O presente trabalho tem por finalidade o uso da abordagem bayesiana para a estimativa de parâmetros sazonais dos modelos periódicos auto-regressivos (PAR). Após a determinação dos estimadores bayesianos, estes são comparados com os estimadores de máxima verossimilhança. A previsão para 12 meses é realizada usando os dois estimadores e os resultados comparados por meio de gráficos, tabelas e pelos erros de previsão. Para ilustrar o problema as séries escolhidas foram as séries hidrológicas da Usinas Hidroelétricas de Furnas e Emborcação. Tais séries foram selecionadas tendo em vista a necessidade de previsões com reduzido erro já que o sistema de operação das usinas hidroelétricas depende muito da quantidade de água existente em seus reservatórios e de planejamento e gerenciamento eficazes. / The objective of this research is to use bayesian method to estimate of sazonal parameters of periodic autoregressive models (PAR). The bayesian estimators are then compared with maximum likelihood estimators. The forecast for 12 months is made by using two estimators and comparing their results though graphs, tables and forecast error. The hydrological time series chosen were from Furnas and Emborcação Hydroeletric Power Plant. These series were chosen having in mind the necessity of series with reduced error in their forecast because system of operation in the Hydroeletric Power Plant depends on the quantity of the water in their resevoirs, eficient planning and management.

O presente trabalho tem por finalidade o uso da abordagem bayesiana para a estimativa de parâmetros sazonais dos modelos periódicos auto-regressivos (PAR). Após a determinação dos estimadores bayesianos, estes são comparados com os estimadores de máxima verossimilhança. A previsão para 12 meses é realizada usando os dois estimadores e os resultados comparados por meio de gráficos, tabelas e pelos erros de previsão. Para ilustrar o problema as séries escolhidas foram as séries hidrológicas da Usinas Hidroelétricas de Furnas e Emborcação. Tais séries foram selecionadas tendo em vista a necessidade de previsões com reduzido erro já que o sistema de operação das usinas hidroelétricas depende muito da quantidade de água existente em seus reservatórios e de planejamento e gerenciamento eficazes. / The objective of this research is to use bayesian method to estimate of sazonal parameters of periodic autoregressive models (PAR). The bayesian estimators are then compared with maximum likelihood estimators. The forecast for 12 months is made by using two estimators and comparing their results though graphs, tables and forecast error. The hydrological time series chosen were from Furnas and Emborcação Hydroeletric Power Plant. These series were chosen having in mind the necessity of series with reduced error in their forecast because system of operation in the Hydroeletric Power Plant depends on the quantity of the water in their resevoirs, eficient planning and management.

The log-normal distribution is a popular model in many areas, especially in biostatistics and survival analysis where the data tend to be right skewed. In our research, a total of ten different estimators of log-normal means are compared theoretically. Simulations are done using different values of parameters and sample size. As a result of comparison, ``A degree of freedom adjusted" maximum likelihood estimator and Bayesian estimator under quadratic loss are the best when using the mean square error (MSE) as a criterion. The ten estimators are applied to a real dataset, an environmental study from Naval Construction Battalion Center (NCBC), Super Fund Site in Rhode Island.

Inverse problems have gained popularity in statistical research recently. This dissertation consists of two statistical inverse problems: a Bayesian approach to detection of small low emission sources on a large random background, and parameter estimation methods for partial differential equation (PDE) models. Source detection problem arises, for instance, in some homeland security applications. We address the problem of detecting presence and location of a small low emission source inside an object, when the background noise dominates. The goal is to reach the signal-to-noise ratio levels on the order of 10^-3. We develop a Bayesian approach to this problem in two-dimension. The method allows inference not only about the existence of the source, but also about its location. We derive Bayes factors for model selection and estimation of location based on Markov chain Monte Carlo simulation. A simulation study shows that with sufficiently high total emission level, our method can effectively locate the source. Differential equation (DE) models are widely used to model dynamic processes in many fields. The forward problem of solving equations for given parameters that define the DEs has been extensively studied in the past. However, the inverse problem of estimating parameters based on observed state variables is relatively sparse in the statistical literature, and this is especially the case for PDE models. We propose two joint modeling schemes to solve for constant parameters in PDEs: a parameter cascading method and a Bayesian treatment. In both methods, the unknown functions are expressed via basis function expansion. For the parameter cascading method, we develop the algorithm to estimate the parameters and derive a sandwich estimator of the covariance matrix. For the Bayesian method, we develop the joint model for data and the PDE, and describe how the Markov chain Monte Carlo technique is employed to make posterior inference. A straightforward two-stage method is to first fit the data and then to estimate parameters by the least square principle. The three approaches are illustrated using simulated examples and compared via simulation studies. Simulation results show that the proposed methods outperform the two-stage method.

