Rational expectations provide people or economic agents making future decision with available information and past experiences. The first approach to the idea of rational expectations was given approximately fifty years ago by John F. Muth. Many models in economics have been studied using the rational expectations idea. The most familiar one among them is the rational expectations version of the Cagans hyperination model where the expectation for tomorrow is formed using all the information available today. This model was reinterpreted by Thomas J. Sargent and Neil Wallace in 1973. After that time, many solution techniques were suggested to solve the Cagan type rational expectations (CTRE) model. Some economists such as Muth [13], Taylor [26] and Shiller [27] consider the solutions admitting an infinite moving-average representation. Blanchard and Kahn [28] find solutions by using a recursive procedure. A general characterization of the solution was obtained using the martingale approach by Broze, Gourieroux and Szafarz in [22], [23]. We choose to study martingale solution of CTRE model. This thesis is comprised of five chapters where the main aim is to study the CTRE model on isolated time scales. Most of the models studied in economics are continuous or discrete. Discrete models are more preferable by economists since they give more meaningful and accurate results. Discrete models only contain uniform time domains. Time scale calculus enables us to study on m-periodic time domains as well as non periodic time domains. In the first chapter, we give basics of time scales calculus and stochastic calculus. The second chapter is the brief introduction to rational expectations and the CTRE model. Moreover, many other solution techniques are examined in this chapter. After we introduce the necessary background, in the third chapter we construct the CTRE Model on isolated time scales. Then we give the general solution of this model in terms of martingales. We continue our work with defining the linear system and higher order CTRE on isolated time scales. We use Putzer Algorithm to solve the system of the CTRE Model. Then, we examine the existence and uniqueness of the solution of the CTRE model. In the fourth chapter, we apply our solution algorithm developed in the previous chapter to models in Finance and stochastic growth models in Economics.

Financial failure is an important subject for both the economical development of the country and for the self - evaluation of individual companies. Increase in the number of financially failed companies points out the misuse of the country resources. Recently, financial failure threatens both small and large companies in Turkey. It is important to determine factors that affect the financial failure by analyzing models and to use these models for auditing the financial situation. In today&rsquo / s Turkey, the statistical methods that are used for this purpose involve single level models applied to cross-sectional data. However, multilevel models applied to panel data are more preferable as they gather more information, and also, enable the calculated financial success probabilities to be more trustworthy. In this thesis, publicly available panel data that are collected from The Istanbul Stock Exchange are investigated. Mainly, financial success of companies from two sectors, namely industry and services, are investigated. For the analysis of this panel data, data exploration methods, missing data imputation, possible solutions to multicollinearity problem, single level logistic regression models and multilevel models are used. By these models, financial success probabilities for each company are calculated / the factors related to the financial failure are determined, and changes in time are observed. Models and early warning systems resulted in correct classification rates of up to 100%. In the services sector, a small number of companies having publicly available data result in a decline in the success of models. It is concluded that sharing data with more subjects observed in a longer time period collected in the same format with academicians, will result in better justified outputs, which are useful for both academicians and managers.

The objective of the proposed research is to develop a probabilistic model of speech production that exploits the multiplicity of mapping between the vocal tract area functions (VTAF) and speech spectra. Two thrusts are developed. In the first, a latent variable model that captures uncertainty in estimating the VTAF from speech data is investigated. The latent variable model uses this uncertainty to generate many-to-one mapping between observations of the VTAF and speech spectra. The second uses the probabilistic model of speech production to improve the performance of traditional speech algorithms, such as enhancement, acoustic model adaptation, etc. In this thesis, we propose to model the process of speech production with a probability map. This proposed model treats speech production as a probabilistic process with many-to-one mapping between VTAF and speech spectra. The thesis not only outlines a statistical framework to generate and train these probabilistic models from speech, but also demonstrates its power and flexibility with such applications as enhancing speech from both perceptual and recognition perspectives.

