεγχο των Mann-Kendall για την εξακρίβωση παρουσίας τάσεων σε βάθος χρόνου, για την περίοδο 1975-2004 δεν διαφαίνεται η ύπαρξη κάποιας σημαντικής τάσης εκτός από τις ετήσιες βροχοπτώσεις του Πύργου που εμφανίζουν μία σημαντικά αρνητική τάση. Την περίοδο από το 1956-2005 προκύπτουν σημαντικά αρνητικές τάσεις τόσο σε εποχική βάση (κυρίως την άνοιξη) όσο και σε ετήσια για τους μισούς από τους οκτώ σταθμούς που εξετάστηκαν. Η Γάμμα κατανομή είναι εκείνη που περιγράφει καλύτερα το φυσικό μέγεθος ύψος βροχόπτωσης και στην περίπτωση μας προσδιορίζονται ανά σταθμό και για την περίοδο 1975-2004 (σε εποχική και ετήσια βάση), οι παράμετροι της με την βοήθεια της μεθόδου μέγιστης πιθανοφάνειας. Στα πλαίσια της φασματικής ανάλυσης, για να εξακριβωθεί η ύπαρξη ή οχι περιοδικότητας στην τιμή της διασποράς των εποχικών και ετήσιων τιμών βροχόπτωσης χρησιμοποιούνται οι 7 σταθμοί για τους οποίους υπάρχει επάρκεια μετρήσεων με εξεταζόμενη περίοδο την πεντηκονταετία 1955-2004 και κάνοντας χρήση της μεθόδου Blackman-Tukey. Προκύπτει με την εν λόγω μέθοδο ότι κατά την διάρκεια του φθινοπώρου και της άνοιξης δεν διαφαίνονται κάποια σαφή στοιχεία περιοδικότητας στην διασπορά των υψών υετού των 7 σταθμών. Αυτό δεν ισχύει όμως για τον χειμώνα αλλά και σε ετήσια βάση, όπου στα φάσματα των τιμών υετού των σταθμών αποκαλύπτονται τρεις περιοχές συχνοτήτων περιοδικότητας που μοιάζουν αρκετά μεταξύ τους. Αυτό αντανακλά το γεγονός ότι σε γενικές γραμμές οι σταθμοί της Δυτικής Ελλάδας επηρεάζονται από τα ίδια περιπου βαρομετρικά συστήματα και άρα είναι φυσιολογικό να εμφανίζουν παρόμοιες συνιστώσες περιοδικότητας στις διασπορές των τιμών υετού τους. / This work deals with the processing of annual and seasonal precipitation series from 12 stations of West Greece for a 30-year study period (1975-2004). Moreover for 8 out for τηε 12 stations where possible, the processing uses a 50-year study period (1956-2005). By using the annual precipitation height as an climatic index it follows that the total of the twelve stations is characterized generally by a combination of semi-wet and wet climatic type. Making use of nonparametric Mann-Kendall test for ascertaining the existence of trend, it doesn't follow any significant trend for the 30-year period (1975-2004), with the exception of the annual precipitation heights of Pirgos that show a significant negative trend. During the 50-year period (1956-2005) significant negative trends occur in seasonal (mainly during spring) and annual basis as well, for half of the eight stations which have been examined. Gamma distribution is tha type of statistical distribution that describes more effectively the physical quantity precipitation height, and in our case its parameters per station are being computed for the period 1975-2004, by using the maximum likelihood method. Under the framework of a Spectral analysis of the precipitation series (for the verification of periodicity in the variances of precipitation rates) , 7 stations are used for a 50-year study period (1955-2004) by using the Blackman-Tukey method. It follows after this method has been used, that precipitation series don't appear any periodicity during autumn and spring seasons. This is in contrast with the winter season and the annual rainfall values as well, where three parts of periodicity in the spectra of the stations appear that bear a common resemblance. This depicts the fact that genarally the total of West Greece stations are influenced by almost the same barometric pressure systems which leads to the variances of precipitation rates to appear common periodicity components.