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This thesis presents simple efficient algorithms to estimate distribution parameters and to construct prediction intervals for location-scale families. Specifically, we study two scenarios: one is a frequentist method for a general location--scale family and then extend to a 3-parameter distribution, another is a Bayesian method for the Gumbel distribution. At the end of the thesis, a generalized bootstrap resampling scheme is proposed to construct prediction intervals for data with an unknown distribution. Our estimator construction begins with the equivariance principle, and then makes use of unbiasedness principle. These two estimates have closed form and are functions of the sample mean, sample standard deviation, sample size, as well as the mean and variance of a corresponding standard distribution. Next, we extend the previous result to estimate a 3-parameter distribution which we call a mixed method. A central idea of the mixed method is to estimate the location and scale parameters as functions of the shape parameter. The sample mean is a popular estimator for the population mean. The mean squared error (MSE) of the sample mean is often large, however, when the sample size is small or the scale parameter is greater than the location parameter. To reduce the MSE of our location estimator, we introduce an adaptive estimator. We will illustrate this by the example of the power Gumbel distribution. The frequentist approach is often criticized as failing to take into account the uncertainty of an unknown parameter, whereas a Bayesian approach incorporates such uncertainty. The present Bayesian analysis for the Gumbel data is achieved numerically as it is hard to obtain an explicit form. We tackle the problem by providing an approximation to the exponential sum of Gumbel random variables. Next, we provide two efficient methods to construct prediction intervals. The first one is a Monte Carlo method for a general location-scale family, based on our previous parameter estimation. Another is the Gibbs sampler, a special case of Markov Chain Monte Carlo. We derive the predictive distribution by making use of an approximation to the exponential sum of Gumbel random variables . Finally, we present a new generalized bootstrap and show that Efron's bootstrap re-sampling is a special case of the new re-sampling scheme. Our result overcomes the issue of the bootstrap of its ``inability to draw samples outside the range of the original dataset.'' We give an applications for constructing prediction intervals, and simulation shows that generalized bootstrap is better than that of the bootstrap when the sample size is small. The last contribution in this thesis is an improved GRS method used in nuclear engineering for construction of non-parametric tolerance intervals for percentiles of an unknown distribution. Our result shows that the required sample size can be reduced by a factor of almost two when the distribution is symmetric. The confidence level is computed for a number of distributions and then compared with the results of applying the generalized bootstrap. We find that the generalized bootstrap approximates the confidence level very well. / Dissertation / Doctor of Philosophy (PhD)

Un essai clinique est une recherche biomédicale pratiquée sur l'Homme dont l'objectif est la consolidation et le perfectionnement des connaissances biologiques ou médicales. Le nombre de sujets nécessaire (NSN) est le nombre minimal de patients à inclure dans l'essai afin d'assurer au test statistique une puissance donnée pour observer un effet donné. Pour ce faire plusieurs centres investigateurs sont sollicités. La période entre l'ouverture du premier centre investigateur et le recrutement du dernier patient est appelée période de recrutement que l'on souhaite modéliser. Les premières modélisations remontent à presque 50 ans avec les travaux de Lee, Williford et al. et Morgan avec l'idée déjà d'une modélisation de la dynamique de recrutement par des processus de Poisson. Un problème émerge lors de recrutement multicentriques du fait du manque de caractérisation de l'ensemble des sources de variabilité agissant sur les différentes dynamiques de recrutement. Le modèle dit Poisson-gamma basé sur un processus de Poisson dont les intensités par centre sont considérées comme un échantillon de loi gamma permet l'étude de variabilité. Ce modèle est au coeur de notre projet. Différents objectifs ont motivés la réalisation de cette thèse. Le premier questionnement porte sur la validité de ces modèles. Elle est établie de façon asymptotique et une étude par simulation permet de donner des informations précises sur la validité du modèle. Par la suite l'analyse de bases de données réelles a permis de constater que lors de certaines phases de recrutement, des pauses dans le recrutement sont observables. Une question se pose alors naturellement : comment et faut-il prendre en compte ces informations dans le modèle de dynamique de recrutement ? Il résulte d'études par simulation que la prise en compte de ces données n'améliore pas les performances prédictives du modèle lorsque les sources d'interruptions sont aléatoires mais dont la loi est inchangée au cours du temps. Une autre problématique observable sur les données et inhérente au problème de recrutement de patients est celle des dites sorties d'étude. Une technique Bayésienne empirique analogue à celle du processus de recrutement peut être introduite pour modéliser les sorties