Background: Functional magnetic resonance imaging (fMRI) can require extensive preprocessing to minimize noise and maximize signal. There is evidence suggesting that fixed-subject preprocessing pipelines, the current standard in fMRI preprocessing, are suboptimal compared to individual-subject pipelines. Aim: We sought to test if individual-subject preprocessing pipeline optimization, compared to fixed, resulted in stronger and more reliable brain-patterns in episodic recognition. Methodology: 27 young healthy controls were scanned via fMRI while performing forced-choice episodic recognition. Several sets of fMRI preprocessing pipelines were tested and optimized in a fixed and individual-subject manner, using methods outlined by Churchill et al. (2011). Results: Individual-subject pipeline optimization, compared to fixed, significantly increased reproducibility, significantly increased the detection of positively and negatively activated voxels, and resulted in a brain-pattern with significant correlation to a task behavioral measure. Conclusions: Individual-subject pipeline optimization, compared to fixed, led to stronger and more reliable brain-patterns that are significantly correlated with behavior.

Background: Functional magnetic resonance imaging (fMRI) can require extensive preprocessing to minimize noise and maximize signal. There is evidence suggesting that fixed-subject preprocessing pipelines, the current standard in fMRI preprocessing, are suboptimal compared to individual-subject pipelines. Aim: We sought to test if individual-subject preprocessing pipeline optimization, compared to fixed, resulted in stronger and more reliable brain-patterns in episodic recognition. Methodology: 27 young healthy controls were scanned via fMRI while performing forced-choice episodic recognition. Several sets of fMRI preprocessing pipelines were tested and optimized in a fixed and individual-subject manner, using methods outlined by Churchill et al. (2011). Results: Individual-subject pipeline optimization, compared to fixed, significantly increased reproducibility, significantly increased the detection of positively and negatively activated voxels, and resulted in a brain-pattern with significant correlation to a task behavioral measure. Conclusions: Individual-subject pipeline optimization, compared to fixed, led to stronger and more reliable brain-patterns that are significantly correlated with behavior.

Given the increase in popularity of Lifetime Value (LTV), the argument is that the topic will assume an increasingly central role in research and marketing. As such, the decision to assess the state of the field in Lifetime Value Modelling, and outline challenges unique to choice researchers in customer relationship management (CRM). As the research has argued, there are an excess of issues and analytical challenges that remain unresolved. The researcher hopes that this thesis inspires new answers and new approaches to resolve LTV. The scope of this project covers the building of a LTV model through multiple regression. This thesis is exclusively focused on modelling tenure. In this regard, there are a variety of benchmark statistical techniques arising from survival analysis, which could be applied, to tenure modelling. Tenure prediction will be looked at using survival analysis and compared with "crossbreed" data mining techniques that use multiple regression in concurrence with statistical techniques. It will be demonstrated how data mining tools complement the statistical models, and show that their mutual usage overcomes many of the shortcomings of each singular tool set, resulting in LTV models that are both accurate and comprehensible. Bank XYZ is used as an example and is based on a real scenario of one of the Banks of South Africa. / Thesis (M.Sc. (Computer Science))--North-West University, Vaal Triangle Campus, 2009.

