A geração e o uso dos mapas de ambiente de rádio (REM - Radio Environment Map) em sistemas de comunicações sem fio vêm sendo alvo de pesquisas recentes na literatura científica. Dentre as possíveis aplicações, o REM fornece informações importantes para os processos de predição e otimização de cobertura em sistemas de comunicações sem fio, pois é baseado em medidas coletadas diretamente da rede. Neste contexto, a geração do REM depende do processamento das medidas e suas localizações para a construção dos mapas, por meio de predições espaciais. Entretanto, a incerteza de localização das medidas coletadas pode degradar a acurácia das predições de forma significativa e, consequentemente, impactar as posteriores decições baseadas no REM. Este trabalho aborda o problema de geração do REM de forma mais realística, formulando um modelo de predição espacial que introduz erros de localização no ambiente de rádio de um sistema de comunicação sem fio. As investigações mostram que os impactos provocados pela incerteza de localização na geração do REM são significativos, especialmente nas técnicas de estimação utilizadas para a aprendizagem de parâmetros do modelo de predição espacial. Com isso, uma técnica de predição espacial é proposta e utiliza ferramentas da área geoestatística para superar os efeitos negativos causados pela incerteza de localização nas medidas. Simulações computacionais são desenvolvidas para a avaliação de desempenho das principais técnicas de predição no contexto de geração do REM, considerando o problema da incerteza de localização. Os resultados de simulação da técnica proposta são promissores e mostram que levar em conta a distribuição estatística dos erros de localização pode resultar em predições com maior acurácia para a geração do REM. A influência de diferentes aspectos da modelagem do ambiente de rádio também é analisada e reforçam a ideia de que a aprendizagem de parâmetros do ambiente de rádio tem um papel importante na acurácia das predições espaciais, que são fundamentais para a geração confiável do REM. Finalmente, um estudo experimental do REM é realizado por meio de uma campanha de medidas, permitindo explorar o desempenho dos algoritmos de aprendizagem de parâmetros e predições desenvolvidos neste trabalho. / The generation and use of radio environment maps (REM) in wireless systems has been the subject of recent research in the scientific literature. Among the possible applications, the REM provides important information for the coverage predicfition and optimization processes in wireless systems, since it is based on measurements collected directly on the network. In this context, the REM generation process depends on the processing of the measurements and their locations for the construction of the maps through spatial predictions. However, the location uncertainty related to the measurements collected can signicantly degrade the accuracy of the spatial predictions and, consequently, impact the decisions based on REM. This work addresses the problem of the REM generation in a more realistic way, through the formulation of a spatial prediction model that introduces location errors in the radio environment of a wireless communication system. The investigations show that the impacts of the location uncertainty on the REM generation are significant, especially in the estimation techniques used to learn the parameters of the spatial prediction model. Thus, a spatial prediction technique is proposed, based on geostatistical tools, to overcome the negative effects caused by the location uncertainty of the REM measurements. Computational simulations are developed for the performance evaluation of the main prediction techniques in the context of REM generation, considering the problem of location uncertainty. The simulation results of the proposed technique are promising and show that taking into account the statistical distribution of location errors can result in more accurate predictions for the REM generation process. The influence of different aspects of the radio environment modeling is also analyzed and reinforce the idea that the learning of radio environment parameters plays an important role in the accuracy of spatial predictions, which are fundamental for the reliable REM generation. Finally, an experimental study is carried out through a measurement campaign with the purpose of generating the REM in practice and to explore the performance of the learning and prediction algorithms developed in this work.

The aim of this thesis is to apply and evaluate potential forecasting models for solar power production, based on data from a photovoltaic facility in Sala, Sweden. The thesis evaluates single step forecasting models as well as multiple step forecasting models, where the three compared models for single step forecasting are persistence, autoregressive integrated moving average (ARIMA) and ARIMAX. ARIMAX is an ARIMA model that also takes exogenous predictors in consideration. In this thesis the evaluated exogenous predictor is wind speed. The two compared multiple step models are multiple step persistence and the Gaussian process (GP). Root mean squared error (RMSE) is used as the measurement of evaluation and thus determining the accuracy of the models. Results show that the ARIMAX models performed most accurate in every simulation of the single step models implementation, which implies that adding the exogenous predictor wind speed increases the accuracy. However, the accuracy only increased by 0.04% at most, which is determined as a minimal amount. Moreover, the results show that the GP model was 3% more accurate than the multiple step persistence; however, the GP model could be further developed by adding more training data or exogenous variables to the model.