d'étude. Ces deux modélisations se couplent très bien et permettent d'estimer la durée de recrutement ainsi que la probabilité de sorties d'étude en se basant sur les données de recrutement d'une étude intermédiaire, donnant des prédictions concernant le processus de randomisation. La dynamique de recrutement possède de multiples facteurs autre que le temps de recrutement. Ces aspects fondamentaux couplés au modèle Poisson-gamma fournissent des indicateurs pertinents pour le suivi des essais. Ainsi est-il possible d'ajuster le nombre de centres au cours de l'essai en fonction d'objectifs prédéfinis, de modéliser et prévoir la chaîne d'approvisionnement nécessaire lors de l'essai et de prévoir l'effet de la randomisation des patients par région sur la puissance du test de l'essai. Il permet également d'avoir un suivi des patients après randomisation permettant ainsi de prévoir un ajustement du nombre de patients en cas de pertes significative d'effectif, ou d'abandonner un essai si les résultats préliminaires sont trop faibles par rapport aux risques connus et observés. La problématique de la dynamique de recrutement peut être couplée avec la dynamique de l'étude en elle-même quand celle-ci est longitudinale. L'indépendance des deux processus permet une estimation facile des différents paramètres. Le résultat est un modèle global du parcours du patient dans l'essai. Deux exemples clés de telles situations sont les données de survie - la modélisation permet alors d'estimer la durée d'un essai quand le critère d'arrêt est le nombre d'événements observés et les modèles de Markov - la modélisation permet alors d'estimer le nombre de patients dans un certain état au bout d'un certain temps. / A clinical trial is a biomedical research which aims to consolidate and improve the biological and medical knowledges. The number of patients required il the minimal number of patients to include in the trial in order to insure a given statistical power of a predefined test. The constitution of this patients' database is one of the fundamental issues of a clinical trial. To do so several investigation centres are opened. The duration between the first opening of a centre and the last recruitment of the needed number of patients is called the recruitemtn duration that we aim to model. The fisrt model goes back 50 years ago with the work of Lee, Williford et al. and Morgan with the idea to model the recruitment dynamic using Poisson processes. One problem emerge, that is the lack of caracterisation of the variabliity of recruitment between centers that is mixed with the mean of the recruitment rates. The most effective model is called the Poisson-gamma model which is based on Poisson processes with random rates (Cox process) with gamma distribution. This model is at the very heart of this project. Different objectives have motivated the realisation of this thesis. First of all the validity of the Poisson-gamma model is established asymptotically. A simulation study that we made permits to give precise informations on the model validity in specific cases (function of the number of centers, the recruitement duration and the mean rates). By studying database, one can observe that there can be breaks during the recruitment dynamic. A question that arise is : How and must we take into account this phenomenon for the prediction of the recruitment duration. The study made tends to show that it is not necessary to take them into account when they are random but their law is stable in time. It also veered around to measure the impact of these breaks on the estimations of the model, that do not impact its validity under some stability hypothesis. An other issue inherent to a patient recruitment dynamic is the phenomenon of screening failure. An empirical Bayesian technique analogue to the one of the recruitment process is used to model the screening failure issue. This hierarchical Bayesian model permit to estimate the duartion of recruitment with screening failure consideration as weel as the probability to drop out from the study using the data at some interim time of analysis, giving predictions on the randomisation dynamic. The recruitment dynamic can be studied in many different ways than just the duration of recruitment. These fundamental aspects coupled with the Poisson-gamma model give relevant indicators for the study follow-up. Multiples applications in this sense are computed. It is therefore possible to adjust the number of centers according to predefined objectives, to model the drug's supply chain per region or center and to predict the effect of the randomisation on the power of the test's study. It also allows to model the folow-up period of the patients by means of transversal or longitudinal methods, that can serve to adjust the number of patients if too many quit during the foloww-up period, or to stop the study if dangerous side effects or no effects are observed on interim data. The problematic of the recruitment dynamic can also be coupled with the dynamic of the study itself when it is longitudinal. The independance between these two processes allows easy estimations of the different parameters. The result is a global model of the patient pathway in the trail. Two key examples of such situations are survival data - the model permit to estimate the duration of the trail when the stopping criterion is the number of events observed, and the Markov model - the model permit to estimate the number of patients in a certain state for a given duartion of analysis.

