Dissertations / Theses on the topic 'Linear random growth models'

This thesis is concerned with introducing competition into random models. It can be observed that there are two natural mechanisms for the evolution of a random model; either by growth or by self interactions. What we do is look at two types of models and introduce competition within them. The first model, the voter model, is an example of a self interacting model and we introduce growth into it. The second model, the Hasting-Levitov model, is a random growth model and we introduce competition within the model. In both cases we construct diffusion approximations to model these systems when the initial population is large for the first case and when the addition of incoming particles is small in the second. Once these diffusion processes have been constructed we then analyse the long term behaviour of them and find their asymptotic distribution, this is done by using the speed measure and scale function.

Cette thèse de doctorat porte sur l'étude du modèle de croissance stochastique Kardar-Parisi-Zhang (KPZ) en 1+1 dimensions et en particulier de l'équation qui le régit. Cette thèse est d'une part destinée à effectuer un état de l'art et dresser un portrait moderne de la recherche des solutions exactes de l'équation KPZ, de leurs propriétés en terme de théorie des grandes déviations et également de leurs applications (en théorie des matrices aléatoires ou en calcul stochastique notamment). D'autre part cette thèse a pour but de formuler un certain nombre de questions ouvertes à l'interface avec la théorie de l'intégrabilité, la théorie des matrices aléatoires et la théorie des gaz de Coulomb.Cette thèse est divisée en trois parties distinctes portant (i) sur les solutions exactes de l'équation KPZ, (ii) sur les solutions à temps court sous la forme d'un principe grandes déviations et (iii) sur les solutions à temps long et leurs extensions aux statistiques linéaires au bord de spectre de matrice aléatoire.Nous présenterons les résultats de cette thèse comprenant notamment (a) une nouvelle solution de l'équation KPZ à tout temps dans un demi-espace, (b) une méthodologie générale pour établir à temps court un principe de grandes déviations pour les solutions de KPZ à partir de leur représentation sous forme de déterminant de Fredholm et (c) une unification de quatre méthodes permettant d'obtenir à temps long un principe de grandes déviations pour les solutions de l'équation KPZ et de manière plus générale d'étudier des statistiques linéaires au bord du spectre de matrices aléatoires
Throughout this Ph.D thesis, we will study the Kardar-Parisi-Zhang (KPZ) stochastic growth model in 1+1 dimensions and more particularly the equation which governs it. The goal of this thesis is two-fold. Firstly, it aims to review the state of the art and to provide a detailed picture of the search of exact solutions to the KPZ equation, of their properties in terms of large deviations and also of their applications to random matrix theory or stochastic calculus. Secondly, is it intended to express a certain number of open questions at the interface with integrability theory, random matrix theory and Coulomb gas theory.This thesis is divided in three distinct parts related to (i) the exact solutions to the KPZ equation, (ii) the short time solutions expressed by a Large Deviation Principle and the associated rate functions and (iii) the solutions at large time and their extensions to linear statistics at the edge of random matrices.We will present the new results of this thesis including (a) a new solution to the KPZ equation at all times in a half-space, (b) a general methodology to establish at short time a Large Deviation Principle for the solutions to the KPZ equation from their representation in terms of Fredholm determinant and (c) the unification of four methods allowing to obtain at large time a Large Deviation Principle for the solution to the KPZ equation and more generally to investigate linear statistics at the soft edge of random matrices

El objetivo de este proyecto de tesis doctoral es el desarrollo de técnicas analítico-numéricas para resolver, en media cuadrática problemas, de valores iniciales de ecuaciones y sistemas de ecuaciones en diferencias y diferenciales aleatorias de tipo lineal. Respecto del estudio aportado sobre ecuaciones en diferencias (véase Capítulo 3), se extienden al contexto aleatorio algunos de los principales resultados que en el caso determinista se conocen para resolver este tipo de ecuaciones así como para estudiar el comportamiento asintótico de su solución. En lo que se refiere a las ecuaciones diferenciales hay que señalar que el elemento unificador del estudio realizado en esta memoria es la extensión al escenario aleatorio del método de Fröbenius para la búsqueda de soluciones de ecuaciones diferenciales en forma de desarrollos en serie de potencias. A largo de los Capítulos 4-7 se abordan problemas tanto de tipo escalar como de tipo matricial tanto de primer como de segundo orden, donde la aleatoriedad se introduce en los modelos a través de las condiciones iniciales y los coeficientes, siendo además la incertidumbre en este último caso, considerada tanto de forma aditiva como multiplicativa. Los problemas basados en ecuaciones diferenciales aleatorias tratados permiten introducir procesos estocásticos importantes como son el proceso exponencial (véase Capítulo 5), los procesos trigonométricos seno y coseno y algunas de sus propiedades algebraicas básicas (véase Capítulo 6). En el último capítulo se estudia la ecuación diferencial de Hermite con coeficientes aleatorios y, bajo ciertas condiciones, se obtienen soluciones en forma de serie aleatoria finita que definen los polinomios de Hermite aleatorios. Además de obtener las soluciones en forma de serie aleatoria convergente en el sentido estocástico de la media cuadrática, para cada uno de los problemas tratados se calculan aproximaciones de las principales propiedades estadísticas del proceso solución.
Calbo Sanjuán, G. (2010). Mean Square Analytic Solutions of Random Linear Models [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/8721
Palancia

This thesis consists of an introduction and five research papers on topics related to conformal mapping, the Loewner equation and its applications, and Bergman-type spaces of holomorphic functions. The first two papers are devoted to the study of integral means of derivatives of conformal mappings. In Paper I, we present improved upper estimates of the universal means spectrum of conformal mappingsof the unit disk. These estimates rely on inequalities  obtained by Hedenmalm and Shimorin using Bergman space techniques, and on computer calculations. Paper II is a survey of recent results on the universal means spectrum, with particular emphasis on Bergman spacetechniques.Paper III concerns Bergman-type spaces of holomorphic functions in subsets of $\textbf{C}^d$ and their reproducing kernel functions. By expanding the norm of a function in a Bergman space along the zero variety of a polynomial, we obtain a series expansion of reproducing kernel functions in terms of kernels associated with lower-dimensionalspaces of holomorphic functions. We show how this general approach can be used to explicitly compute kernel functions for certain weighted Bergman and Bargmann-Fock spaces defined in domains in $\textbf{C}^2$.The last two papers contribute to the theory of Loewner chains and theirapplications in the analysis of planar random growth model defined in terms of compositions of conformal maps.In Paper IV, we study Loewner chains generated by unimodular L\'evy processes.We first establish the existence of a capacity scaling limit for the associated growing hulls in terms of whole-plane Loewner chains driven by a time-reversed process. We then analyze the properties of Loewner chains associated with a class of two-parameter compound Poisson processes, and we describe the dependence of the geometric properties of the hulls on the parameters of the driving process. In Paper V, we consider a variation of the Hastings-Levitov growth model, with anisotropic growth. We again establish results concerning scaling limits, when the number of compositions increases and the basic conformal mappings tends to the identity. We show that the resulting limit sets can be associated with solutions to the Loewner equation.We also prove that, in the limit, the evolution of harmonic measure on the boundary is deterministic and is determined by the flow associated with an ordinary differential equation, and we give a description of the fluctuations around this deterministic limit flow.

QC 20100414

This study consists of the sensitivity analysis for two previously developed tumor growth models: Gompertz model and quotient model. The two models are considered in both continuous and discrete time. In continuous time, model parameters are estimated using least-square method, while in discrete time, the partial-sum method is used. Moreover, frequentist and Bayesian methods are used to construct confidence intervals and credible intervals for the model parameters. We apply the Markov Chain Monte Carlo (MCMC) techniques with the Random Walk Metropolis algorithm with Non-informative Prior and the Delayed Rejection Adoptive Metropolis (DRAM) algorithm to construct parameters' posterior distributions and then obtain credible intervals.

Random effect models have become a mainstream statistical technique over the last decades; and the same can be said for response transformation models such as the Box-Cox transformation. The latter ensures that the assumptions of normality and of homoscedasticity of the response distribution are fulfilled, which are essential conditions for the use of a linear model or a linear mixed model. However, methodology for response transformation and simultaneous inclusion of random effects has been developed and implemented only scarcely, and is so far restricted to Gaussian random effects. The first aim of this thesis is to develop such methodology, thereby not requiring parametric assumptions on the distribution of the random effects. This is achieved by extending the “Nonparametric Maximum Likelihood” towards a “Nonparametric Profile Maximum Likelihood” (NPPML) technique. The implemented techniques allow to deal with overdispersion as well as two-level data scenarios in general linear models. The second part of this thesis considers the transformation of mixed-effects logistic models, with the aim of improving model fit. In binary data, link functions other than the logit can be used to connect predictors with the response. The Box-Cox transformation is used in mixed–effects binary regression models as an alternative link function for linearization purposes. The NPPML approach is used similarly as before, with some adjustments. The proposed approach is implemented in the R package boxcoxmix. Simulation studies and applications on real data are carried out to study the performance of this approach.