O tópico de identificação de sistemas aparece em vários ramos da ciência, com especial importância ao campo de Controle Automático. Entretanto, os problemas encontrados na construção de uma representação precisa de um sistema, como a falta de informações prévias, e as diversas decisões de projeto que devem ser tomadas para a resolução de problemas de identificação de sistemas por meios mais tradicionais, podem ser solucionados através da análise empírica do sistema. Nesse sentido, os processos Gaussianos apresentam-se como uma alternativa viável para a modelagem não-paramétrica de sistemas, trazendo a vantagem da estimação da incerteza do modelo. Para verificar o potencial dos processos Gaussianos em problemas de identificação de sistemas, foi realizada a identificação do modelo longitudinal de um veículo de grande porte, tendo alcançado um desempenho satisfatório, mesmo quando se utilizou poucos dados de treinamento. A partir do modelo aprendido, foi projetado um controlador preditivo baseado em modelo para controlar a velocidade do veículo. O controlador levou em consideração a variância da predição do modelo GP (Gaussian Process - Processos Gaussianos) em consideração durante o processo de otimização do sinal de controle. O controlador proposto alcançou um baixo erro no seguimento da referência, mesmo em situações extremas, como estradas íngremes. Entretanto, em alguns tipos de problemas, o resultado só pode ser mensurado a partir da combinação de uma sequência de ações, ou sinais de controle, aplicados ao longo da execução do processo, como é o caso do problema de direção ecológica (eco-driving). Nesses casos, estratégias que otimizem sinais de controle instantâneos podem não ser viáveis, sendo necessária a utilização de estratégias em que toda a política de controle seja otimizada de uma vez. Além disso, a avaliação do custo, ou execução de todo um episódio do processo, pode ser dispendiosa, é desejável que uma solução seja encontrada com a menor quantidade de interações possíveis com o sistema real. Uma técnica apropriada para essa situação é a Otimização Bayesiana, um algoritmo de otimização caixa-preta bastante eficiente. Porém, um dos problemas dessa solução é a incapacidade de lidar com um grande número de dimensões. Sendo assim, nesse trabalho, foi proposto o Coordinate Descent Bayesian Optimisation, um algoritmo baseado na Otimização Bayesiana, que busca o ótimo em espaços de alta dmensionalidade de maneira mais eficiente pois otimiza cada dimensão individualmente, em um esquema de descida coordenada. / The system identification topic appears in various branches of science, with particular emphasis on Automatic Control field. However, problems encountered in building an accurate representation of a system, such as lack of prior information, and the various design decisions which have to be taken to deal with system identification problems by more traditional means, can be solved through the empirical analysis of the system. In this sense, the Gaussian processes are presented as a viable alternative for non-parametric modelling systems, bringing the advantage of estimating the uncertainty of the model. To investigate the potential of Gaussian processes of system identification problems, identifying the longitudinal model of a large vehicle was performed, achieving reasonable performance even when used little training data. From the obtained model, a Model Predictive Controller was designed to control the vehicle speed. The controller took into account the variance of the GP model prediction on the control signal optimization and achieved low reference tracking error, even on hard conditions, like steep roads. However, in some kinds of problems, the observable outcome can often be described as the combined effect of an entire sequence of actions, or controls, applied throughout its execution. In these cases, strategies to optimise control policies for individual stages of the process might not be applicable, and instead the whole policy might have to be optimised at once. Also, the cost to evaluate the policy\'s performance might also be high, being desirable that a solution can be found with as few interactions with the real system as possible. One appropriate candidate is Bayesian Optimization, a very efficient black-box optimization algorithm. But one of the main problems of this solution is the inability of dealing with a large number of dimensions. For that reason, in this work it was proposed Coordinate Descent Bayesian Optimisation, an algorithm to search more efficiently over high-dimensional policy-parameter spaces with BO, by searching over each dimension individually, in a sequential coordinate descent-like scheme.