Cette thèse propose une analyse de la dynamique macroéconomique de l’économie camerounaise. On commence par une analyse quantitative générale du cycle des affaires au Cameroun, fondée sur des données macroéconomiques annuelles que nous avons nous-mêmes assemblées. Cette première exploration laisse apparaître un certain nombre de caractéristiques qui se prêtent bien à une modélisation de type néo-keynesien. Nous construisons alors un modèle dynamique stochastique d’équilibre général (DSGE) de l’économie camerounaise. Ce modèle comporte les blocs de construction de modèles DSGE néo-keynésiens standards (par exemple, la rigidité des prix et des salaires des rigidités, et des coûts d'ajustement), mais il inclut également un certain nombre de caractéristiques spécifiques (telles que l'exportation des matières premières et les revenus du pétrole entre autre) dont on montre qu’elles jouent un rôle important dans la dynamique de l'économie camerounaise. Le modèle est estimé et évalué selon une approche bayésienne. La performance du modèle DSGE en termes de prévision est comparée à celle d’un modèle de marche aléatoire, à celle d’un modèle vectoriel auto-régressif (VAR) et, enfin, à celle d’un modèle vectoriel auto-régressif de type Bayesien (BVAR). Nous trouvons que, le modèle DSGE est plus précis en matière de prévision au moins dans un horizon de court-terme. Pour ce qui est des fluctuations macroéconomiques, les chocs des prix des produits de base génèrent une expansion de la production, une augmentation de l'emploi et une baisse de l'inflation tandis que des chocs liés aux prix du pétrole ont un impact direct sur le coût marginal de production qui augmente et provoque une augmentation de l'inflation en même temps que production et emploi baissent. Notons que, les chocs extérieurs et les chocs d'offre domestiques représentent une grande part des fluctuations de la production et de l'investissement. Aussi, l'évolution de la production sur l'ensemble de l'échantillon est dominée par le choc de prix des matières premières et le choc des prix du pétrole. / This thesis aims at analyzing the macroeconomic dynamics of the Cameroonian economy. It begins with a quantitative analysis of the business cycle in Cameroon, based on annual macroeconomic data, especially gathered for this purpose. This preliminary inquiry highlights a number of features that can be accounted for in a new-keynesian modelling framework. A dynamic stochastic general equilibrium (DSGE) model of the new-keynesian family is thus constructed as a mean of describing the salient feautures of the Cameroonian economy. It has the traditional blocks of new-keynesian DSGE models (Sticky prices and wages, adjustment costs, etc). But it also accounts for a number of characteristics of the Cameroonian economy that are shown to be influential in the dynamics of the cameroonian economy (e.g. oil revenues or primary goods exports). The model is then estimated and evaluated, based on a Bayesian approach. Its forecasting performance is also assessed through comparison to the performances of a random walk model, a vector autoregressive (VAR) model and a Bayesian VAR (BVAR) model. It turns out that, at least for short horizons, the DSGE model shows the highest perfromance. As to macroeconomic fluctuations, the estimated model suggests that commodity price shocks generate an output expansion, an increase in employment and a fall in inflation. In addition, oil price shocks have a direct impact on marginal costs which increase and provoke a rising in inflation while output and employment tend to fall. Foreign shoks and domestic supply shocks account for a large share of output and investment fluctuations. The evolution of output over the whole sample is dominated by commodity price shocks and oil price shocks as one would expect.