La percolation avec contrainte consiste en l'étude de modèles de percolation pour lesquels on conditionne le sous-graphe aléatoire obtenu après suppression des arêtes à vérifier une contrainte particulière. La première partie de cette thèse traite d'un modèle spécifique de percolation avec contrainte : le modèle de corner percolation. Nous montrons que dans un régime à directions privilégiées, il existe presque sûrement une infinité de chemins infinis d'arêtes, et nous déterminons la direction asymptotique commune de ces chemins, en utilisant deux approches différentes. La seconde partie de cette thèse aborde des systèmes de particules en interaction. Nous nous intéressons à des variantes de deux modèles classiques dans ce domaine : le modèle de Richardson et le processus de contact. Ces derniers peuvent être vus comme des versions simplifiées de modèles représentant l'évolution au cours du temps d'une épidémie, et possèdent une dynamique d'infection et de guérison. On s'intéresse à l'incorporation dans ces modèles d'une dynamique de mélange, qui correspond au déplacement des individus. Nous montrons plusieurs résultats sur le modèle de Richardson avec mélange et le processus de contact avec mélange, notamment un théorème de forme asymptotique pour l'ensemble des individus infecté. Pour prouver ce théorème, nous utilisons un théorème de forme asymptotique général que nous avons montré pour une classe de systèmes de particules en interaction, que l'on appelle modèles à croissance aléatoire linéaire : ce théorème fait l'objet de la dernière partie de cette thèse
Constrained percolation is the study of percolation models in which the random subgraph obtained after edge removal is conditioned to verify a particular constraint. The first part of this thesis deals with a specific constrained percolation model: the corner percolation model. We show that in a regime with preferred directions, there are almost surely infinitely many infinite edge paths, and we determine the common asymptotic direction of these paths, using two different approaches. The second part of this thesis deals with interacting particle systems. We focus on variants of two classical models in this field: the Richardson model and the contact process. The latter can be seen as simplified versions of models representing the evolution over time of an epidemic, with infection and recovery dynamics. We focus on the incorporation into these models of a mixing dynamics, corresponding to the movement of individuals. We show several results on the Richardson model with mixing and the contact process with mixing, including an asymptotic shape theorem for the set of infected individuals. To prove this theorem, we use a general asymptotic shape theorem that we have shown for a class of interacting particle systems, which we call linear random growth models: this theorem is the subject of the last part of this thesis

FERREIRA, Roberto Tatiwa. Forecasting quarterly brazilian GDP growth rate with linear and nonlinear diffusion index models. Tese (Doutorado). Universidade Federal do Ceará, Programa de Pós Graduação em Economia, CAEN, Fortaleza, 2005.
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The present study uses linear and non-linear diffusion index models to produce one-step-ahead forecast of quarterly Brazilian GDP growth rate. Diffusion index models are like dynamic factors models. These factors are latent variables that represent a common property from the explanatory variables, then allowing a considerably reduction of its number in econometric models elaborated to attend the main objective of this work. The non-linear diffusion index models used in this thesis are not only parsimonious ones, but also they try to capture economic cycles using for this goal a Threshold diffusion index model and a Markov-Switching diffusion index model. The former is used, besides for forecasting purpose, also to test if there is a non-linear pattern in the quarterly Brazilian GDP growth rate.
Esta Tese estuda modelos lineares e não lineares de índices de difusão para prever, em um período à frente, a taxa de crescimento trimestral do PIB brasileiro. Os modelos de índice de difusão assemelham-se aos modelos de fatores dinâmicos. Estes fatores são variáveis não observáveis e representam uma característica em comum às variáveis explicativas, permitindo a redução significativa do número dessas no modelo econométrico proposto para atender o objetivo principal deste trabalho. Além de parcimoniosos, os modelos utilizados nesta Tese se propõem a capitar as fases de recessão e expansão econômica, através de modelos não lineares do tipo Threshold Effect e Markov-Switching, servindo o primeiro destes dois para testar a hipótese de que existe não linearidades na variável sob estudo.

We considered a non-centered parameterization of the standard random-effects model, which is based on the Cholesky decomposition of the variance-covariance matrix. The regression type structure of the non-centered parameterization allows to choose a simple, conditionally conjugate normal prior on the Cholesky factor. Based on the non-centered parameterization, we search for a parsimonious variance-covariance matrix by identifying the non-zero elements of the Cholesky factors using Bayesian variable selection methods. With this method we are able to learn from the data for each effect, whether it is random or not, and whether covariances among random effects are zero or not. An application in marketing shows a substantial reduction of the number of free elements of the variance-covariance matrix. (author's abstract)
Series: Research Report Series / Department of Statistics and Mathematics

Linear mixed-effects (LME) models are frequently used for modeling longitudinal data. One complicating factor in the analysis of such data is that samples are sometimes obtained from a population with significant underlying heterogeneity, which would be hard to capture by a single LME model. Such problems may be addressed by a finite mixture of linear mixed-effects (FMLME) models, which segments the population into subpopulations and models each subpopulation by a distinct LME model. Often in the initial stage of a study, a large number of predictors are introduced. However, their associations to the response variable vary from one component to another of the FMLME model. To enhance predictability and to obtain a parsimonious model, it is of great practical interest to identify the important effects, both fixed and random, in the model. Traditional variable selection techniques such as stepwise deletion and subset selection are computationally expensive even with modest numbers of covariates and components in the mixture model. In this thesis, we introduce a penalized likelihood approach and propose a nested EM algorithm for efficient numerical computations. The estimators are shown to possess consistency and sparsity properties and asymptotic normality. We illustrate the performance of the proposed method through simulations and a real data example.
Les modèles linéaires mixtes (LME) sont fréquemment employés pour la modélisation des données longitudinales. Un facteur qui complique l'analyse de ce genre de données est que les échantillons sont parfois obtenus à partir d'une population d'importante hétérogénéité sous-jacente, qui serait difficile à capter par un seul LME. De tels problèmes peuvent être surmontés par un mélange fini de modèles linéaires mixtes (FMLME), qui segmente la population en sous-populations et modélise chacune de ces dernières par un LME distinct. Souvent, un grand nombre de variables explicatives sont introduites dans la phase initiale d'une étude. Cependant, leurs associations à la variable réponse varient d'un composant à l'autre du modèle FMLME. Afin d'améliorer la prévisibilité et de recueillir un modèle parcimonieux, il est d'un grand intérêt pratique d'identifier les effets importants, tant fixes qu'aléatoires, dans le modèle. Les techniques conventionnelles de sélection de variables telles que la suppression progressive et la sélection de sous-ensembles sont informatiquement chères, même lorsque le nombre de composants et de covariables est relativement modeste. La présente thèse introduit une approche basée sur la vraisemblance pénalisée et propose un algorithme EM imbriqué qui est computationnellement efficace. On démontre aussi que les estimateurs possèdent des propriétés telles que la cohérence, la parcimonie et la normalité asymptotique. On illustre la performance de la méthode proposée au moyen de simulations et d'une application sur un vrai jeu de données.