Comenzarnos realizando una aproximación al concepto de modelo estadístico desde el punto de vista geométrico, centrándonos principalmente en consideraciones sobre la introducción de distancias, y en particular estudiando la métrica informacional y sus propiedades. Dada una variedad paramétrica correspondiente a un modelo estadístico, hemos efectuado un estudio del espacio tangente y del espacio tangente dual en un punto a la variedad, introduciendo representaciones adecuadas de los mismos. Tales representaciones han permitido identificar a los elementos del espacio muestral con campos tensoriales covariantes de primer orden en la variedad, mientras que las variables aleatorias pueden ser identificados con campos tensoriales contravariantes también de primer orden. Hemos introducido dos definiciones de distancias, en sentido estricto pseudodistancias, entre valores muestrales basadas ambas en distancias en el espacio tangente dual entre formas lineales asociadas. La primera, a la que denominamos distancia inmediata, es definida a partir de la distancia euclídea en el espacio tangente dual. Se han obtenido expresiones explícitas para la distancia cuando los individuos estadísticos son muestras correspondientes a las distribuciones Poisson, Weibull, Gamma, Exponencial, Binomial, Binomial Negativa, Multinomial, Multinomial negativa, Wald, Logística, Normal univariante y Normal multivariante. Se han estudiarlo ciertas propiedades relacionadas con la distancia inmediata, entre las que destacamos su invarianza frente a cambios de la medida de referencia y transformaciones por estadísticas suficientes, y su no decrecimiento al aumentar el número de parámetros de las variedades. La distancia estructural es definida a partir de la distancia sobre el conjunto imagen del espacio muestral. Se demuestra que coincide con la distancia inmediata si el conjunto imagen es un conjunto convexo y también que dicho conjunto no es convexo si la dimensión del espacio muestral es uno y el número de parámetros de la variedad mayor o igual a dos. Se ha obtenido la expresión explícita para la distancia estructural entre muestras de tamaño uno correspondientes a una distribución normal univariante. Se han estudiado las aplicaciones de las distancias entre individuos a técnicas clásicas de inferencia estadística, definiendo nuevos procedimientos de estimación de parámetros y contraste de hipótesis desde el punto de vista geométrico. Se comprueba cómo utilizando la distancia inmediata se recuperan gran parte de los resultados clásicos, en particular las ecuaciones de verosimilitud y el contraste de hipótesis mediante el test de los multiplicadores de Lagrange. Hemos comprobado también como utilizando en estimación de parámetros la distancia estructural en un ejemplo en que éste difiere de la inmediata, se obtienen resultados que difieren respecto a la máxima verosimilitud clásica y que podemos considerar más acordes con resultados intuitivos al dejar indeterminada la estimación de la varianza trabajando con muestras de tamaño uno de una distribución Normal univariante. Se ha introducido una clase de funciones de densidad de probabilidad que pueden ser caracterizadas en una variedad paramétrica de dimensión finita. Se comprueba que las variedades resultantes son de curvatura constante y positiva. Se han obtenido las expresiones para las geodésicas y la distancia de Rao entre dos distribuciones. Hemos efectuado un estudio probabilístico en varios ejemplos y finalmente consideramos la aplicación de tales familias a la estimación no paramétrica de funciones de densidad gracias a su capacidad de adaptación. Se ha abordado el problema de la estimación de parámetros en las familias anteriormente citadas. Comprobamos los inconvenientes de la estimación máximo verosímil y para subsanarlos hemos propuesto un algoritmo tipo “stepwise” que toma en cuenta la significación de los incrementos de la verosimilitud al modificar el número de parámetros de las familias. Utilizamos diversas simulaciones para comprobar la bondad del algoritmo, obteniendo resultados satisfactorios tanto al trabajar con distribuciones clásicos como con las nuevas familias. Se han comparado los resultados con otros métodos clásicos de estimación no paramétrica, en particular con el método de los Kernel. También se ha estudiado el método de minimizar la esperanza del cuadrado de la distancia estructural entre individuos (MESD). Para poder llevar a cabo tal estudio se ha desarrollado una aproximación a la distinción Riemanniana y se han utilizado técnicas de minimización numérica de funciones de varias variables con restricciones. Se han obtenido algunos ejemplos que muestran un mejor comportamiento de la estimación MESD frente a la MLE. Finalmente se han considerado dos ejemplos prácticos consistentes en la estimación de una función de densidad bimodal a partir de unos datos en forma de histograma y en la clasificación de diversos patrones electroforéticos asimilándolos a funciones de densidad. En limbos ejemplos los resultados parecen validar completamente la metodología empleada. / We have studied the concept of statistical model from a geometric point of view considering particularly the information metric and the problem of introducing distances. Given a parametric manifold representing a statistical model and given a point of the manifold, we have defined two different distances between elements of sample space (statistical individuals) by means of a suitable representation of statistical individuals as linear forms of the dual tangent space to the manifold in the given point. Some properties have been studied and the explicit expressions for some examples have been obtained. Several techniques of statistical inference: parameter estimation, hypothesis tests, discrimination; have been studied in the light of the distances between elements of sample spaces. Some classical results have been recovered, in particular Iikelihood equations and Lagrange multipliers test. We have introduced a class of probability density functions that may be represented in finite dimensional manifolds. Geometrical properties of such manifolds have been studied and the Rao distance between two distributions has been obtained. We have considered several examples. We have also studied the problem of parameter estimation in the functions defined previously; we have developed a stepwise algorithm for nonparametric density estimation in order to some problems arising with classical maximum likelihood estimation when we handle a large number of parameters. We also present some examples applied lo biological data.

