Durante as últimas décadas, o melhoramento genético em bovinos leiteiros no Brasil baseou-se somente na importação de material genético, resultando em ganhos genéticos de pequena magnitude para as características de interesse econômico. Dessa forma, existe a necessidade eminente de avaliações genéticas dos animais sob condições nacionais de ambiente, de maneira a se prover um aumento na produção de leite aliado à qualidade. Neste contexto, o conhecimento sobre a composição do leite é de extrema importância para o entendimento de como alguns fatores ambientais e, principalmente genéticos podem influenciar no aumento dos conteúdos de proteína (PROT), gordura (GOR) e ácidos graxos (AG) benéficos e na redução da contagem de células somáticas, visando a melhoria da qualidade nutricional deste produto. Diante disso, o objetivo desse trabalho foi predizer os teores de AG de interesse usando regressão linear bayesiana, bem como estimar componentes de variância, coeficientes de herdabilidade e comparar modelos de diferentes ordens de ajuste por meio de funções polinomiais de Legendre, sob modelos de regressão aleatória. Amostras de leite foram submetidas a análises de cromatografia gasosa e espectrometria em infravermelho médio para determinação dos ácidos graxos. A comparação dos resultados obtidos por ambos os métodos foi realizada por meio da correlação de Pearson, análise de Bland-Altman e regressão linear bayesiana e, posteriormente, equações de predição foram desenvolvidas para os ácidos graxos mirístico (C14:0) e linoléico conjugado (CLA), a partir de regressões lineares simples e múltipla bayesiana considerando-se prioris nãoinformativas e informativas. Polinômios ortogonais de Legendre de 1ª a 6ª ordens foram utilizados para o ajuste das regressões aleatórias das características. A predição dos AG por meio da aplicação da regressão linear foi viável, com erros de predição variando entre 0,01 e 4,84g por 100g de gordura para o C14:0 e 0,002 e 1,85 por 100g de gordura para o CLA, sendo neste caso os menores erros de predição obtidos quando adotada a regressão múltipla com priori não informativa. Os modelos que melhor se ajustaram para GOR, PROT, C16:0, C18:0, C18:1c9, CLA, saturados (SAT), insaturados (INSAT), monoinsaturados (MONO) e poliinsaturados (POLI) foi o de 1ª ordem, e para escore de célula somática (ESC) e C14:0 o de 2ª ordem. As estimativas de herdabilidade obtidas variaram de 0,08 a 0,11 para GOR; 0,28 a 0,35 para PROT; 0,03 a 0,22 para ECS; 0,12 a 0,31 para C16:0; 0,08 a 0,14 para C18:0; 0,24 a 0,43 para C14:0; 0,07 a 0,17 para C18:1c9; 0,13 a 0,39 para CLA; 0,14 a 0,31 para SAT; 0,04 a 0,14 para INSAT; 0,04 a 0,13 para MONO; 0,09 a 0,20 para POLI e 0,12 para PROD, nos modelos que melhor se ajustaram. Concluise que melhorias na qualidade nutricional do leite podem ser obtidas por meio da inclusão das características produtivas e do perfil de ácidos graxos em programas de seleção genética. / During the last decades, genetic improvement in dairy cattle in Brazil was based only on the importation of genetic material, resulting in small genetic gains for economic interest traits. There is a perceived need for genetic evaluation under national environment conditions to provide an increase in milk production allied to quality. In this context, the knowledge of the milk composition is very important for understanding how certain environmental factors and especially genetic factors may influence the increase in protein content (PROT), fat (FAT), beneficial fatty acids (FA) and in reducing somatic cell count, aiming to improve the nutritional quality of this product. The aim of this study was to predict the levels of interest FA using Bayesian linear regression and estimate the components of variance, coefficients of heritability and compare models with different orders of adjustment by Legendre polynomials functions, in random regression models. Milk samples were subjected to gas chromatography analysis and mid-infrared spectrometry for the determination of fatty acids. The comparison of the results obtained by both methods was performed using Pearson\'s correlation, Bland-Altman analysis and Bayesian linear regression, subsequently, prediction