Regression analysis refers to techniques for modeling and analyzing several variables in statistical learning. There are various types of regression models. In our study, we analyzed Generalized Partial Linear Models (GPLMs), which decomposes input variables into two sets, and additively combines classical linear models with nonlinear model part. By separating linear models from nonlinear ones, an inverse problem method Tikhonov regularization was applied for the nonlinear submodels separately, within the entire GPLM. Such a particular representation of submodels provides both a better accuracy and a better stability (regularity) under noise in the data. We aim to smooth the nonparametric part of GPLM by using a modified form of Multiple Adaptive Regression Spline (MARS) which is very useful for high-dimensional problems and does not impose any specific relationship between the predictor and dependent variables. Instead, it can estimate the contribution of the basis functions so that both the additive and interaction effects of the predictors are allowed to determine the dependent variable. The MARS algorithm has two steps: the forward and backward stepwise algorithms. In the rst one, the model is built by adding basis functions until a maximum level of complexity is reached. On the other hand, the backward stepwise algorithm starts with removing the least significant basis functions from the model. In this study, we propose to use a penalized residual sum of squares (PRSS) instead of the backward stepwise algorithm and construct PRSS for MARS as a Tikhonov regularization problem. Besides, we provide numeric example with two data sets / one has interaction and the other one does not have. As well as studying the regularization of the nonparametric part, we also mention theoretically the regularization of the parametric part. Furthermore, we make a comparison between Infinite Kernel Learning (IKL) and Tikhonov regularization by using two data sets, with the difference consisting in the (non-)homogeneity of the data set. The thesis concludes with an outlook on future research.

The Plasmodium vivax Duffy Binding Protein (DBP) is the ligand in the major pathway for P. vivax invasion of human reticulocytes, making it an appealing vaccine candidate. Region II of DBP (DBP-RII) is the minimal portion of the ligand that mediates recognition of the Duffy Antigen Receptor for Chemokines (DARC receptor) on the reticulocyte surface and constitutes the primary vaccine target. Analysis of natural variation in the coding sequences of DBP-RII revealed signature evidence for selective pressure driving variation in the residues of the putative receptor-binding site. We hypothesize that anti-DBP immunity in P. vivax infections is strain-specific and hindered by polymorphic residues altering sensitivity to immune antibody inhibition. To comprehend the human IgG response following P. vivax infections we investigated the specificity of IgG in Pursat Province, Western Cambodia. Using ELISAs, we quantified the antibody titer against five variant alleles of DBP-RII. We also sequenced the DBP-RII of the field isolates to determine their relationship to the variant alleles used in the ELISAs. When correlating the IgG titer between the DBP variants a strain-specific immune response was observed in patients with a high antibody titer to DBP-RII_AH as compared to the other variants. This was different from the correlation of high antibody titers between DBP-RII_P and DBP-RII_7.18 (ρ=0.88, p-value<0.0001) and DBP-RII_P and DBP-RII_O (ρ=0.87, p-value<0.0001). There appeared to be little correlation between specific polymorphic residues and IgG titer. Understanding the immune response to the polymorphisms within PvDBP will allow further identification of epitopes to enable the production of a more effective P. vivax vaccine

A generalized design-comparable effect size modeling and estimation for multiple baseline designs across individuals has been proposed and evaluated by Restricted Maximum Likelihood method in a hierarchical linear model using R. This report evaluates the exact approach of the modeling and estimation by SAS. Three models (MB3, MB4 and MB5) with same fixed effects and different random effects are estimated by PROC MIXED procedure with REML method. The unadjusted size and adjusted effect size are then calculated by matrix operation package PROC IML. The estimations for the fixed effects of the three models are similar to each other and to that of R. The variance components estimated by the two software packages are fairly close for MB3 and MB4, but the results are different for MB5 which exhibits boundary conditions for variance-covariance matrix. This result suggests that the nlme library in R works differently than the PROC MIXEDREML method in SAS under extreme conditions. / text