The recent technology of single-cell RNA sequencing can be used to investigate molecular, transcriptional, changes in cells as they develop. I reviewed the literature on the technology, and made a large scale quantitative comparison of the different implementations of single cell RNA sequencing to identify their technical limitations. I investigate how to model transcriptional changes during cellular development. The general forms of expression changes with respect to development leads to nonparametric regression models, in the forms of Gaussian Processes. I used Gaussian process models to investigate expression patterns in early embryonic development, and compared the development of mice and humans. When using in vivo systems, ground truth time for each cell cannot be known. Only a snapshot of cells, all being in different stages of development can be obtained. In an experiment measuring the transcriptome of zebrafish blood precursor cells undergoing the development from hematopoietic stem cells to thrombocytes, I used a Gaussian Process Latent Variable model to align the cells according to the developmental trajectory. This way I could investigate which genes were driving the development, and characterise the different patterns of expression. With the latent variable strategy in mind, I designed an experiment to study a rare event of murine embryonic stem cells entering a state similar to very early embryos. The GPLVM can take advantage of the nonlinear expression patterns involved with this process. The results showed multiple activation events of genes as cells progress towards the rare state. An essential feature of cellular biology is that precursor cells can give rise to multiple types of progenitor cells through differentiation. In the immune system, naive T-helper cells differentiate to different sub-types depending on the infection. For an experiment where mice were infected by malaria, the T-helper cells develop into two cell types, Th1 and Tfh. I model this branching development using an Overlapping Mixture of Gaussian Processes, which let me identify both which cells belong to which branch, and learn which genes are involved with the different branches. Researchers have now started performing high-throughput experiments where spatial context of gene expression is recorded. Similar to how I identify temporal expression patterns, spatial expression patterns can be identified nonparametrically. To enable researchers to make use of this technique, I developed a very fast method to perform a statistical test for spatial dependence, and illustrate the result on multiple data sets.

O tópico de identificação de sistemas aparece em vários ramos da ciência, com especial importância ao campo de Controle Automático. Entretanto, os problemas encontrados na construção de uma representação precisa de um sistema, como a falta de informações prévias, e as diversas decisões de projeto que devem ser tomadas para a resolução de problemas de identificação de sistemas por meios mais tradicionais, podem ser solucionados através da análise empírica do sistema. Nesse sentido, os processos Gaussianos apresentam-se como uma alternativa viável para a modelagem não-paramétrica de sistemas, trazendo a vantagem da estimação da incerteza do modelo. Para verificar o potencial dos processos Gaussianos em problemas de identificação de sistemas, foi realizada a identificação do modelo longitudinal de um veículo de grande porte, tendo alcançado um desempenho satisfatório, mesmo quando se utilizou poucos dados de treinamento. A partir do modelo aprendido, foi projetado um controlador preditivo baseado em modelo para controlar a velocidade do veículo. O controlador levou em consideração a variância da predição do modelo GP (Gaussian Process - Processos Gaussianos) em consideração durante o processo de otimização do sinal de controle. O controlador proposto alcançou um baixo erro no seguimento da referência, mesmo em situações extremas, como estradas íngremes. Entretanto, em alguns tipos de problemas, o resultado só pode ser mensurado a partir da combinação de uma sequência de ações, ou sinais de controle, aplicados ao longo da execução do processo, como é o caso do problema de direção ecológica (eco-driving). Nesses casos, estratégias que otimizem sinais de controle instantâneos podem não ser viáveis, sendo necessária a utilização de estratégias em que toda a política de controle seja otimizada de uma vez. Além disso, a avaliação do custo, ou execução de todo um episódio do processo, pode ser dispendiosa, é desejável que uma solução seja encontrada com a menor quantidade de interações possíveis com o sistema real. Uma técnica apropriada para essa situação é a Otimização Bayesiana, um algoritmo de otimização caixa-preta bastante eficiente. Porém, um dos problemas dessa solução é a incapacidade de lidar com um grande número de dimensões. Sendo assim, nesse trabalho, foi proposto o Coordinate Descent Bayesian Optimisation, um algoritmo baseado na Otimização Bayesiana, que busca o ótimo em espaços de alta dmensionalidade de maneira mais eficiente pois otimiza cada dimensão individualmente, em um esquema de descida coordenada. / The system identification topic appears in various branches of science, with particular emphasis on Automatic Control field. However, problems encountered in building an accurate representation of a system, such as lack of prior information, and the various design decisions which have to be taken to deal with system identification problems by more traditional means, can be solved through the empirical analysis of the system. In this sense, the Gaussian processes are presented as a viable alternative for non-parametric modelling systems, bringing the advantage of estimating the uncertainty of the model. To investigate the potential of Gaussian processes of system identification problems, identifying the longitudinal model of a large vehicle was performed, achieving reasonable performance even when used little training data. From the obtained model, a Model Predictive Controller was designed to control the vehicle speed. The controller took into account the variance of the GP model prediction on the control signal optimization and achieved low reference tracking error, even on hard conditions, like steep roads. However, in some kinds of problems, the observable outcome can often be described as the combined effect of an entire sequence of actions, or controls, applied throughout its execution. In these cases, strategies to optimise control policies for individual stages of the process might not be applicable, and instead the whole policy might have to be optimised at once. Also, the cost to evaluate the policy\'s performance might also be high, being desirable that a solution can be found with as few interactions with the real system as possible. One appropriate candidate is Bayesian Optimization, a very efficient black-box optimization algorithm. But one of the main problems of this solution is the inability of dealing with a large number of dimensions. For that reason, in this work it was proposed Coordinate Descent Bayesian Optimisation, an algorithm to search more efficiently over high-dimensional policy-parameter spaces with BO, by searching over each dimension individually, in a sequential coordinate descent-like scheme.