[pt] Este trabalho apresenta um novo modelo de previsão de curto prazo de carga elétrica que reúne técnicas de inteligência computacional e métodos estatísticos. Ele permite aproveitar as vantagens de inteligência computacional, relativas à criação de classes da série de entrada e ao processamento de variáveis climáticas de forma lingüística, e aquelas provenientes de modelos estatísticos, onde os parâmetros e a ordem do modelo são conhecidos e o intervalo de confiança das previsões é determinado. O modelo é uma extensão do método desenvolvido por P.C. Gupta, onde são empregadas técnicas de inteligência computacional junto com o método original. O modelo resultante compreende um classificador, um previsor e um procedimento para aprimorar as estimativas. O classificador é implementado por uma rede neural artificial com aprendizado não-supervisionado, enquanto o previsor emprega modelos estatísticos, combinando métodos de média móvel, amortecimento exponencial e auto- regressivo. Um sistema com lógica nebulosa utiliza variáveis climáticas no aprimoramento da previsão obtida. / [en] A new short-term load forecasting procedure is presented in this work, mixing techniques from the statistical models and those from computational intelligence (CI). It takes advantage of the CI techniques to establish the various load profiles and to process climatic variables in a linguistic way, and those from the statistical side, where the parameters and the order of the model are known and a spread measure is determined. The model is an adaptation of the method developed by P.C.Gupta, where CI techniques are added to the original method. The final model includes a classifer scheme, a predictive scheme and a procedure to improve the estimations. The classifier is implemented via an artificial neural network using a non-supervised learning moving average, exponential smoothing and ARMA type of models. A fuzzy logic procedure uses climating variables to improve the forecast.

Les déplacements des barrages en béton sont influencés par de nombreux facteurs tels que lacharge hydrostatique, les effets thermiques et les effets irréversibles. Pour interpréter les mesures,séparer les différentes influences et identifier un éventuel comportement pathologique,des modèles physico-statistiques de type régression multi-linéaire sont couramment utilisés parl’ingénierie. L’estimation de la composante thermique est cependant une source d’incertitudesignificative pour ces modèles. Les objectifs de cette thèse sont alors de mettre en évidenceles mécanismes à l’origine des déplacements thermiques, de clarifier les hypothèses des modèlesactuels et de déterminer les principales sources d’incertitudes parmi les influences environnementalesafin de proposer des pistes d’amélioration de la modélisation statistique. Deux nouveauxmodèles physico-statistiques ont alors été développés pour prendre en compte l’influence de latempérature de l’eau qui s’est révélée être l’un des facteurs prépondérants d’incertitude. Dansun premier temps, uniquement la valeur moyenne a été introduite. Puis, parallèlement à desmesures in-situ, des profils réalistes sont pris en compte sur la hauteur du barrage. Ces modèlesont été testés sur un environnement virtuel (modèle aux éléments finis) puis sur un cas d’étuderéel, montrant une diminution significative de la dispersion résiduelle ainsi qu’une augmentationdu caractère prédictif. / Concrete dam displacements are influenced by various factors such as hydrostatic load, thermaleffects, and irreversible effects. In order to interpret measurements, to split apart all the differentinfluences and to identify a potential pathological behaviour, physico-statistical modelssuch as multi-linear regression are commonly employed in dam engineering. Nevertheless, thethermal component estimation is an important source of uncertainty for these models. Thus, theobjectives of this thesis are to highlight the mechanism that generate thermal displacement, toclarify model hypothesis, to determine the main sources of uncertainty from environnemental influencesso as to propose improvements of statistical modelling. Two original physico-statisticalmodels have been develloped to account for water temperature which has been identified as amain source of uncertainty. Firstly, only the mean value has been introduced. Then, in parallelto in-situ measurements, realistic temperature profils are accounted for over the dam’s height.These models have been tested both on a virtual environnement (finite element model) and ona real study case. The results show a significant reduction of the residual dispersion and anincrease of the predictive capacity of the models.