[EN] This thesis concerns the analysis of differential equations with uncertain input parameters, in the form of random variables or stochastic processes with any type of probability distributions. In modeling, the input coefficients are set from experimental data, which often involve uncertainties from measurement errors. Moreover, the behavior of the physical phenomenon under study does not follow strict deterministic laws. It is thus more realistic to consider mathematical models with randomness in their formulation. The solution, considered in the sample-path or the mean square sense, is a smooth stochastic process, whose uncertainty has to be quantified. Uncertainty quantification is usually performed by computing the main statistics (expectation and variance) and, if possible, the probability density function. In this dissertation, we study random linear models, based on ordinary differential equations with and without delay and on partial differential equations. The linear structure of the models makes it possible to seek for certain probabilistic solutions and even approximate their probability density functions, which is a difficult goal in general. A very important part of the dissertation is devoted to random second-order linear differential equations, where the coefficients of the equation are stochastic processes and the initial conditions are random variables. The study of this class of differential equations in the random setting is mainly motivated because of their important role in Mathematical Physics. We start by solving the randomized Legendre differential equation in the mean square sense, which allows the approximation of the expectation and the variance of the stochastic solution. The methodology is extended to general random second-order linear differential equations with analytic (expressible as random power series) coefficients, by means of the so-called Fröbenius method. A comparative case study is performed with spectral methods based on polynomial chaos expansions. On the other hand, the Fröbenius method together with Monte Carlo simulation are used to approximate the probability density function of the solution. Several variance reduction methods based on quadrature rules and multilevel strategies are proposed to speed up the Monte Carlo procedure. The last part on random second-order linear differential equations is devoted to a random diffusion-reaction Poisson-type problem, where the probability density function is approximated using a finite difference numerical scheme. The thesis also studies random ordinary differential equations with discrete constant delay. We study the linear autonomous case, when the coefficient of the non-delay component and the parameter of the delay term are both random variables while the initial condition is a stochastic process. It is proved that the deterministic solution constructed with the method of steps that involves the delayed exponential function is a probabilistic solution in the Lebesgue sense. Finally, the last chapter is devoted to the linear advection partial differential equation, subject to stochastic velocity field and initial condition. We solve the equation in the mean square sense and provide new expressions for the probability density function of the solution, even in the non-Gaussian velocity case.
[ES] Esta tesis trata el análisis de ecuaciones diferenciales con parámetros de entrada aleatorios, en la forma de variables aleatorias o procesos estocásticos con cualquier tipo de distribución de probabilidad. En modelización, los coeficientes de entrada se fijan a partir de datos experimentales, los cuales suelen acarrear incertidumbre por los errores de medición. Además, el comportamiento del fenómeno físico bajo estudio no sigue patrones estrictamente deterministas. Es por tanto más realista trabajar con modelos matemáticos con aleatoriedad en su formulación. La solución, considerada en el sentido de caminos aleatorios o en el sentido de media cuadrática, es un proceso estocástico suave, cuya incertidumbre se tiene que cuantificar. La cuantificación de la incertidumbre es a menudo llevada a cabo calculando los principales estadísticos (esperanza y varianza) y, si es posible, la función de densidad de probabilidad. En este trabajo, estudiamos modelos aleatorios lineales, basados en ecuaciones diferenciales ordinarias con y sin retardo, y en ecuaciones en derivadas parciales. La estructura lineal de los modelos nos permite buscar ciertas soluciones probabilísticas e incluso aproximar su función de densidad de probabilidad, lo cual es un objetivo complicado en general. Una parte muy importante de la disertación se dedica a las ecuaciones diferenciales lineales de segundo orden aleatorias, donde los coeficientes de la ecuación son procesos estocásticos y las condiciones iniciales son variables aleatorias. El estudio de esta clase de ecuaciones diferenciales en el contexto aleatorio está motivado principalmente por su importante papel en la Física Matemática. Empezamos resolviendo la ecuación diferencial de Legendre aleatorizada en el sentido de media cuadrática, lo que permite la aproximación de la esperanza y la varianza de la solución estocástica. La metodología se extiende al caso general de ecuaciones diferenciales lineales de segundo orden aleatorias con coeficientes analíticos (expresables como series de potencias), mediante el conocido método de Fröbenius. Se lleva a cabo un estudio comparativo con métodos espectrales basados en expansiones de caos polinomial. Por otro lado, el método de Fröbenius junto con la simulación de Monte Carlo se utilizan para aproximar la función de densidad de probabilidad de la solución. Para acelerar el procedimiento de Monte Carlo, se proponen varios métodos de reducción de la varianza basados en reglas de cuadratura y estrategias multinivel. La última parte sobre ecuaciones diferenciales lineales de segundo orden aleatorias estudia un problema aleatorio de tipo Poisson de difusión-reacción, en el que la función de densidad de probabilidad es aproximada mediante un esquema numérico de diferencias finitas. En la tesis también se tratan ecuaciones diferenciales ordinarias aleatorias con retardo discreto y constante. Estudiamos el caso lineal y autónomo, cuando el coeficiente de la componente no retardada i el parámetro del término retardado son ambos variables aleatorias mientras que la condición inicial es un proceso estocástico. Se demuestra que la solución determinista construida con el método de los pasos y que involucra la función exponencial retardada es una solución probabilística en el sentido de Lebesgue. Finalmente, el último capítulo lo dedicamos a la ecuación en derivadas parciales lineal de advección, sujeta a velocidad y condición inicial estocásticas. Resolvemos la ecuación en el sentido de media cuadrática y damos nuevas expresiones para la función de densidad de probabilidad de la solución, incluso en el caso de velocidad no Gaussiana.
[CAT] Aquesta tesi tracta l'anàlisi d'equacions diferencials amb paràmetres d'entrada aleatoris, en la forma de variables aleatòries o processos estocàstics amb qualsevol mena de distribució de probabilitat. En modelització, els coeficients d'entrada són fixats a partir de dades experimentals, les quals solen comportar incertesa pels errors de mesurament. A més a més, el comportament del fenomen físic sota estudi no segueix patrons estrictament deterministes. És per tant més realista treballar amb models matemàtics amb aleatorietat en la seua formulació. La solució, considerada en el sentit de camins aleatoris o en el sentit de mitjana quadràtica, és un procés estocàstic suau, la incertesa del qual s'ha de quantificar. La quantificació de la incertesa és sovint duta a terme calculant els principals estadístics (esperança i variància) i, si es pot, la funció de densitat de probabilitat. En aquest treball, estudiem models aleatoris lineals, basats en equacions diferencials ordinàries amb retard i sense, i en equacions en derivades parcials. L'estructura lineal dels models ens fa possible cercar certes solucions probabilístiques i inclús aproximar la seua funció de densitat de probabilitat, el qual és un objectiu complicat en general. Una part molt important de la dissertació es dedica a les equacions diferencials lineals de segon ordre aleatòries, on els coeficients de l'equació són processos estocàstics i les condicions inicials són variables aleatòries. L'estudi d'aquesta classe d'equacions diferencials en el context aleatori està motivat principalment pel seu important paper en Física Matemàtica. Comencem resolent l'equació diferencial de Legendre aleatoritzada en el sentit de mitjana quadràtica, el que permet l'aproximació de l'esperança i la variància de la solució estocàstica. La metodologia s'estén al cas general d'equacions diferencials lineals de segon ordre aleatòries amb coeficients analítics (expressables com a sèries de potències), per mitjà del conegut mètode de Fröbenius. Es duu a terme un estudi comparatiu amb mètodes espectrals basats en expansions de caos polinomial. Per altra banda, el mètode de Fröbenius juntament amb la simulació de Monte Carlo són emprats per a aproximar la funció de densitat de probabilitat de la solució. Per a accelerar el procediment de Monte Carlo, es proposen diversos mètodes de reducció de la variància basats en regles de quadratura i estratègies multinivell. L'última part sobre equacions diferencials lineals de segon ordre aleatòries estudia un problema aleatori de tipus Poisson de difusió-reacció, en què la funció de densitat de probabilitat és aproximada mitjançant un esquema numèric de diferències finites. En la tesi també es tracten equacions diferencials ordinàries aleatòries amb retard discret i constant. Estudiem el cas lineal i autònom, quan el coeficient del component no retardat i el paràmetre del terme retardat són ambdós variables aleatòries mentre que la condició inicial és un procés estocàstic. Es prova que la solució determinista construïda amb el mètode dels passos i que involucra la funció exponencial retardada és una solució probabilística en el sentit de Lebesgue. Finalment, el darrer capítol el dediquem a l'equació en derivades parcials lineal d'advecció, subjecta a velocitat i condició inicial estocàstiques. Resolem l'equació en el sentit de mitjana quadràtica i donem noves expressions per a la funció de densitat de probabilitat de la solució, inclús en el cas de velocitat no Gaussiana.
This work has been supported by the Spanish Ministerio de Economía y Competitividad grant MTM2017–89664–P. I acknowledge the doctorate scholarship granted by Programa de Ayudas de Investigación y Desarrollo (PAID), Universitat Politècnica de València.
Jornet Sanz, M. (2020). Mean square solutions of random linear models and computation of their probability density function [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/138394
TESIS

Hypothesis-free learning is increasingly popular given the large amounts of data becoming available. Structure learning, a hypothesis-free approach, of graphical models is a field of growing interest due to the power of such models and lack of domain knowledge when applied on complex real-world data. State-of-the-art techniques improve on scalability of structure learning, which is often characterized by a large problem space. Nonetheless, these techniques still suffer computational bottlenecks that are yet to be approached. In this work, we focus on two popular models: dynamical linear systems and Markov random fields. For each case, we investigate major computational bottlenecks of baseline learning techniques. Next, we propose two frameworks that provide higher scalability using appropriate problem reformulation and efficient structure based heuristics. We perform experiments on synthetic and real data to validate our theoretical analysis. Current results show that we obtain a quality similar to expensive baseline techniques but with higher scalability.
Master of Science

Includes bibliographical references.
The analysis of growth data is important as it allows us to assess how fast things grow and determine various factors that have impact on their growth. In the current study, growth measurements on body features (body mass, wing length, head length, bill (culmen) length, foot length, and tarsus length) for Grey-headed Gulls populating Bonaero Park and Modderfontein Pan in Gauteng province, South Africa, and for Swift Terns on Robben Island were taken. Different methods such as polynomial regressions, non-parametric models and non-linear mixed effects models have been used to fit models to growth data. In recent years, non-linear mixed effects models have become an important tool for growth models. We have fitted univariate inverse exponential, Gompertz, logistic, and Richards non-linear mixed effects models to each of the six body features. We have modeled these six features simultaneously by adding a categorical covariate, which distinguishes between different features, to the model. This approach allows for straightforward comparison of growth between the different body features. In growth studies, the knowledge of the age of each individual is an essential information for growth analysis. For Swift Terns, the exact age of most chicks was unknown, but a small portion of the sample was followed from nestling up to the end of the study period. For chicks with unknown age, we estimated age by fitting the growth curve, obtained from birds with known age, to the mass measurements of the chick with unknown age. It was found that the logistic models were most appropriate to describe the growth of body mass and wing length while the Gompertz models provided best fits for bill, tarsus, head and foot for Grey-headed Gulls. For Swift Terns, the inverse exponential model provided the best univariate fit for four of six features. The logistic model, with a variance function increasing as a power of fitted values, with a different power for each feature and autoregressive correlation structure for within bird errors with errors from different features within the same subject assumed to be independent, gave the best model to describe the growth of all body features taken simultaneously for both Grey-headed Gull and Swift Tern data. It was shown that growth of Grey-headed Gull and Swift Tern chicks occurs in the following order (foot, body mass, tarsus)-(bill, head)-( wing) and (tarsus, foot)-(body mass, bill, head)-(wing) , respectively.

Abstract In a two-level hierarchical linear model(HLM2), the outcome as well as covariates may have missing values at any of the levels. One way to analyze all available data in the model is to estimate a multivariate normal joint distribution of variables, including the outcome, subject to missingness conditional on covariates completely observed by maximum likelihood(ML); draw multiple imputation (MI) of missing values given the estimated joint model; and analyze the hierarchical model given the MI [1,2]. The assumption is data missing at random (MAR). While this method yields efficient estimation of the hierarchical model, it often estimates the model given discrete missing data that is handled under multivariate normality. In this thesis, we evaluate how robust it is to estimate a hierarchical linear model given discrete missing data by the method. We simulate incompletely observed data from a series of hierarchical linear models given discrete covariates MAR, estimate the models by the method, and assess the sensitivity of handling discrete missing data under the multivariate normal joint distribution by computing bias, root mean squared error, standard error, and coverage probability in the estimated hierarchical linear models via a series of simulation studies. We want to achieve the following aim: Evaluate the performance of the method handling binary covariates MAR. We let the missing patterns of level-1 and -2 binary covariates depend on completely observed variables and assess how the method handles binary missing data given different values of success probabilities and missing rates. Based on the simulation results, the missing data analysis is robust under certain parameter settings. Efficient analysis performs very well for estimation of level-1 fixed and random effects across varying success probabilities and missing rates. MAR estimation of level-2 binary covariate is not well estimated when the missing rate in level-2 binary covariate is greater than 10%. The rest of the thesis is organized as follows: Section 1 introduces the background information including conventional methods for hierarchical missing data analysis, different missing data mechanisms, and the innovation and significance of this study. Section 2 explains the efficient missing data method. Section 3 represents the sensitivity analysis of the missing data method and explain how we carry out the simulation study using SAS, software package HLM7, and R. Section 4 illustrates the results and useful recommendations for researchers who want to use the missing data method for binary covariates MAR in HLM2. Section 5 presents an illustrative analysis National Growth of Health Study (NGHS) by the missing data method. The thesis ends with a list of useful references that will guide the future study and simulation codes we used.