equations were developed for the fatty acids myristic (C14:0) and conjugated linoleic (CLA) from simple linear regressions and multiple Bayesian considering non-informative and informative priors. Legendre orthogonal polynomials from 1st to 6th orders were used to fit the random regression of the traits. That was viable the prediction of FA by applying the linear regression with prediction errors ranging from 0.01 to 4.84 g per 100 g of fat for C14:0 and 0.002 to 1.85 per 100 g of fat for CLA, in this case the smaller prediction errors obtained when adopted the multiple regression with non-informative priori. The models that best fit for FAT, PROT, C16:0, C18:0, C18:1C9, CLA, saturated (SAT), unsaturated (UNSAT), monounsaturated (MONO) and polyunsaturated (POLY) was the one of 1st order and for somatic cell scores (SCS) and C14:0 the one of 2nd order. The estimates of heritability ranged from 0.08 to 0.11 for FAT; 0.28 to 0.35 for PROT; 0.03 to 0.22 for SCS; 0.12 to 0.31 for C16:0; 0.08 to 0.14 for C18:0; 0.24 to 0.43 for C14:0; 0.07 to 0.17 for C18:1C9; 0.13 to 0.39 for CLA; 0.14 to 0.31 for SAT; 0.04 to 0.14 for UNSAT; 0.04 to 0.13 for MONO, 0.09 to 0.20 for POLY and 0.12 for PROD, in the models that best fit. We conclude that improvements in the nutritional quality of milk can be obtained through the inclusion of productive traits and fatty acid profile in genetic selection programs.

Durante as últimas décadas, o melhoramento genético em bovinos leiteiros no Brasil baseou-se somente na importação de material genético, resultando em ganhos genéticos de pequena magnitude para as características de interesse econômico. Dessa forma, existe a necessidade eminente de avaliações genéticas dos animais sob condições nacionais de ambiente, de maneira a se prover um aumento na produção de leite aliado à qualidade. Neste contexto, o conhecimento sobre a composição do leite é de extrema importância para o entendimento de como alguns fatores ambientais e, principalmente genéticos podem influenciar no aumento dos conteúdos de proteína (PROT), gordura (GOR) e ácidos graxos (AG) benéficos e na redução da contagem de células somáticas, visando a melhoria da qualidade nutricional deste produto. Diante disso, o objetivo desse trabalho foi predizer os teores de AG de interesse usando regressão linear bayesiana, bem como estimar componentes de variância, coeficientes de herdabilidade e comparar modelos de diferentes ordens de ajuste por meio de funções polinomiais de Legendre, sob modelos de regressão aleatória. Amostras de leite foram submetidas a análises de cromatografia gasosa e espectrometria em infravermelho médio para determinação dos ácidos graxos. A comparação dos resultados obtidos por ambos os métodos foi realizada por meio da correlação de Pearson, análise de Bland-Altman e regressão linear bayesiana e, posteriormente, equações de predição foram desenvolvidas para os ácidos graxos mirístico (C14:0) e linoléico conjugado (CLA), a partir de regressões lineares simples e múltipla bayesiana considerando-se prioris nãoinformativas e informativas. Polinômios ortogonais de Legendre de 1ª a 6ª ordens foram utilizados para o ajuste das regressões aleatórias das características. A predição dos AG por meio da aplicação da regressão linear foi viável, com erros de predição variando entre 0,01 e 4,84g por 100g de gordura para o C14:0 e 0,002 e 1,85 por 100g de gordura para o CLA, sendo neste caso os menores erros de predição obtidos quando adotada a regressão múltipla com priori não informativa. Os modelos que melhor se ajustaram para GOR, PROT, C16:0, C18:0, C18:1c9, CLA, saturados (SAT), insaturados (INSAT), monoinsaturados (MONO) e poliinsaturados (POLI) foi o de 1ª ordem, e para escore de célula somática (ESC) e C14:0 o de 2ª ordem. As estimativas de herdabilidade obtidas variaram de 0,08 a 0,11 para GOR; 0,28 a 0,35 para PROT; 0,03 a 0,22 para ECS; 0,12 a 0,31 para C16:0; 0,08 a 0,14 para C18:0; 0,24 a 0,43 para C14:0; 0,07 a 0,17 para C18:1c9; 0,13 a 0,39 para CLA; 0,14 a 0,31 para SAT; 0,04 a 0,14 para INSAT; 0,04 a 0,13 para MONO; 0,09 a 0,20 para POLI e 0,12 para PROD, nos modelos que melhor se ajustaram. Concluise que melhorias na qualidade