Introdução: A incidência de doenças crônicas não transmissíveis (DCNT) vem aumentando em todo o mundo. Estudos comprovam que o consumo de frutas, legumes e verduras (FLV) reduzem a incidência de DCNT na população Objetivo: Avaliar os determinantes do consumo de FLV em adultos residentes no município de São Paulo Metodologia: É um estudo transversal, abrangendo 1267 mulheres e 855 homens, com idade igual ou superior a 18 anos. A análise de regressão linear foi baseada no modelo hierárquico de fatores associados ao consumo de FLV. As variáveis foram agrupadas em categorias hierárquicas, abrangendo dos fatores distais aos proximais. Essas categorias foram, nessa ordem, sócio-demográfica, comportamental e de consumo alimentar. Resultados: Para ambos os sexos, verificou-se que as seguintes variáveis estavam diretamente associadas ao consumo de FLV: idade e anos de estudo, na categoria sócio-demográfica; prática de atividade física no lazer e ter feito dieta no último ano, na categoria comportamental e consumo de peixe na categoria de consumo alimentar. A densidade domiciliar mostrou-se inversamente associada ao consumo de FLV em ambos os sexos. Somente para as mulheres ser ou já ter sido casada foi diretamente associado ao consumo de FLV e ser fumante mostrou-se inversamente associado. O consumo de alimentos que indicam um padrão de consumo não saudável como açúcares e carne vermelha com gordura mostrou-se inversamente associado ao consumo de FLV em ambos os sexos. Conclusão: O consumo de FLV e seus determinantes são diferentes para homens e mulheres, sendo a maior freqüência de consumo ocorre no sexo feminino. / The burden of noncommunicable diseases (NCD) increases in the whole world. Studies prove that consumption do fruits and vegetables (FV) reduce the incidence of NTCD in the population. The present study aims to evaluate by telephones interviews the determinants of Fruit and vegetable's intake in adults living in São Paulo City. This is a cross-sectional study, ranging over 1267 women and 855 men, aged 18 years old or more. Multiple linear regression analysis was based on a hierarchical model of factors associated with FV intake. The variables were grouped into a hierarchy of categories, ranging from distal determinants to proximate ones. These categories included, in this order, socio-demographic, behavioral and food consumption. For both gender, we found that the following variables were directly associated with FV intake: age and years of study, in the socio-demographic category, physical activity in leisure time and have been on a diet in the last year, in the behavioral category and fish consumption in the nutritional category. The domiciliary density was inversely associated with FLV consumption for both genders. Only for women marital status was directly associated with FV intake and tobacco use were inversely associated. The dietary intake of food that indicates an unhealthy diet, like sugar and read meat with fat were inversely associated with FV intake for both gender. Consumption of FV and their determinants are different for man and women and the major consumption occurs with women.