A Work Project, presented as part of the requirements for the Award of a Masters Degree in Finance from the NOVA – School of Business and Economics
Predicting GDP growth is a concern of several economic agents. The right way to model such variable is far from consensual. This paper’s goal is to compare different models for GDP growth forecasting in the euro area. For comparative purposes, an autoregressive model (which is used as benchmark) and two Autoregressive Distributed Models (ADL), which contain financial and non-financial variables, chosen based on the literature, are used. The main conclusion is that the ADL(2,1,1) considered has superior forecast performance in- and out-of-sample, although in this last case depending on the evaluation metric.

Hierarchical Linear Modeling (HLM) sample size recommendations are mostly made with traditional group-design research in mind, as HLM as been used almost exclusively in group-design studies. Single-case research can benefit from utilizing hierarchical linear growth modeling, but sample size recommendations for growth modeling with HLM are scarce and generally do not consider the sample size combinations typical in single-case research. The purpose of this Monte Carlo simulation study was to expand sample size research in hierarchical linear growth modeling to suit single-case designs by testing larger level-1 sample sizes (N1), ranging from 10 to 80, and smaller level-2 sample sizes (N2), from 5 to 35, under the presence of autocorrelation to investigate bias and power. Estimates for the fixed effects were good for all tested sample-size combinations, irrespective of the strengths of the predictor-outcome correlations or the level of autocorrelation. Such low sample sizes, however, especially in the presence of autocorrelation, produced neither good estimates of the variances nor adequate power rates. Power rates were at least adequate for conditions in which N2 = 20 and N1 = 80 or N2 = 25 and N1 = 50 when the squared autocorrelation was .25.Conditions with lower autocorrelation provided adequate or high power for conditions with N2 = 15 and N1 = 50. In addition, conditions with high autocorrelation produced less than perfect power rates to detect the level-1 variance.

CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior
The present study uses linear and non-linear diffusion index models to produce one-stepahead forecast of quarterly Brazilian GDP growth rate. Diffusion index models are like dynamic factors models. These factors are latent variables that represent a common property from the explanatory variables, then allowing a considerably reduction of its number in econometric models elaborated to attend the main objective of this work. The non-linear diffusion index models used in this thesis are not only parsimonious ones, but also they try to capture economic cycles using for this goal a Threshold diffusion index model and a Markov-Switching diffusion index model. The former is used, besides for forecasting purpose, also to test if there is a non-linear pattern in the quarterly Brazilian GDP growth rate.
Esta Tese estuda modelos lineares e nÃo lineares de Ãndices de difusÃo para prever, em um perÃodo à frente, a taxa de crescimento trimestral do PIB brasileiro. Os modelos de Ãndice de difusÃo assemelham-se aos modelos de fatores dinÃmicos. Estes fatores sÃo variÃveis nÃo observÃveis e representam uma caracterÃstica em comum Ãs variÃveis explicativas, permitindo a reduÃÃo significativa do nÃmero dessas no modelo economÃtrico proposto para atender o objetivo principal deste trabalho. AlÃm de parcimoniosos, os modelos utilizados nesta Tese se propÃem a capitar as fases de recessÃo e expansÃo econÃmica, atravÃs de modelos nÃo lineares do tipo Threshold Effect e Markov-Switching, servindo o primeiro destes dois para testar a hipÃtese de que existe nÃo linearidades na variÃvel sob estudo.

In chapter 1, we consider the biases that may arise when an unmeasured confounder is omitted from a structural equation model (SEM) and sensitivity analysis techniques to correct for such biases. We give an analysis of which effects in an SEM are and are not biased by an unmeasured confounder. It is shown that a single unmeasured confounder will bias not just one but numerous effects in an SEM. We present sensitivity analysis techniques to correct for biases in total, direct, and indirect effects when using SEM analyses, and illustrate these techniques with a study of aging and cognitive function. In chapter 2, we consider longitudinal mediation with latent growth curves. We define the direct and indirect effects using counterfactuals and consider the assumptions needed for identifiability of those effects. We develop models with a binary treatment/exposure followed by a model where treatment/exposure changes with time allowing for treatment/exposure-mediator interaction. We thus formalize mediation analysis with latent growth curve models using counterfactuals, makes clear the assumptions and extends these methods to allow for exposure mediator interactions. We present and illustrate the techniques with a study on Multiple Sclerosis(MS) and depression. In chapter 3, we report on a pilot study in blended learning that took place during the Fall 2013 and Summer 2014 semesters here at Harvard. We blended the traditional BIO 200: Principles of Biostatistics and created ID 200: Principles of Biostatistics and epidemiology. We used materials from the edX course PH207x: Health in Numbers: Quantitative Methods in Clinical \& Public Health Research and used. These materials were used as a video textbook in which students would watch a given number of these videos prior to class. Using surveys as well as exam data we informally assess these blended classes from the student's perspective as well as a comparison of these students with students in another course, BIO 201: Introduction to Statistical Methods in Fall 2013 as well as students from BIO 200 in Fall semesters of 1992 and 1993. We then suggest improvements upon our original course designs and follow up with an informal look at how these implemented changes affected the second offering of the newly blended ID 200 in Summer 2014.
Biostatistics

L'analyse de sensibilité est un outil puissant qui permet d'analyser des modèles mathématiques et des codes de calculs. Elle révèle les variables d'entrées les plus influentes sur la variable de sortie, en leur affectant une valeur appelée "indice de sensibilité". Dans ce cadre, les effets de Shapley, récemment définis par Owen, permettent de gérer des variables d'entrées dépendantes. Cependant, l'estimation de ces indices ne peut se faire que dans deux cadres très particuliers : lorsque la loi du vecteur d'entrée est connue ou lorsque les entrées sont gaussiennes et le modèle est linéaire. Cette thèse se divise en deux parties. Dans la première partie, l'objectif est d'étendre les estimateurs des effets de Shapley lorsque seul un échantillon des entrées est disponible et leur loi est inconnue. Dans la deuxième partie porte sur le cas linéaire gaussien. Le problème de la grande dimension est abordé et des solutions sont proposées lorsque les variables forment des groupes indépendants. Enfin, l'étude montre comment les effets de Shapley du cadre linéaire gaussien peuvent estimer ceux d'un cadre plus général
Sensitivity analysis is a powerful tool to study mathematical models and computer codes. It reveals the most impacting input variables on the output variable, by assigning values to the the inputs, that we call "sensitivity indices". In this setting, the Shapley effects, recently defined by Owen, enable to handle dependent input variables. However, one can only estimate these indices in two particular cases: when the distribution of the input vector is known or when the inputs are Gaussian and when the model is linear. This thesis can be divided into two parts. First, the aim is to extend the estimation of the Shapley effects when only a sample of the inputs is available and their distribution is unknown. The second part focuses on the linear Gaussian framework. The high-dimensional problem is emphasized and solutions are suggested when there are independent groups of variables. Finally, it is shown how the values of the Shapley effects in the linear Gaussian framework can estimate of the Shapley effects in more general settings

Linear mixed-effects (LME) modeling is a widely used statistical method for analyzing repeated measures or longitudinal data. Such longitudinal studies typically aim to investigate and describe the trajectory of a desired outcome. Longitudinal data have the advantage over cross-sectional data by providing more accuracy for the model. LME models allow researchers to account for random variation among individuals and between individuals. In this project, adolescent health was chosen as a topic of research due to the many changes that occur during this crucial time period as a precursor to overall well-being in adult life. Understanding the factors that influence how adolescents' mental well-being is affected may aid in interventions to reduce the risk of a negative impact. Self-esteem, in particular, has been associated with many components of physical and mental health and is a crucial focus in adolescent health. Research in self-esteem is extensive yet, sometimes inconclusive or contradictory since past research has been cross-sectional in nature. Several factors associated with self-esteem development are considered. Participation in religious services has also been an interest in research for its impact on depression. Depression development and its predictors are evaluated using LME models. Along with this line, this project will address the research problems identified through the following specific topics (i) to investigate the impact of early adolescent anxiety disorders on self-esteem development from adolescence to young adulthood; (ii) to study the role of maternal self-esteem and family socioeconomic status on adolescent self-esteem development through young adulthood; and (iii) to explore the efficacy of religious service attendance in reducing depressive symptoms. These topics present a good introduction to the LME approach and are of significant public health importance. The present study explores varying scenarios of the statistical methods and techniques employed in the analysis of longitudinal data. This thesis provides an overview of LME models and the model selection process with applications. Although this project is motivated by adolescent health study, the basic concepts of the methods introduced have generally broader applications in other fields provided that the relevant technical specifications are met.