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

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

Dans cette thèse, nous développons des modèles et des méthodes statistiques pour le traitement d’images de microscopie confocale de la peau dans le but de détecter une maladie de la peau appelée lentigo. Une première contribution consiste à proposer un modèle statistique paramétrique pour représenter la texture dans le domaine des ondelettes. Plus précisément, il s’agit d’une distribution gaussienne généralisée dont on montre que le paramètre d’échelle est caractéristique des tissus sousjacents. La modélisation des données dans le domaine de l’image est un autre sujet traité dans cette thèse. A cette fin, une distribution gamma généralisée est proposée. Notre deuxième contribution consiste alors à développer un estimateur efficace des paramètres de cette loi à l’aide d’une descente de gradient naturel. Finalement, un modèle d’observation de bruit multiplicatif est établi pour expliquer la distribution gamma généralisée des données. Des méthodes d’inférence bayésienne paramétrique sont ensuite développées avec ce modèle pour permettre la classification d’images saines et présentant un lentigo. Les algorithmes développés sont appliqués à des images réelles obtenues d’une étude clinique dermatologique. / In this work, we develop statistical models and processing methods for confocal microscopy images. The first contribution consists of a parametric statistical model to represent textures in the wavelet domain. Precisely, a generalized Gaussian distribution is proposed, whose scale parameter is shown to be discriminant of the underlying tissues. The thesis deals also with modeling data in the image domain using the generalized gamma distribution. The second contribution develops an efficient parameter estimator for this distribution based on a natural gradient approach. The third contribution establishes a multiplicative noise observation model to explain the distribution of the data. Parametric Bayesian inference methods are subsequently developed based on this model to classify healthy and lentigo images. All algorithms developed in this thesis have been applied to real images from a dermatologic clinical study.

Made available in DSpace on 2016-06-02T20:06:04Z (GMT). No. of bitstreams: 1 3603.pdf: 602959 bytes, checksum: 3078931e73ff3d01b4122cbac2c7f0a0 (MD5) Previous issue date: 2011-03-24 / Financiadora de Estudos e Projetos / In this work, the aim was to analyze in the classic and bayesian context, the GARMA model with three different continuous distributions: Gaussian, Inverse Gaussian and Gamma. We analyzed the performance and the goodness of fit of the three models, as well as the performance of the coverage percentile. In the classic analyze we consider the maximum likelihood estimator and by simulation study, we verified the consistency, the bias and de mean square error of the models. To the bayesian approach we proposed a non-informative prior distribution for the parameters of the model, resulting in a posterior distribution, which we found the bayesian estimatives for the parameters. This study still was not found in the literature. So, we can observe that the bayesian inference showed a good quality in the analysis of the serie, which can be comprove with the last section of this work. This, consist in the analyze of a real data set corresponding in the rate of tuberculosis cases in metropolitan area of Sao Paulo. The results show that, either the classical and bayesian approach, are good alternatives to describe the behavior of the real time serie. / Neste trabalho, o objetivo foi analisar no contexto clássico e bayesiano, o modelo GARMA com três distribuições contínuas: Gaussiana (Normal), Inversa Gaussiana e Gama, e também o desempenho e a qualidade do ajuste dos modelos de interesse, bem como o desempenho dos percentis de cobertura para eles. Para o estudo clássico foi considerado os estimadores de máxima verossimilhança e por meio de simulação verificou-se a consistência, o viés e o erro quadrático médio dos mesmos. Para a abordagem bayesiana é proposta uma distribuição a priori não informativa para os parâmetros dos modelos resultando em uma distribuição a posteriori, o qual a partir daí pode-se encontrar as estimativas bayesianas para os parâmetros, sendo que este estudo ainda não foi encontrado na literatura. Com isso pode-se observar que a inferência bayesiana mostrou boa eficiência no processo de análise da série, o que pode ser comprovado também com a última etapa do trabalho. Esta, consiste na análise de um conjunto de dados reais correspondente a taxa de casos de tuberculose na região metropolitana de São Paulo. Os resultados mostram que, tanto o estudo clássico quanto o bayesiano, são capazes de descrever bem o comportamento da série.