nutricional do leite podem ser obtidas por meio da inclusão das características produtivas e do perfil de ácidos graxos em programas de seleção genética. / During the last decades, genetic improvement in dairy cattle in Brazil was based only on the importation of genetic material, resulting in small genetic gains for economic interest traits. There is a perceived need for genetic evaluation under national environment conditions to provide an increase in milk production allied to quality. In this context, the knowledge of the milk composition is very important for understanding how certain environmental factors and especially genetic factors may influence the increase in protein content (PROT), fat (FAT), beneficial fatty acids (FA) and in reducing somatic cell count, aiming to improve the nutritional quality of this product. The aim of this study was to predict the levels of interest FA using Bayesian linear regression and estimate the components of variance, coefficients of heritability and compare models with different orders of adjustment by Legendre polynomials functions, in random regression models. Milk samples were subjected to gas chromatography analysis and mid-infrared spectrometry for the determination of fatty acids. The comparison of the results obtained by both methods was performed using Pearson\'s correlation, Bland-Altman analysis and Bayesian linear regression, subsequently, prediction equations were developed for the fatty acids myristic (C14:0) and conjugated linoleic (CLA) from simple linear regressions and multiple Bayesian considering non-informative and informative priors. Legendre orthogonal polynomials from 1st to 6th orders were used to fit the random regression of the traits. That was viable the prediction of FA by applying the linear regression with prediction errors ranging from 0.01 to 4.84 g per 100 g of fat for C14:0 and 0.002 to 1.85 per 100 g of fat for CLA, in this case the smaller prediction errors obtained when adopted the multiple regression with non-informative priori. The models that best fit for FAT, PROT, C16:0, C18:0, C18:1C9, CLA, saturated (SAT), unsaturated (UNSAT), monounsaturated (MONO) and polyunsaturated (POLY) was the one of 1st order and for somatic cell scores (SCS) and C14:0 the one of 2nd order. The estimates of heritability ranged from 0.08 to 0.11 for FAT; 0.28 to 0.35 for PROT; 0.03 to 0.22 for SCS; 0.12 to 0.31 for C16:0; 0.08 to 0.14 for C18:0; 0.24 to 0.43 for C14:0; 0.07 to 0.17 for C18:1C9; 0.13 to 0.39 for CLA; 0.14 to 0.31 for SAT; 0.04 to 0.14 for UNSAT; 0.04 to 0.13 for MONO, 0.09 to 0.20 for POLY and 0.12 for PROD, in the models that best fit. We conclude that improvements in the nutritional quality of milk can be obtained through the inclusion of productive traits and fatty acid profile in genetic selection programs.

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The present study is concerned with developing some statistical models to evaluate and analyze software reliability. We have developed the analytical structure of the logistic model to be used for testing and evaluating the reliability of a software package. The proposed model has been shown to be useful in the testing and debugging stages of the developmental process of a software package. It is important that prior to releasing a software package to marketing that we have achieved a target reliability with an acceptable degree of confidence. The proposed model has been evaluated and compared with several existing statistical models that are commonly used. Real software failure data was used for the comparison of the proposed logistic model with the others. The proposed model gives better results or it is equally effective. The logistic model was also used to model the mean time between failure of software packages. Real failure data was used to illustrate the usefulness of the proposed statistical procedures. Using the logistic model to characterize software failures we proceed to develop Bayesian analysis of the subject model. This modeling was based on two different difference equations whose parameters were estimated with Bayesian regressions subject to specific prior and mean square loss function.