The objectives of this research are to measure the aquifer properties (S, T, and K) of selected watersheds delineated to the U.S. Geological Survey gauging stations using streamflow recession and baseflow data and to describe the relations among the properties of shallow aquifers and the physical properties of the basins, such as slope, regolith type and thickness, and land use type. Geographic Information System (GIS) techniques are utilized to investigate critical physiographic controls on transmissivity and storage coefficients on a regional basis. Moreover, the effect of evapotranspiration on recession index is illustrated. Finally, a detailed quantitative comparison of results for the Piedmont and the Blue Ridge Physiographic Provinces in southeast of the U.S. is provided. Recession index, annual groundwater recharge, and annual baseflow data were obtained from 44 USGS-gauging stations with drainage areas larger than 2 (mi2) and less than 400 (mi2). These gauging stations are located in Georgia and North Carolina. Analyses of data focused on GIS techniques to estimate watershed parameters such as total stream length, drainage density, groundwater slope, and aquifer half-width. The hydraulic diffusivity, transmissivity, and storage coefficient of watersheds were computed using hydrograph techniques and the Olmsted and Hely, and Rorabaugh mathematical models. Median recession index values for the Blue Ridge and Piedmont Provinces are 87.8 and 74.5 (d/log cycle), respectively. Median areal diffusivity values for the Blue Ridge and Piedmont are 35,000 and 44,200 (ft2/d), respectively. Median basin-specific estimates of transmissivity for basins in the Blue Ridge and Piedmont are 150 and 410 (ft2/d), respectively. The large values of transmissivity obtained for the Piedmont regolith may be attributed to the thick regolith, low values of basin relief, and voids that develop as a result of fracturing, foliation, weathering, and fractured quartz veins in the saprolite. Median basin-specific estimates of storage coefficient for basins in the Blue Ridge and Piedmont are 0.005 and 0.009, respectively. In general, the results from this study reveal great differences in basin-specific hydraulic parameters of the regolith material within the Piedmont compared to that of the Blue Ridge Physiographic Province.

The National health and nutrition examination survey (NHANES) is a respected nation-wide program in charge of assessing the health and nutritional status of adults and children in United States. Recent cal research found that folic acid play an important role in preventing baby birth defects. In this paper, we use the generalized estimating equation (GEE) method to study the generalized linear model (GLM) with compound symmetric correlation matrix for the NHANES data and investigate significant factors to ence the intake of food folic acid.

This paper develops a new approach to the analysis of longitudinal paired comparison data, where comparisons of the same objects by the same judges are made on more than one occasion. As an alternative to other recent approaches to such data, which are based on Kalman filter- ing, our approach treats the problem as one of multivariate multinomial data, allowing dependence terms between comparisons over time to be incorporated. The resulting model can be fitted as a Poisson log-linear model and has parallels with the quadratic binary exponential distribution of Cox. An example from the British Household Panel Survey illustrates the approach. (author´s abstract) / Series: Research Report Series / Department of Statistics and Mathematics

This thesis develops hierarchical spatial models for the analysis of correlated and overdispersed count data based on the negative binomial distribution. Model development is motivated by a large scale study of fire frequency in British Columbia, conducted by the Pacific Forestry Service. Specific to our analysis, the main focus lies in examining the interaction between wildfire and forest insect outbreaks. In particular, we wish to relate the frequency of wildfire to the severity of mountain pine beetle (MPB) outbreaks in the province. There is a widespread belief that forest insect outbreaks lead to an increased frequency of wildfires; however, empirical evidence to date has been limited and thus a greater understanding of the association is required. This is critically important as British Columbia is currently experiencing a historically unprecedented MPB outbreak. We specify regression models for fire frequency incorporating random effects in a generalized linear mixed modeling framework. Within such a framework, both spatial correlation and extra-Poisson variation can be accommodated through random effects that are incorporated into the linear predictor of a generalized linear model. We consider a range of models, and conduct model selection and inference within the Bayesian framework with implementation based on Markov Chain Monte Carlo.

In this thesis we study two discrete optimization problems: Traffic Light Synchronization and Location with Customers Orderings. A widely used approach to solve the synchronization of traffic lights on transport networks is the maximization of the time during which cars start at one end of a street and can go to the other without stopping for a red light (bandwidth maximization). The mixed integer linear model found in the literature, named MAXBAND, can be solved by optimization solvers only for small instances. In this manuscript we review in detail all the constraints of the original linear model, including those that describe all the cyclic routes in the graph, and we generalize some bounds for integer variables which so far had been presented only for problems that do not consider cycles. Furthermore, we summarized the first systematic algorithm to solve a simpler version of the problem on a single street. We also propose a solution algorithm that uses Tabu Search and Variable Neighbourhood Search and we carry out a computational study. In addition we propose a linear formulation for the shortest path problem with traffic lights constraints (SPTL). On the other hand, the simple plant location problem with order (SPLPO) is a variant of the simple plant location problem (SPLP) where the customers have preferences on the facilities which will serve them. In particular, customers define their preferences by ranking each of the potential facilities. Even though the SPLP has been widely studied in the literature, the SPLPO has been studied much less and the size of the instances that can be solved is very limited. In this manuscript, we propose a heuristic that uses a Lagrangean relaxation output as a starting point of a semi-Lagrangean relaxation algorithm to find good feasible solutions (often the optimal solution). We also carry out a computational study to illustrate the good performance of our method. Last, we introduce the partial and stochastic versions of SPLPO and apply the Lagrangean algorithm proposed for the deterministic case to then show examples and results.