In this work, we study the so-called combined models, generalized linear mixed models with extension to allow for overdispersion, in the context of genetics and breeding. Such flexible models accommodates cluster-induced correlation and overdispersion through two separate sets of random effects and contain as special cases the generalized linear mixed models (GLMM) on the one hand, and commonly known overdispersion models on the other. We use such models while obtaining heritability coefficients for non-Gaussian characters. Heritability is one of the many important concepts that are often quantified upon fitting a model to hierarchical data. It is often of importance in plant and animal breeding. Knowledge of this attribute is useful to quantify the magnitude of improvement in the population. For data where linear models can be used, this attribute is conveniently defined as a ratio of variance components. Matters are less simple for non-Gaussian outcomes. The focus is on time-to-event and count traits, where the Weibull-Gamma-Normal and Poisson-Gamma-Normal models are used. The resulting expressions are sufficiently simple and appealing, in particular in special cases, to be of practical value. The proposed methodologies are illustrated using data from animal and plant breeding. Furthermore, attention is given to the occurrence of negative estimates of variance components in the Poisson-Gamma-Normal model. The occurrence of negative variance components in linear mixed models (LMM) has received a certain amount of attention in the literature whereas almost no work has been done for GLMM. This phenomenon can be confusing at first sight because, by definition, variances themselves are non-negative quantities. However, this is a well understood phenomenon in the context of linear mixed modeling, where one will have to make a choice between a hierarchical and a marginal view. The variance components of the combined model for count outcomes are studied theoretically and the plant breeding study used as illustration underscores that this phenomenon can be common in applied research. We also call attention to the performance of different estimation methods, because not all available methods are capable of extending the parameter space of the variance components. Then, when there is a need for inference on such components and they are expected to be negative, the accuracy of the method is not the only characteristic to be considered. / Neste trabalho foram estudados os chamados modelos combinados, modelos lineares generalizados mistos com extensão para acomodar superdispersão, no contexto de genética e melhoramento. Esses modelos flexíveis acomodam correlação induzida por agrupamento e superdispersão por meio de dois conjuntos separados de efeitos aleatórios e contem como casos especiais os modelos lineares generalizados mistos (MLGM) e os modelos de superdispersão comumente conhecidos. Tais modelos são usados na obtenção do coeficiente de herdabilidade para caracteres não Gaussianos. Herdabilidade é um dos vários importantes conceitos que são frequentemente quantificados com o ajuste de um modelo a dados hierárquicos. Ela é usualmente importante no melhoramento vegetal e animal. Conhecer esse atributo é útil para quantificar a magnitude do ganho na população. Para dados em que modelos lineares podem ser usados, esse atributo é convenientemente definido como uma razão de componentes de variância. Os problemas são menos simples para respostas não Gaussianas. O foco aqui é em características do tipo tempo-até-evento e contagem, em que os modelosWeibull-Gama-Normal e Poisson-Gama-Normal são usados. As expressões resultantes são suficientemente simples e atrativas, em particular nos casos especiais, pelo valor prático. As metodologias propostas são ilustradas usando dados de melhoramento animal e vegetal. Além disso, a atenção é voltada à ocorrência de estimativas negativas de componentes de variância no modelo Poisson-Gama- Normal. A ocorrência de componentes de variância negativos em modelos lineares mistos (MLM) tem recebido certa atenção na literatura enquanto quase nenhum trabalho tem sido feito para MLGM. Esse fenômeno pode ser confuso a princípio porque, por definição, variâncias são quantidades não-negativas. Entretanto, este é um fenômeno bem compreendido no contexto de modelagem linear mista, em que a escolha deverá ser feita entre uma interpretação hierárquica ou marginal. Os componentes de variância do modelo combinado para respostas de contagem são estudados teoricamente e o estudo de melhoramento vegetal usado como ilustração confirma que esse fenômeno pode ser comum em pesquisas aplicadas. A atenção também é voltada ao desempenho de diferentes métodos de estimação, porque nem todos aqueles disponíveis são capazes de estender o espaço paramétrico dos componentes de variância. Então, quando há a necessidade de inferência de tais componentes e é esperado que eles sejam negativos, a acurácia do método de estimação não é a única característica a ser considerada.