The class of models which is studied in this paper, multi-unit longitudinal models, combines both the cross-sectional and the longitudinal aspects of observations. Many empirical investigations involve the analysis of data structures that are both cross-sectional (observations are taken on several units at a specific time period or at a specific location) and longitudinal (observations on the same unit are taken over time or space). Multi-unit longitudinal data structures arise in economics and business where panels of subjects are studied over time, biostatistics where groups of patients on different treatments are observed over time, and in situations where data are taken over time and space. Modelling issues in multi-unit longitudinal models with random coefficients and patterned correlation structure are illustrated in the context of two data sets. The first data set deals with short time series data on annual death rates and alcohol consumption for twenty-five European countries. The second data set deals with glaceologic time series data on snow temperature at 14 different locations within a small glacier in the Austrian Alps. A practical model building approach, consisting of model specification, estimation, and diagnostic checking, is outlined. (author's abstract)
Series: Forschungsberichte / Institut für Statistik

Machine learning methods are now extensively applied in various scientific research areas to make models. Unlike regular models, machine learning based models use a data-driven approach. Machine learning algorithms can learn knowledge that are hard to be recognized, from available data. The data-driven approaches enhance the role of algorithms and computers and then accelerate the computation using alternative views. In this thesis, we explore the possibility of applying machine learning models in the prediction of chromatographic retention behaviors. Chromatographic separation is a key technique for the discovery and analysis of fullerenes. In previous studies, differential equation models have achieved great success in predictions of chromatographic retentions. However, most of the differential equation models require experimental measurements or theoretical computations for many parameters, which are not easy to obtain. Fullerenes/metallofullerenes are rigid and spherical molecules with only carbon atoms, which makes the predictions of chromatographic retention behaviors as well as other properties much simpler than other flexible molecules that have more variations on conformations. In this thesis, I propose the polarizability of a fullerene molecule is able to be estimated directly from the structures. Structural motifs are used to simplify the model and the models with motifs provide satisfying predictions. The data set contains 31947 isomers and their polarizability data and is split into a training set with 90% data points and a complementary testing set. In addition, a second testing set of large fullerene isomers is also prepared and it is used to testing whether a model can be trained by small fullerenes and then gives ideal predictions on large fullerenes.
Machine learning models are capable to be applied in a wide range of areas, such as scientific research. In this thesis, machine learning models are applied to predict chromatography behaviors of fullerenes based on the molecular structures. Chromatography is a common technique for mixture separations, and the separation is because of the difference of interactions between molecules and a stationary phase. In real experiments, a mixture usually contains a large family of different compounds and it requires lots of work and resources to figure out the target compound. Therefore, models are extremely import for studies of chromatography. Traditional models are built based on physics rules, and involves several parameters. The physics parameters are measured by experiments or theoretically computed. However, both of them are time consuming and not easy to be conducted. For fullerenes, in my previous studies, it has been shown that the chromatography model can be simplified and only one parameter, polarizability, is required. A machine learning approach is introduced to enhance the model by predicting the molecular polarizabilities of fullerenes based on structures. The structure of a fullerene is represented by several local structures. Several types of machine learning models are built and tested on our data set and the result shows neural network gives the best predictions.

FundaÃÃo de Amparo à Pesquisa do Estado do CearÃ
Data set of 220, 336 and 19,303 records, respectively of Poll Dorset, Somalis Brasileira and Santa InÃs sheep, born between 1996 and 2008, belonging to Gaasa AgropecuÃria Ltda, supported by Programa de Melhoramento GenÃtico de Caprinos e Ovinos de Corte (GENECOC) of Embrapa Caprinos e Ovinos, were analyzed with the aim to evaluate distinct polynomial functions with different order of fit for fixed and random regressions of growth trajectory and to estimate (co)variances components and genetic parameters of this trajectory. Fixed effects used in analysis for all breeds were contemporary group (animals born in the same year-season), sex and birth type (single, twin, triple). Separately, for each breed, 24 models, with different orders, were evaluated to verify the best fit for fixed trajectory and for random regression of additive direct, maternal and permanent environmental effects. Ordinary and Legendre polynomials, varying of two (linear) to four (cubic) orders, were evaluated for fixed regression of average growth trajectory. Legendre and quadratic bspline functions, varying of three (quadratic) to four (cubic) orders, were evaluated for random regressions. For all breeds, Legendre polynomials of order fourth were sufficient to fit random regression. However, in fixed regression, ordinary polynomials were best to Poll Dorset and Santa InÃs breeds, while Legendre were best for Somalis Brasileira. Fixed trajectory was linear for Poll Dorset and Somalis Brasileira and quadratic for Santa InÃs. In Poll Dorset, direct heritability was low (<0.05) until 100 days, when so increased until 212 days reaching 0.74. In major portion of trajectory, maternal heritability for this breed were higher than direct heritability, this last overpass the first only after 150 days of age, about 100 days after weaning of animals. In Somalis Brasileira breed, the standard of direct heritability estimates presented two parabolas: one between birth and 73 day, with maximum of 0.21 at 49 days, and other from 73 day to rest of trajectory, with maximum of 0.53 at 253-256 days. Maternal heritability increased until 76 day, with maximum of 0,95, decreasing for 0.47 at 261 day, increasing again until final of trajectory, reaching 0.80. In Santa InÃs breed, direct heritabilities at days 1, 50, 150, 250 and 411 were 0.24, 0.12, 0.44, 0.84 and 0.96, respectively, while maternal heritabilities for the same ages, respectively, were 0.24, 0.19, 0.09, 0.02 and 0.01. In all breeds, genetic correlations among weights in subsequent ages were high, tend to unity, with negative correlations between weights at early ages and weights at late ages. There is sufficient genetic variability to permit selection of these breeds for alter its growth trajectory. However, differences in standard of this variability suggest different procedures for selection of each breed. Genetic control of weights at initial ages is not the same in late ages. This aspect is important for establishment of adequate strategies of selection. Selection of animals for slaughter in early age must be different of that to replacement animals
Foram avaliados 220, 336 e 19.303 registros de pesos de ovinos, respectivamente das raÃas Poll Dorset, Somalis Brasileira e Santa InÃs, nascidos entre 1996 e 2008, de propriedade da fazenda Gaasa AgropecuÃria Ltda, associada ao Programa de Melhoramento GenÃtico de Caprinos e Ovinos de Corte (GENECOC) da Embrapa Caprinos e Ovinos, com o objetivo de avaliar distintas funÃÃes polinomiais com diferentes ordens para o melhor ajuste das regressÃes fixas e aleatÃrias da trajetÃria de crescimento e estimar os componentes de (co) variÃncia e parÃmetros genÃticos desta trajetÃria. Os efeitos fixos utilizados nas anÃlises para todas as raÃas foram grupo de contemporÃneos (animais nascidos no mesmo ano e estaÃÃo), sexo e tipo de nascimento (simples, duplo, triplo). Separadamente, para cada uma das raÃas, foram avaliados 24 modelos, com diferentes ordens, para verificar o melhor ajuste simultÃneo de regressÃo fixa da trajetÃria de crescimento e da regressÃo aleatÃria para efeitos genÃticos aditivo direto e materno e de ambiente permanente do animal. Para ajuste da regressÃo fixa da trajetÃria mÃdia de crescimento, foram avaliados polinÃmios ordinÃrios e de Legendre, com ordens variando de dois (linear) a quatro (cÃbica). Para as regressÃes aleatÃrias, foram avaliadas as funÃÃes de Legendre e b-spline quadrÃtica, com ordens variando de trÃs (quadrÃtica) a quatro (cÃbica). Para todas as raÃas, funÃÃes com polinÃmios de Legendre de quarta ordem foram suficientes para ajustar a parte aleatÃria. Entretanto, para a parte fixa, os polinÃmios ordinÃrios foram melhores para as raÃas Poll Dorset e Santa InÃs, enquanto os de Legendre foram melhores para a raÃa Somalis Brasileira. A trajetÃria fixa foi linear para as raÃas Poll Dorset e Somalis Brasileira, e quadrÃtica para a raÃa Santa InÃs. Na raÃa Poll Dorset, a herdabilidade direta se manteve baixa (<0,05) atà cerca de 100 dias de idade, quando passou a aumentar atà os 212 dias de idade, atingindo um valor de 0,74. Na maior parte da trajetÃria, as herdabilidades maternas nesta raÃa superaram as herdabilidades diretas, sendo que esta Ãltima somente ultrapassou a primeira apÃs os 150 dias de idade, cerca de 100 dias apÃs o desmame dos animais. Na raÃa Somalis Brasileira, o padrÃo das estimativas de herdabilidade direta apresentou duas parÃbolas: uma entre o nascimento e o dia 73, com valor mÃximo de 0,21 aos 49 dias, e uma outra entre 73 dias e o restante da trajetÃria, com valor mÃximo de 0,53 aos 253-256 dias. A herdabilidade materna aumentou atà o dia 76, com mÃxima de 0,95, reduzindo para 0,47 no dia 261, voltando a subir novamente atà o final da trajetÃria, alcanÃando o valor de 0,80. Na raÃa Santa InÃs, as herdabilidades diretas nos dias 1, 50, 150, 250 e 411 foram iguais a 0,24, 0,12, 0,44, 0,84, e 0,96, respectivamente, enquanto as herdabilidades maternas nas respectivas idades foram 0,24, 0,19, 0,09, 0,02 e 0,01. Em todas as raÃas, as correlaÃÃes genÃticas entre pesos de idades subseqÃentes, prÃximas entre si, foram elevadas, tendendo à unidade, havendo correlaÃÃes negativas entre pesos tomados em idades mais jovens e aqueles tomados em idades mais avanÃadas. Existe variabilidade genÃtica suficiente para permitir seleÃÃo destas raÃas, de forma a alterar suas trajetÃrias de crescimento. Entretanto, as diferenÃas no padrÃo desta variabilidade sugerem diferentes procedimentos de seleÃÃo para cada uma das raÃas. O controle genÃtico sob os pesos nas fases iniciais do crescimento nÃo à o mesmo que atua em idades mais tardias. Este aspecto à importante para o estabelecimento de adequadas estratÃgias de seleÃÃo. A seleÃÃo de animais para abate em idade jovem deve assim ser diferente daquela para animais de reposiÃÃo no rebanho