Research about unmanned ground vehicles (UGVs) has received an increased amount of attention in recent years, partly due to the many applications of UGVs in areas where it is inconvenient or impossible to have human operators, such as in mines or urban search and rescue. Two closely linked problems that arise when developing such vehicles are motion planning and control of the UGV. This thesis explores these subjects for a UGV with an unknown, and possibly time-variant, dynamical model. A framework is developed that includes three components: a machine learning algorithm to estimate the unknown dynamical model of the UGV, a motion planner that plans a feasible path for the vehicle and a controller making the UGV follow the planned path. The motion planner used in the framework is a lattice-based planner based on input sampling. It uses a dynamical model of the UGV together with motion primitives, defined as a sequence of states and control signals, which are concatenated online in order to plan a feasible path between states. Furthermore, the controller that makes the vehicle follow this path is a model predictive control (MPC) controller, capable of taking the time-varying dynamics of the UGV into account as well as imposing constraints on the states and control signals. Since the dynamical model is unknown, the machine learning algorithm Bayesian linear regression (BLR) is used to continuously estimate the model parameters online during a run. The parameter estimates are then used by the MPC controller and the motion planner in order to improve the performance of the UGV. The performance of the proposed motion planning and control framework is evaluated by conducting a series of experiments in a simulation study. Two different simulation environments, containing obstacles, are used in the framework to simulate the UGV, where the performance measures considered are the deviation from the planned path, the average velocity of the UGV and the time to plan the path. The simulations are either performed with a time-invariant model, or a model where the parameters change during the run. The results show that the performance is improved when combining the motion planner and the MPC controller with the estimated model parameters from the BLR algorithm. With an improved model, the vehicle is capable of maintaining a higher average velocity, meaning that the plan can be executed faster. Furthermore, it can also track the path more precisely compared to when using a less accurate model, which is crucial in an environment with many obstacles. Finally, the use of the BLR algorithm to continuously estimate the model parameters allows the vehicle to adapt to changes in its model. This makes it possible for the UGV to stay operational in cases of, e.g., actuator malfunctions.

Missing data continues to be an issue not only the field of statistics but in any field, that deals with data. This is due to the fact that almost all the widely accepted and standard statistical software and methods assume complete data for all the variables included in the analysis. As a result, in most studies, statistical power is weakened and parameter estimates are biased, leading to weak conclusions and generalizations. Many studies have established that multiple imputation methods are effective ways of handling missing data. This paper examines three different imputation methods (predictive mean matching, Bayesian linear regression and linear regression, non Bayesian) in the MICE package in the statistical software, R, to ascertain which of the three imputation methods imputes data that yields parameter estimates closest to the parameter estimates of a complete data given different percentages of missingness. In comparing the parameter estimates of the complete data and the imputed data, the parameter estimates in each model were evaluated and compared. The paper extends the analysis by generating a pseudo data of the original data to establish how the imputation methods perform under varying conditions.

Bayesian statistics is an important approach to modern statistical analyses. It allows us to use our prior knowledge of the unknown parameters to construct a model for our data set. The foundation of Bayesian analysis is Bayes' Rule, which in its proportional form indicates that the posterior is proportional to the prior times the likelihood. We will demonstrate how we can apply Bayesian statistical techniques to fit a linear regression model and a hierarchical linear regression model to a data set. We will show how to apply different distributions to Bayesian analyses and how the use of a prior affects the model. We will also make a comparison between the Bayesian approach and the traditional frequentist approach to data analyses.