[pt] O uso da técnica bootstrap para construção de intervalos de confiança e testes de hipóteses vem aumentando consideravelmente desde seu surgimento, em 1979, devido principalmente ao rápido avanço computacional ocorrido nas últimas décadas. Neste trabalho utilizamos o bootstrap paramétrico e não-paramétrico para estudar o comportamento dos hiperparametros em modelos de espaço de estados nos casos de nível e tendência linear locais. Intervalos de confiança baseados em quatro métodos bootstrap diferentes são calculados e comparados quanto à probabilidade de cobertura, produzindo resultados satisfatórios. Constatamos também a eficiência dos testes boopstrap para os casos em que os hiperparâmetros caem no limite do espaço paramétrico, situação que inviabiliza o uso dos testes clássicos por violar uma das condições de regularidade do estimador de máxima verossimilhança. / [en] Bootstrap procedures to calculate confidence intervals and hypotheses tests had considerable growth since its first appearance, in 1979, mostly due to the rapid computational developments that occurred in the last decades. In this work we employ the parametric and nonparametric boorstrap to study the behaviour of hyperparameters in state-space models in the case of local level and linear trend. Confidence intervals based on four different bootstrap methods are computed and compared using the coverage probabilities, with satisfactory results. We also verify the efficiency of bootstrap tests in cases where the hyperparameters lie on the boundary of the parameter space, situation that makes the classical tests inadequate to use, as it violates one of the regularity conditions of the maximum likelihood estimator.

Orientador: Rubén Augusto Romero Lázaro / Resumo: Tradicionalmente, o problema de Planejamento da Expansão de Sistemas de Transmissão (PEST) é solucionado considerando apenas um único cenário de geração, embora sistemas elétricos reais operem em diferentes cenários de geração. Nessa pesquisa são propostos modelos matemáticos para resolver o problema de PEST, considerando múltiplos cenários de geração de forma que o plano de expansão obtido permita uma operação adequada do sistema. No modelo proposto, o custo de investimento é maior em relação aos planos de expansão encontrados pelo planejamento tradicional, que considera apenas um cenário de geração. Para reduzir o correspondente custo de investimento são apresentadas estratégias eficientes para encontrar planos de expansão para o problema de PEST considerando múltiplos cenários. As estratégias utilizadas foram: permitir pequenos cortes de carga; permitir o deslocamento do nível de geração em uma pequena faixa de geração mínima e máxima em relação à geração ideal e permitir pequenas sobrecargas nas linhas de transmissão. Adicionalmente, uma combinação entre essas estratégias é apresentada e o problema PEST também foi resolvido para o planejamento multiestágio, considerando múltiplos cenários de geração. O método proposto foi implementado com o uso da linguagem de modelagem algébrica AMPL e resolvido com o uso do solver comercial CPLEX. Os resultados encontrados correspondem à propostas de solução que são válidas para diferentes cenários de geração e apresentam diferentes alt... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: Traditionally, the Transmission Network Expansion Problem is solved considering only a single generation scenario. However, a real power system operates in different generation scenarios. This work presents the disjunctive linear model for the Transmission Network Expansion Problem considering multiple generation scenarios to provide a single expansion plan, which must operate in a appropriate way in each one of the different scenarios. The investment cost of the proposed model is greater in relation to the traditional expansion plans, that consider single generation scenario. In order to reduce the investment costs, efficient strategies are presented to find the expansion plans for multiples scenarios. Therefore those strategies are: allow small load cuts; allow generation level displacement in a narrow generation range in relation to the ideal one; and allow small overload in the transmission lines. Moreover, a combination between those strategies is shown and the Transmission Network Expansion Problem was also solved for multistage planning for multiple generation scenarios. The proposed method was implemented using A Mathematical Programming Language (AMPL) and the commercial solver CPLEX. The results were of optimal quality, considering the characteristics of the used solver, and they were compared with methods found in the specialized literature. / Doutor