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
The analysis of growth curves of animals has been widely used to increase the efficiency of beef cattle ranching. Related to growth curves with nonlinear mixed models strategic, studies have strategic applications in genetic improving programs in defining selection criteria for earliness and weight gain, aimed at, that for each individual is estimated a random coefficient, facilitating identification and selection of more efficient animals based on the coefficients. This methodology considers the variability between and within individuals. The objective of this study was to evaluate the efficiency of the adjustment of growth curves by nonlinear mixed models. Nonlinear models, Michaelis-Menten Modified, Logistic, von Bertalanffy, Gompertz, Richards and Brody, were fitted, with and without the incorporation of random effects for analysis of growth in beef cattle Tabapuã race. For comparison between fixed and mixed models were used the following adjustment quality evaluators: Akaike s information criterion (AIC), Bayesian information criterion (BIC), mean absolute deviation (DMA), mean square error (MSE) and coefficient of determination (R2). The use of nonlinear mixed model was efficient to describe bovine growth curves.
A análise de curvas de crescimento de animais tem sido muito utilizada para aumentar a eficiência da pecuária de corte. Estudos relacionados a curvas de crescimento com modelos não lineares mistos podem ter aplicações estratégicas em programas de melhoramento genético na definição de critérios de seleção para precocidade e ganho de peso, tendo em vista, que para cada indivíduo é estimado um coeficiente aleatório, facilitando a identificação e seleção de animais mais eficientes com base nos coeficientes. Essa metodologia considera a variabilidade entre e dentro de indivíduos. O objetivo deste trabalho foi avaliar a eficiência do ajuste de curvas de crescimento através de modelos não lineares mistos. Foram ajustados os modelos não lineares Michaelis-Menten Modificado, Logístico, von Bertalanffy, Gompertz, Richards e Brody, com e sem a incorporação de efeitos aleatórios para análise de curva de crescimento de bovinos de corte da raça Tabapuã. Para comparação entre modelos fixos e mistos foram utilizados os seguintes avaliadores de qualidade de ajuste: critério de informação de Akaike (AIC), critério de informação bayesiano (BIC), desvio médio absoluto (DMA), erro quadrático médio (EQM) e coeficiente de determinação (R2). A utilização de modelos não lineares mistos foi eficiente para descrever curvas de crescimento de bovinos.

This study demonstrates a fully Bayesian approach to multilevel/hierarchical linear growth modeling using freely available software. Further, the study incorporates informative prior distributions for fixed effect estimates using an objective approach. The objective approach uses previous sample results to form prior distributions included in subsequent samples analyses, a process referred to as Bayesian updating. Further, a method for model checking is outlined based on fit indices including information criteria (i.e., Akaike information criterion, Bayesian information criterion, and deviance information criterion) and approximate Bayes factor calculations. For this demonstration, five distinct samples of schools in the process of implementing School-Wide Positive Behavior Interventions and Supports (SWPBIS) collected from 2008 to 2013 were used with the unit of analysis being the school. First, the within-year SWPBIS fidelity growth was modeled as a function of time measured in months from initial measurement occasion. Uninformative priors were used to estimate growth parameters for the 2008-09 sample, and both uninformative and informative priors based on previous years' samples were used to model data from the 2009-10, 2010-11, 2011-12, 2012-13 samples. Bayesian estimates were also compared to maximum likelihood (ML) estimates, and reliability information is provided. Second, an additional three examples demonstrated how to include predictors into the growth model with demonstrations for: (a) the inclusion of one school-level predictor (years implementing) of SWPBIS fidelity growth, (b) several school-level predictors (relative socio-economic status, size, and geographic location), and (c) school and district predictors (sustainability factors hypothesized to be related to implementation processes) in a three-level growth model. Interestingly, Bayesian models estimated with informative prior distributions in all cases resulted in more optimal fit indices than models estimated with uninformative prior distributions.

This dissertation has multiple aims in studying hierarchical linear models in biomedical data analysis. In Chapter 1, the novel idea of studying the durations of adolescent growth spurts as a predictor of adulthood obesity is defined, established, and illustrated. The concept of contextual effects modeling is introduced in this first section as we study secular trend of adulthood obesity and how this trend is mitigated by the durations of individual adolescent growth spurts and the secular average length of adolescent growth spurts. It is found that individuals with longer periods of fast height growth in adolescence are more prone to having favorable BMI profiles in adulthood. In Chapter 2 we study the estimation of contextual effects in a hierarchical generalized linear model (HGLM). We simulate data and study the effects using the higher level group sample mean as the estimate for the true mean versus using an Empirical Bayes (EB) approach (Shin and Raudenbush 2010). We study this comparison for logistic, probit, log-linear, ordinal and nominal regression models. We find that in general the EB estimate lends a parameter estimate much closer to the true value, except for cases with very small variability in the upper level, where it is a more complicated situation and there is likely no need for contextual effects analysis. In Chapter 3 the HGLM studies are made clearer with large-scale simulations. These large scale simulations are shown for logistic regression and probit regression models for binary outcome data. With repetition we are able to establish coverage percentages of the confidence intervals of the true contextual effect. Coverage percentages show the percentage of simulations that have confidence intervals containing the true parameter values. Results confirm observations from the preliminary simulations in the previous section of this paper, and an accompanying example of adulthood hypertension shows how these results can be used in an application.

Signal extraction in tree-ring research is considered as a general time series decomposition problem. A linear aggregate model for a hypothetical ring-width series is proposed, which allows the problem to be reduced to the estimation and extraction of five discrete classes of signals. These classes represent the signals due to trend, climate, endogenous disturbance, exogenous disturbance, and random error. For each class of signal, some mathematical/statistical techniques of estimation are described and reviewed. Except for the exogenous disturbance signal, the techniques only require information contained within the ring-width series, themselves. A unified mathematical framework for solving this decomposition problem has not yet been explicitly formulated. However, the general applicability of ARMA time series models to this problem and the power and flexibility of state space modelling suggest that these techniques will provide the closest thing to a unified framework in the future.

Understanding the complex dynamics that underpin the response of structures in the occurrence of earthquakes is of paramount importance in ensuring community resilience. The operational continuity of structures is influenced by the performance of nonstructural components, also known as secondary structures. Inherent vulnerability characteristics, nonlinearities and uncertainties in their properties or in the excitation pose challenges that render their response determination as a non-straightforward task. This dissertation settles in the context of mathematical modelling and response quantification of seismically driven secondary systems. The case of bilinear hysteretic, rigid-plastic and free-standing rocking oscillators is first considered, as a representative class of secondary systems of distinct behaviour excited at a single point in the primary structure. The equations governing their full dynamic interaction with linear primary oscillators are derived with the purpose of assessing the appropriateness of simplified analysis methods where the secondary-primary feedback action is not accounted for. Analyses carried out in presence of pulse-type excitation have shown that the cascade approximation can be considered satisfactory for bilinear systems provided the secondary-primary mass ratio is adequately low and the system does not approach resonance. For the case of sliding and rocking systems, much lighter secondary systems need to be considered if the cascade analysis is to be adopted, with the validity of the approximation dictated by the selection of the input parameters. Based on the premise that decoupling is permitted, new analytical solutions are derived for the pulse driven nonlinear oscillators considered, conveniently expressing the seismic response as a function of the input parameters and the relative effects are quantified. An efficient numerical scheme for a general-type of excitation is also presented and is used in conjunction with an existing nonstationary stochastic far-field ground motion model to determine the seismic response spectra for the secondary oscillators at given site and earthquake characteristics. Prompted by the presence of uncertainty in the primary structure, and in line with the classical modal analysis, a novel approach for directly characterising uncertainty in the modal shapes, frequencies and damping ratios of the primary structure is proposed. A procedure is then presented for the identification of the model parameters and demonstrated with an application to linear steel frames with uncertain semi-rigid connections. It is shown that the proposed approach reduces the number of the uncertain input parameters and the size of the dynamic problem, and is thus particularly appealing for the stochastic assessment of existing structural systems, where partial modal information is available e.g. through operational modal analysis testing. Through a numerical example, the relative effect of stochasticity in a bi-directional seismic input is found to have a more prominent role on the nonlinear response of secondary oscillators when compared to the uncertainty in the primary structure. Further extending the analyses to the case of multi-attached linear secondary systems driven by deterministic seismic excitation, a convenient variant of the component-mode synthesis method is presented, whereby the primary-secondary dynamic interaction is accounted for through the modes of vibration of the two components. The problem of selecting the vibrational modes to be retained in analysis is then addressed for the case of secondary structures, which may possess numerous low frequency modes with negligible mass, and a modal correction method is adopted in view of the application for seismic analysis. The influence of various approaches to build the viscous damping matrix of the primary-secondary assembly is also investigated, and a novel technique based on modal damping superposition is proposed. Numerical applications are demonstrated through a piping secondary system multi-connected on a primary frame exhibiting various irregularities in plan and elevation, as well as a multi-connected flexible secondary system. Overall, this PhD thesis delivers new insights into the determination and understanding of the response of seismically driven secondary structures. The research is deemed to be of academic and professional engineering interest spanning several areas including seismic engineering, extreme events, structural health monitoring, risk mitigation and reliability analysis.