1 Introduction In this doctoral thesis, we address several representative problems that arise in the context of learning from multiple heterogeneous agents. These problems are relevant to many modern applications such as crowdsourcing and internet advertising. In scenarios such as crowdsourcing, there is a planner who is interested in learning a task and a set of noisy agents provide the training data for this learning task. Any learning algorithm making use of the data provided by these noisy agents must account for their noise levels. The noise levels of the agents are unknown to the planner, leading to a non-trivial difficulty. Further, the agents are heterogeneous as they differ in terms of their noise levels. A key challenge in such settings is to learn the noise levels of the agents while simultaneously learning the underlying model. Another challenge arises when the agents are strategic. For example, when the agents are required to perform a task, they could be strategic on the efforts they put in. As another example, when required to report their costs incurred towards performing the task, the agents could be strategic and may not report the costs truthfully. In general, the performance of the learning algorithms could be severely affected if the information elicited from the agents is incorrect. We address the above challenges that arise in the following representative learning problems. Multi-label Classification from Heterogeneous Noisy Agents Multi-label classification is a well-known supervised machine learning problem where each instance is associated with multiple classes. Since several labels can be assigned to a single instance, one of the key challenges in this problem is to learn the correlations between the classes. We first assume labels from a perfect source and propose a novel topic model called Multi-Label Presence-Absence Latent Dirichlet Allocation (ML-PA-LDA). In the current day scenario, a natural source for procuring the training dataset is through mining user-generated content or directly through users in a crowdsourcing platform. In the more practical scenario of crowdsourcing, an additional challenge arises as the labels of the training instances are provided by noisy, heterogeneous crowd-workers with unknown qualities. With this as the motivation, we further adapt our topic model to the scenario where the labels are provided by multiple noisy sources and refer to this model as ML-PA-LDA-MNS (ML-PA-LDA with Multiple Noisy Sources). With experiments on standard datasets, we show that the proposed models achieve superior performance over existing methods. Active Linear Regression with Heterogeneous, Noisy and Strategic Agents In this work, we study the problem of training a linear regression model by procuring labels from multiple noisy agents or crowd annotators, under a budget constraint. We propose a Bayesian model for linear regression from multiple noisy sources and use variational inference for parameter estimation. When labels are sought from agents, it is important to minimize the number of labels procured as every call to an agent incurs a cost. Towards this, we adopt an active learning approach. In this specific context, we prove the equivalence of well-studied criteria of active learning such as entropy minimization and expected error reduction. For the purpose of annotator selection in active learning, we observe a useful connection with the multi-armed bandit framework. Due to the nature of the distribution of the rewards on the arms, we resort to the Robust Upper Confidence Bound (UCB) scheme with truncated empirical mean estimator to solve the annotator selection problem. This yields provable guarantees on the regret. We apply our model to the scenario where annotators are strategic and design suitable incentives to induce them to put in their best efforts. Ranking with Heterogeneous Strategic Agents We look at the problem where a planner must rank multiple strategic agents, a problem that has many applications including sponsored search auctions (SSA). Stochastic multi-armed bandit (MAB) mechanisms have been used in the literature to solve this problem. Existing stochastic MAB mechanisms with a deterministic payment rule, proposed in the literature, necessarily suffer a regret of (T 2=3), where T is the number of time steps. This happens because these mechanisms address the worst case scenario where the means of the agents’ stochastic rewards are separated by a very small amount that depends on T . We however take a detour and allow the planner to indicate the resolution, , with which the agents must be distinguished. This immediately leads us to introduce the notion of -Regret. We propose a dominant strategy incentive compatible (DSIC) and individually rational (IR), deterministic MAB mechanism, based on ideas from the Upper Confidence Bound (UCB) family of MAB algorithms. The proposed mechanism - UCB achieves a -regret of O(log T ). We first establish the results for single slot SSA and then non-trivially extend the results to the case of multi-slot SSA.