This thesis proposes and discusses a statistical model for interpreting forensic DNA mixtures. We develop methods for estimation of model parameters and assessing the uncertainty of the estimated quantities. Further, we discuss how to interpret the mixture in terms of predicting the set of contributors. We emphasise the importance of challenging any interpretation of a particular mixture, and for this purpose we develop a set of diagnostic tools that can be used in assessing the adequacy of the model to the data at hand as well as in a systematic validation of the model on experimental data. An important feature of this work is that all methodology is developed entirely within the framework of the adopted model, ensuring a transparent and consistent analysis. To overcome the challenge that lies in handling the large state space for DNA profiles, we propose a representation of a genotype that exhibits a Markov structure. Further, we develop methods for efficient and exact computation in a Bayesian network. An implementation of the model and methodology is available through the R package DNAmixtures.

The dissertation consists of four self-contained essays on consumption. Essays 1 and 2 consider different measures of aggregate consumption, and Essays 3 and 4 consider how the distributions of income and wealth affect consumption from a macro and micro perspective, respectively. Essay 1 considers the empirical practice of seemingly interchangeable use of two measures of consumption; total consumption expenditure and consumption expenditure on nondurable goods and services. Using data from Sweden and the US in an error correction model, it is shown that consumption functions based on the two measures exhibit significant differences in several aspects of econometric modelling. Essay 2, coauthored with Thomas Holgersson, considers derivation of a univariate and a multivariate version of a test for asymmetry, based on the third central moment. The logic behind the test is that the dependent variable should correspond to the specification of the econometric model; symmetric with linear models and asymmetric with non-linear models. The main result in the empirical application of the test is that orthodox theory seems to be supported for consumption of both nondurable and durable consumption. The consumption of durables shows little deviation from symmetry in the four-country sample, while the consumption of nondurables is shown to be asymmetric in two out of four cases, the UK and the US. Essay 3 departs from the observation that introducing income uncertainty makes the consumption function concave, implying that the distributions of wealth and income are omitted variables in aggregate Euler equations. This implication is tested through estimation of the distributions over time and augmentation of consumption functions, using Swedish data for 1963-2000. The results show that only the dispersion of wealth is significant, the explanation of which is found in the marked changes of the group of households with negative wealth; a group that according to a concave consumption function has the highest marginal propensity to consume. Essay 4 attempts to empirically specify the nature of the alleged concavity of the consumption function. Using grouped household level Swedish data for 1999-2001, it is shown that the marginal propensity to consume out of current resources, i.e. current income and net wealth, is strictly decreasing in current resources and net wealth, but approximately constant in income. Also, an empirical reciprocal to the stylized theoretical consumption function is estimated, and shown to bear a close resemblance to the theoretical version.

This thesis is divided into three main parts. In the first, we discuss that, although permutation tests can provide exact control of false positives under the reasonable assumption of exchangeability, there are common examples in which global exchangeability does not hold, such as in experiments with repeated measurements or tests in which subjects are related to each other. To allow permutation inference in such cases, we propose an extension of the well known concept of exchangeability blocks, allowing these to be nested in a hierarchical, multi-level definition. This definition allows permutations that retain the original joint distribution unaltered, thus preserving exchangeability. The null hypothesis is tested using only a subset of all otherwise possible permutations. We do not need to explicitly model the degree of dependence between observations; rather the use of such permutation scheme leaves any dependence intact. The strategy is compatible with heteroscedasticity and can be used with permutations, sign flippings, or both combined. In the second part, we exploit properties of test statistics to obtain accelerations irrespective of generic software or hardware improvements. We compare six different approaches using synthetic and real data, assessing the methods in terms of their error rates, power, agreement with a reference result, and the risk of taking a different decision regarding the rejection of the null hypotheses (known as the resampling risk). In the third part, we investigate and compare the different methods for assessment of cortical volume and area from magnetic resonance images using surface-based methods. Using data from young adults born with very low birth weight and coetaneous controls, we show that instead of volume, the permutation-based non-parametric combination (NPC) of thickness and area is a more sensitive option for studying joint effects on these two quantities, giving equal weight to variation in both, and allowing a better characterisation of biological processes that can affect brain morphology.