Orientador: Jamil Viana Pereira
Resumo: Neste trabalho, será abordada a teoria matemática utilizada no estudo de quatro modelos clássicos de crescimento populacional: Malthus, Verhulst, Gompertz e Montroll. Serão apresentadas e/ou discutidas algumas de suas características, propriedades, diferenças e diferentes métodos para obtenção de seus parâmetros. Posteriormente, estes modelos e métodos serão aplicados a um conjunto de dados relativos ao crescimento populacional do Brasil. Também foi elaborada uma atividade para ser aplicada no Ensino Médio, na qual se explora, por tabelas e gráficos, a forma como os alunos observam certos fenômenos de crescimento, bem como, construtivamente e com auxílio de dados, a forma como ocorrem esses crescimentos de fato.
Abstract: In this work, the mathematical theory of four classic population growth models (Malthus, Verhulst, Gompertz and Montroll) will be addressed. Some of their characteristics, properties, differences and different methods for obtaining their parameters will be presented and/or discussed. Subsequently, these models and methods will be applied to a Brazilian population growth data set. An activity was also elaborated to be applied in high school. It explores, by tables and graphs, how students observe some growth phenomena, as well as, constructively and with the help of data, how these growths really occur.
Mestre

The purpose of this research was to compare results from two approaches to measuring change over time. The multilevel model (MLM) and latent growth model (LGM) were imposed and the parameter estimates were compared, along with model fit. The study came out of education and used data collected from 191 teachers as part of a professional development intervention in science, which took place over four years. There were missing data as a result of teacher attrition. Teachers reported use of reform-oriented practices (ROP) was used as the outcome, and teacher-level variables were examined for their impact on initial ROP and change in ROP from baseline to one year after the intervention. Change in ROP was examined using a piecewise change model where two linear slopes were modeled. The first slope estimated the change from baseline to T1, or the initial change after the intervention while the second slope estimated the change from T1 to T3, or the secondary change. Parameter estimates obtained from MLM and LGM for a model using the error covariance structure commonly assumed in MLM (i.e., random slopes, homogeneous level-1 variance) were nearly identical. Models with various alternative covariance structures (commonly associated with the LGM framework) were examined, and results were nearly identical. Most of the model fit information was in agreement regarding the best fitting model being the model that assumed the typical MLM error covariance structure with the exception of the standardized root mean square residual (SRMR) fit index. The results from the models demonstrated that ROP increased after participating in the first year of the intervention and this level was sustained, though did not increase significantly in subsequent years. There was more variation in ROP at baseline. This information tells us that the intervention was successful in that after participating in the intervention the teachers' used ROP more frequently. The success of the intervention did not depend on any of the predictors that we assessed, and, as a group, the teachers became more similar in their use of reform-oriented practices over time.

Thesis (MSc)--Stellenbosch University, 2011.
ENGLISH ABSTRACT: An integro-differential equation describing the dynamical behaviour of phytoplankton cells is considered in which the effects of cell division and aggregation are incorporated by coupling the coagulation-fragmentation equation with growth, and the McKendrick-von Foerster renewal model of an age-structured population. Under appropriate conditions on the model parameters, the associated initial-boundary value problem is shown to be well posed in a physically relevant Banach space using the theory of strongly continuous semigroups of operators, the theory of perturbation of positive semigroups and the semilinear abstract Cauchy problems theory. In particular, we provide sufficient conditions for honesty of the model. Finally, the results on the effects of the growth-fragmentation-coagulation on the overall evolution of the phytoplankton population are summarised.
AFRIKAANSE OPSOMMING: ’n Integro-differensiaalvergelyking wat die dinamiese ontwikkeling van fitoplanktonselle beskryf, word beskou. Die uitwerking van seldeling en -aggregasie is geïnkorporeer deur die vergelyking van koagulasie en fragmentasie met groeiaan die McKendrick-von Foerster hernuwingsmodel van ’n ouderdomsgestruktureerde populasie te koppel. Die teorie van sterk kontinue semigroepe van operatore, steuringsteorie van positiewe semigroepe en die teorie van semilineêre abstrakte Cauchy probleme word aangewend om, onder gepaste voorwaardes met betrekking tot die model se parameters, te bewys dat die geassosieerde beginwaarde-probleem met randvoorwaardes ‘goed gestel’ is in ’n fisies relevante Banach-ruimte. In die besonder word voldoende voorwaardes vir eerlikheid van die model verskaf. Ten slotte word ’n opsomming van die resultate met betrekking tot die gekombineerde uitwerking van groei-fragmentasie- koagulasie op die gesamentlike ontwikkeling van die fitoplanktonpopulasie verskaf.

Après une introduction générale et la présentation d'un exemple explicite dans le chapitre 1, nous exposons certains outils et techniques généraux dans le chapitre 2.- dans le chapitre 3, nous démontrons l'existence d'un principe de grandes déviations (PGD) pour les composantes de Cartan le long des marches aléatoires sur les groupes linéaires semi -simples G. L'hypothèse principale porte sur le support S de la mesure de la probabilité en question et demande que S engendre un semi-groupe Zariski dense. - Dans le chapitre 4, nous introduisons un objet limite (une partie de la chambre de Weyl) que l'on associe à une partie bornée S de G et que nous appelons le spectre joint J(S) de S. Nous étudions ses propriétés et démontrons que J(S) est une partie convexe compacte d'intérieur non-vide dès que S engendre un semi -groupe Zariski dense. Nous relions le spectre joint avec la notion classique du rayon spectral joint et la fonction de taux du PGD pour les marches aléatoires. - Dans le chapitre 5, nous introduisons une fonction de comptage exponentiel pour un S fini dans G, nous étudions ses propriétés que nous relions avec J(S) et démontrons un théorème de croissance exponentielle dense. - Dans le chapitre 6, nous démontrons le PGD pour les composantes d'Iwasawa le long des marches aléatoires sur G. L'hypothèse principale demande l'absolue continuité de la mesure de probabilité par rapport à la mesure de Haar.- Dans le chapitre 7, nous développons des outils pour aborder une question de Breuillard sur la rigidité du rayon spectral d'une marche aléatoire sur le groupe libre. Nous y démontrons un résultat de rigidité géométrique
After giving a detailed introduction andthe presentation of an explicit example to illustrateour study in Chapter 1, we exhibit some general toolsand techniques in Chapter 2. Subsequently,- In Chapter 3, we prove the existence of a large deviationprinciple (LDP) with a convex rate function, forthe Cartan components of the random walks on linearsemisimple groups G. The main hypothesis is onthe support S of the probability measure in question,and asks S to generate a Zariski dense semigroup.- In Chapter 4, we introduce a limit object (a subsetof the Weyl chamber) that we associate to a boundedsubset S of G. We call this the joint spectrum J(S)of S. We study its properties and show that for asubset S generating a Zariski dense semigroup, J(S)is convex body, i.e. a convex compact subset of nonemptyinterior. We relate the joint spectrum withthe classical notion of joint spectral radius and therate function of LDP for random walks on G.- In Chapter 5, we introduce an exponential countingfunction for a nite S in G. We study its properties,relate it to joint spectrum of S and prove a denseexponential growth theorem.- In Chapter 6, we prove the existence of an LDPfor Iwasawa components of random walks on G. Thehypothesis asks for a condition of absolute continuityof the probability measure with respect to the Haarmeasure.- In Chapter 7, we develop some tools to tackle aquestion of Breuillard on the rigidity of spectral radiusof a random walk on a free group. We prove aweaker geometric rigidity result

In this thesis, we study numerical analysis for random processes and fields. We investigate the behavior of the approximation accuracy for specific linear methods based on a finite number of observations. Furthermore, we propose techniques for optimizing performance of the methods for particular classes of random functions. The thesis consists of an introductory survey of the subject and related theory and four papers (A-D). In paper A, we study a Hermite spline approximation of quadratic mean continuous and differentiable random processes with an isolated point singularity. We consider a piecewise polynomial approximation combining two different Hermite interpolation splines for the interval adjacent to the singularity point and for the remaining part. For locally stationary random processes, sequences of sampling designs eliminating asymptotically the effect of the singularity are constructed. In Paper B, we focus on approximation of quadratic mean continuous real-valued random fields by a multivariate piecewise linear interpolator based on a finite number of observations placed on a hyperrectangular grid. We extend the concept of local stationarity to random fields and for the fields from this class, we provide an exact asymptotics for the approximation accuracy. Some asymptotic optimization results are also provided. In Paper C, we investigate numerical approximation of integrals (quadrature) of random functions over the unit hypercube. We study the asymptotics of a stratified Monte Carlo quadrature based on a finite number of randomly chosen observations in strata generated by a hyperrectangular grid. For the locally stationary random fields (introduced in Paper B), we derive exact asymptotic results together with some optimization methods. Moreover, for a certain class of random functions with an isolated singularity, we construct a sequence of designs eliminating the effect of the singularity. In Paper D, we consider a Monte Carlo pricing method for arithmetic Asian options. An estimator is constructed using a piecewise constant approximation of an underlying asset price process. For a wide class of Lévy market models, we provide upper bounds for the discretization error and the variance of the estimator. We construct an algorithm for accurate simulations with controlled discretization and Monte Carlo errors, andobtain the estimates of the option price with a predetermined accuracy at a given confidence level. Additionally, for the Black-Scholes model, we optimize the performance of the estimator by using a suitable variance reduction technique.