O movimento dos lábios é um recurso visual relevante para a detecção da atividade de voz do locutor e para o reconhecimento da fala. Quando os lábios estão se movendo eles transmitem a idéia de ocorrências de diálogos (conversas ou períodos de fala) para o observador, enquanto que os períodos de silêncio podem ser representados pela ausência de movimentações dos lábios (boca fechada). Baseado nesta idéia, este trabalho foca esforços para detectar a movimentação de lábios e usá-la para realizar a detecção de atividade de voz. Primeiramente, é realizada a detecção de pele e a detecção de face para reduzir a área de extração dos lábios, sendo que as regiões mais prováveis de serem lábios são computadas usando a abordagem Bayesiana dentro da área delimitada. Então, a pré-segmentação dos lábios é obtida pela limiarização da região das probabilidades calculadas. A seguir, é localizada a região da boca pelo resultado obtido na pré-segmentação dos lábios, ou seja, alguns pixels que não são de lábios e foram detectados são eliminados, e em seguida são aplicados algumas operações morfológicas para incluir alguns pixels labiais e não labiais em torno da boca. Então, uma nova segmentação de lábios é realizada sobre a região da boca depois de aplicada uma transformação de cores para realçar a região a ser segmentada. Após a segmentação, é aplicado o fechamento das lacunas internas dos lábios segmentados. Finalmente, o movimento temporal dos lábios é explorado usando o modelo das cadeias ocultas de Markov (HMMs) para detectar as prováveis ocorrências de atividades de fala dentro de uma janela temporal. / Lips motion are relevant visual feature for detecting the voice active of speaker and speech recognition. When the lips are moving, they carries an idea of occurrence of dialogues (talk) or periods of speeches to the watcher, whereas the periods of silences may be represented by the absence of lips motion (mouth closed). Based on this idea, this work focus efforts to obtain the lips motion as features and to perform visual voice activity detection. First, the algorithm performs skin segmentation and face detection to reduce the search area for lip extraction, and the most likely lip regions are computed using a Bayesian approach within the delimited area. Then, the pre-segmentation of the lips is obtained by thresholding the calculated probability region. After, it is localized the mouth region by resulted obtained in pre-segmentation of the lips, i.e., some nonlips pixels detected are eliminated, and it are applied a simple morphological operators to include some lips pixels and non-lips around the mouth. Thus, a new segmentation of lips is performed over mouth region after transformation of color to enhance the region to be segmented. And, is applied the closing of gaps internal of lips segmented. Finally, the temporal motion of the lips is explored using Hidden Markov Models (HMMs) to detect the likely occurrence of active speech within a temporal window.

A historical review is performed to study the impact of acoustical knowledge on concert hall developments. It shows that although acoustics developed from myth to real science, there is still a gap between its fast growing knowledge and relatively slow applications to improve designs. Architectural acoustics research and education shall help populating the tacit knowledge and experience of acousticians to reduce the gap between design and knowledge. The established paradigm in this field is to identify the performance goals of concert halls, recognize the available design information in different stages, and establish models to link them together. Placed in this general picture, this thesis focuses on providing design support for preliminary stage. It develops a model to link accessible design features with the most important acoustics performance index, reverberation time. A literature review on exiting reverberation time prediction methods shows that they are based on either too demanding or over-simplified for this stage. This study intends to develop a model that makes maximum use of available information and improves prediction accuracy in comparison with existing simplified methods. Through literature survey and data analysis, three factors (geometrical shape, non-uniform material distribution and scattering effect) are recognized as significant for reverberation time prediction. This thesis developed a simplified model taking these factors into consideration and calibrated this model with empirical data through Bayesian statistical method.