Submitted by Fabio Sobreira Campos da Costa (fabio.sobreira@ufpe.br) on 2017-04-25T14:46:06Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) TESE VERSÃO FINAL (CD).pdf: 688894 bytes, checksum: fc5c0291423dc50d4989c1c2d8d4af65 (MD5) / Made available in DSpace on 2017-04-25T14:46:06Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) TESE VERSÃO FINAL (CD).pdf: 688894 bytes, checksum: fc5c0291423dc50d4989c1c2d8d4af65 (MD5) Previous issue date: 2016-11-04 / Young e Bakir (1987) propôs a classe de Modelos Lineares Log-Gama Generalizados (MLLGG) para analisar dados de sobrevivência. No nosso trabalho, estendemos a classe de modelos propostapor Young e Bakir (1987) permitindo uma estrutura não linear para os parâmetros de regressão. A nova classe de modelos é denominada como Modelos Não Lineares Log-Gama Generalizados (MNLLGG). Com o objetivo de obter a correção de viés de segunda ordem dos estimadores de máxima verossimilhança (EMV) na classe dos MNLLGG, desenvolvemos uma expressão matricial fechada para o estimador de viés de Cox e Snell (1968). Analisamos, via simulação de Monte Carlo, os desempenhos dos EMV e suas versões corrigidas via Cox e Snell (1968) e através da metodologia bootstrap (Efron, 1979). Propomos também resíduos e técnicas de diagnóstico para os MNLLGG, tais como: alavancagem generalizada, influência local e influência global. Obtivemos, em forma matricial, uma expressão para o fator de correção de Bartlett à estatística da razão de verossimilhanças nesta classe de modelos e desenvolvemos estudos de simulação para avaliar e comparar numericamente o desempenho dos testes da razão de verossimilhanças e suas versões corrigidas em relação ao tamanho e poder em amostras finitas. Além disso, derivamos expressões matriciais para os fatores de correção tipo-Bartlett às estatísticas escore e gradiente. Estudos de simulação foram feitos para avaliar o desempenho dos testes escore, gradiente e suas versões corrigidas no que tange ao tamanho e poder em amostras finitas. / Young e Bakir (1987) proposed the class of generalized log-gamma linear regression models (GLGLM) to analyze survival data. In our work, we extended the class of models proposed by Young e Bakir (1987) considering a nonlinear structure for the regression parameters. The new class of models is called generalized log-gamma nonlinear regression models (GLGNLM). We also propose matrix formula for the second-order bias of the maximum likelihood estimate of the regression parameter vector in the GLGNLM class. We use the results by Cox and Snell (1968) and bootstrap technique [Efron (1979)] to obtain the bias-corrected maximum likelihood estimate. Residuals and diagnostic techniques were proposed for the GLGNLM, such as generalized leverage, local and global influence. An general matrix notation was obtained for the Bartlett correction factor to the likelihood ratio statistic in this class of models. Simulation studies were developed to evaluate and compare numerically the performance of likelihood ratio tests and their corrected versions regarding size and power in finite samples. Furthermore, general matrix expressions were obtained for the Bartlett-type correction factor for the score and gradient statistics. Simulation studies were conducted to evaluate the performance of the score and gradient tests with their corrected versions regarding to the size and power in finite samples.