Modelos não lineares como o Logístico e o Gompertz são amplamente usados para descrever vários processos biológicos por meio da curva de crescimento dada pela equação do modelo. O objetivo deste trabalho foi ajustar o modelo Chanter, assim como o Logístico e o Gompertz, utilizando um conjunto de dados do fruto do cacaueiro. O modelo Chanter é um híbrido entre o modelo Logístico e o modelo Gompertz cujos parâmetros podem ser interpretados similarmente. A comparação sobre a qualidade do ajuste entre os modelos foi feita utilizando as seguintes medidas estatísticas: o critério de informação de Akaike (AIC), o critério Peso de Akaike, o critério de informação de Bayes (BIC), o desvio padrão residual (DPR) e as medidas de não linearidade vício de Box e curvatura de Bates e Watts além de um estudo de simulação. Verificou-se que o modelo Chanter dentre os modelos estudados neste trabalho é o mais adequado para o ajuste dos dados do fruto do cacaueiro.
Nonlinear models such as Logistic and Gompertz are widely used to describe several biological processes using a growth curve given by the equation of the model. The objective of this work was to adjust the Chanter model, as well as the Logistic and the Gompertz, using a data set of cocoa fruit. The Chanter model is a hybrid between the Logistic model and the Gompertz model whose parameters can be interpreted similarly. A comparison of the quality of fit between the models was made using the following statistical measures: the Akaike information criterion (AIC), the Akaike weight criterion, Bayes information criterion (BIC), residual standard deviation (RSD), and measures of non-linearity Box addiction and Bates and Watts curvature as well as a simulation study. It was verified that the Chanter model is the most suitable one among the studied models for modeling the cocoa data.

Em experimentos que envolvam um fator quantitativo e um qualitativo, é aconselhável que, se detectado efeito significativo da interação entre os fatores na análise de variância, recorra-se a análise de regressão no desdobramento da mesma, no entanto nem sempre a utilização de modelos de regressão linear é a forma mais adequada para avaliar o efeito do fator quantitativo. Neste trabalho é apresentada a forma de ajuste de um modelo de regressão não linear em um experimento com medida repetida no tempo. No experimento considerou-se o ganho de peso, em quilos, de ovinos, machos e fêmeas, da raça Santa Inês em doze idades diferentes. Conduzido como parcela subdividida, pois fator tempo não foi aleatorizado, a análise variância necessita de correção dos graus de liberdade devido à condição de esfericidade não satisfeita. A correção de Geisser e Greenhouse (G-G) foi utilizada para os efeitos da interação e do tempo. O teste F na análise de variância apresentou resultado significativo para interação entre os fatores e, no desdobramento da interação, para avaliação do efeito do fator tempo em cada nível do fator sexo foi proposto o ajuste do modelo Gompertz bem como um teste de aderência para o modelo. Após o ajuste do modelo aos dados de peso de ovinos também foi considerado no estudo a comparação dos parâmetros das curvas de machos e fêmeas. Pela análise proposta foi possível concluir que o modelo univariado, com esquema de parcelas subdivididas, pode ser utilizado em experimentos de crescimento animal, porém sua aplicação está sujeita a verificação da condição de esfericidade. Também foi verificado que incorporar, no desdobramento de interações, o ajuste do modelo Gompertz é um procedimento viável e permitiu avaliar a real qualidade de ajuste do modelo aos dados. Com a comparação dos parâmetros das curvas ajustadas verificou-se que ovinos machos e fêmeas apresentam valores estatisticamente iguais para os parâmetros α e γ, ambos relacionados com o peso ao nascer dos animais. O peso máximo esperado para fêmea (40,7kg) é estatisticamente inferior ao encontrado para os machos (57,3kg), no entanto, sua taxa de crescimento (0,011kg/dia para fêmeas) é superior (0,007kg/dia para machos), ou seja, as fêmeas atingem o peso de estabilização mais rapidamente que os machos.
In experiments involving a qualitative and a quantitative factor, it is advisable that if a significant interaction is detected between factors in the analysis of variance, one should perform regression analysis of the splitting factors. However, the use of linear regression models is not always the most appropriate way to assess the effect of the quantitative factor. This paper presents a way to fit a nonlinear regression model in an experiment with repeated measurements over time. In the experiment, the weight gain of male and female Santa Inês breed sheep, in pounds, in twelve different ages is measured. Conducted in a split-plot design, as the time factor was not randomized, the analysis of variance requires correction of the degrees of freedom, as the sphericity condition is not satisfied. The Greenhouse and Geisser correction (G-G) was used for the purposes of interaction and time. The F test in the analysis of variance showed a significant result for the interaction between the factors and the splitting of the interaction. In order to evaluate the effect of the time factor at each level of the gender factor, a Gompertz model was proposed, as well as a test of model adherence. After fitting the model to the data, a comparison study of the parameters for males and females was also made. For the proposed analysis, we concluded that the univariate model, with split-plot design, can be used in experiments of animal growth, but its application is prone to verification of the sphericity condition. They also found that the incorporation of the splitting of interactions, by adjusting the Gompertz model, is a viable procedure and allowed to evaluate the real quality of fit. By comparing the fitted parameter values, it was found that males and females have statistically identical values for the parameters α and γ, both related to the birth weight of the animals. The maximum weight expected for a female (40.7 kg) is statistically lower than that found for the males (57.3 kg), however, their growth rate (0.011 kg / day for females) is greater than the males\' (0.007 kg / day for males), i.e., females reach weight stabilization faster than males.

Resumo: Foram estimados parâmetros genéticos para pesos do nascimento à idade adulta de animais da raça Canchim por meio de análises uni, bi e multicaracterística, e por modelos de regressão aleatória. Os dados analisados são provenientes do rebanho da raça Canchim da Embrapa Pecuária Sudeste, localizada no município de São Carlos, São Paulo. Os pesos foram obtidos do nascimento até os nove anos e meio de idade. Nas análises uni, bi e multicaracterística foram utilizados pesos em ao nascimento, desmama, 12, 18, 24 e 30 meses de idade e, na idade adulta. Na análise unicaracterística foram utilizados quatro modelos, em que, diferentes efeitos aleatórios (efeito genético materno e de ambiente permanente materno) foram adicionados em seqüência. Nas análises de regressão aleatória, foram utilizados pesos de fêmeas do nascimento até os nove anos e meio de idade, considerando como funções base polinômios de Legendre e funções "b-splines". A variância residual foi modelada utilizando 1, 4, 11 e 19 classes. Foram utilizados 12 modelos de regressão aleatória sobre polinômios de Legendre de segunda à sétima ordem para modelar a trajetória da variância dos efeitos genético aditivo direto e aditivo materno e de ambiente permanente direto e materno. Vinte modelos de regressão aleatória sobre funções "bsplines" foram considerados, empregando polinômios linear, quadrático e cúbico para cada segmento individual. Polinômios do mesmo grau foram considerados no modelo para todos os efeitos aleatórios. Até sete segmentos foram utilizados para os efeitos genético direto e de ambiente permanente do animal. Para os efeitos genético aditivo materno e de ambiente permanente materno foi utilizado um único segmento com dois nós nos extremos da curva Os efeitos maternos influenciam os pesos do nascimento aos dois anos de idade sendo o peso à desmama... (Resumo completo, clicar acesso eletrônico abaixo)
Abstract: Genetic parameters were estimated for weights taken from birth to mature age in Canchim (5/8 Charolais + 3/8 Zebu) cattle of breed by one, two and multitrait analyses and by random regression models. The data analyzed were from a herd of Canchim beef cattle belonging to Embrapa's Southeast Cattle Research Center, located in São Carlos county, state of São Paulo. Weights were taken from birth to nine and half years of age. Weights at birth, weaning, 12, 18, 24 and 30 months of age and at mature age were analyzed using one, two and multitrait models. In onetrait analyses, four models were tested, in which different random effects (genetic and environment permanent maternal effects) were added. For random regression models age of cow varied from birth to 3.542 days of age. Legendre polynomials and b-splines functions of age at recording were used as basis functions in random regression models. Residual variances were modeled by a step function with 1, 4, 11 and 19 classes. A total of 12 random regression models using Legendre polynomials as basis functions, from second to seventh order, were used to model direct and maternal genetic effects, animal and maternal permanent environmental effects. A total of twenty analyses, considering linear, quadratic and cubic b-splines functions and up to nine knots, were carried out. Spline functions of the same order were considered for all random effects. Maternal effects influenced weights from birth until two years of age, being weaning weight the most affected by maternal effects. Direct heritabilities obtained by twotrait and multitrait analyses were higher than estimates obtained from onetrait analyses. In order to estimate genetic parameters for weights after selection it is important to consider weights before selection and the multitrait analyses is the most adequate. The model with direct and maternal genetic effects, animal and maternal... (Complete abstract click electronic access below)
Orientador: Maurício Mello de Alencar
Coorientadora: Lúcia Galvão de Albuquerque
Banca: Humberto Tonhati
Banca: Henrique Nunes de Oliveira
Banca: Lenira El Faro Zadra
Banca: Maria Eugênia Zerlotti Mercadante
Doutor

In an effort to assess the predictive ability of exchange rate models when data on African countries is sampled, this paper studies nonlinear modelling and prediction of the nominal exchange rate series of the United States dollar to currencies of thirty-eight African states using the smooth transition autoregressive (STAR) model. A three step analysis is undertaken. One, it investigates nonlinearity in all nominal exchange rate series examined using a chain of credible statistical in-sample tests. Significantly, evidence of nonlinear exponential STAR (ESTAR) dynamics is detected across all series. Two, linear models are provided another chance to make it right by shuffling to data on African countries to investigate their predictive power against the tough random walk without drift model. Linear models again failed significantly. Lastly, the predictive ability of nonlinear models against both the random walk without drift and the corresponding linear models is investigated. Nonlinear models display useful forecasting gains over all contending models.