abstract: In this work, I present a Bayesian inference computational framework for the analysis of widefield microscopy data that addresses three challenges: (1) counting and localizing stationary fluorescent molecules; (2) inferring a spatially-dependent effective fluorescence profile that describes the spatially-varying rate at which fluorescent molecules emit subsequently-detected photons (due to different illumination intensities or different local environments); and (3) inferring the camera gain. My general theoretical framework utilizes the Bayesian nonparametric Gaussian and beta-Bernoulli processes with a Markov chain Monte Carlo sampling scheme, which I further specify and implement for Total Internal Reflection Fluorescence (TIRF) microscopy data, benchmarking the method on synthetic data. These three frameworks are self-contained, and can be used concurrently so that the fluorescence profile and emitter locations are both considered unknown and, under some conditions, learned simultaneously. The framework I present is flexible and may be adapted to accommodate the inference of other parameters, such as emission photophysical kinetics and the trajectories of moving molecules. My TIRF-specific implementation may find use in the study of structures on cell membranes, or in studying local sample properties that affect fluorescent molecule photon emission rates. / Dissertation/Thesis / Masters Thesis Applied Mathematics 2019

This thesis deals with the problem of estimating the probability of failure of a system from computer simulations. When only an expensive-to-simulate model of the system is available, the budget for simulations is usually severely limited, which is incompatible with the use of classical Monte Carlo methods. In fact, estimating a small probability of failure with very few simulations, as required in some complex industrial problems, is a particularly difficult topic. A classical approach consists in replacing the expensive-to-simulate model with a surrogate model that will use little computer resources. Using such a surrogate model, two operations can be achieved. The first operation consists in choosing a number, as small as possible, of simulations to learn the regions in the parameter space of the system that will lead to a failure of the system. The second operation is about constructing good estimators of the probability of failure. The contributions in this thesis consist of two parts. First, we derive SUR (stepwise uncertainty reduction) strategies from a Bayesian-theoretic formulation of the problem of estimating a probability of failure. Second, we propose a new algorithm, called Bayesian Subset Simulation, that takes the best from the Subset Simulation algorithm and from sequential Bayesian methods based on Gaussian process modeling. The new strategies are supported by numerical results from several benchmark examples in reliability analysis. The methods proposed show good performances compared to methods of the literature.

<p>The dissertation focuses on solving some important theoretical and methodological problems associated with Bayesian modeling of infinite dimensional `objects', popularly called nonparametric Bayes. The term `infinite dimensional object' can refer to a density, a conditional density, a regression surface or even a manifold. Although Bayesian density estimation as well as function estimation are well-justified in the existing literature, there has been little or no theory justifying the estimation of more complex objects (e.g. conditional density, manifold, etc.). Part of this dissertation focuses on exploring the structure of the spaces on which the priors for conditional densities and manifolds are supported while studying how the posterior concentrates as increasing amounts of data are collected.</p><p>With the advent of new acquisition devices, there has been a need to model complex objects associated with complex data-types e.g. millions of genes affecting a bio-marker, 2D pixelated images, a cloud of points in the 3D space, etc. A significant portion of this dissertation has been devoted to developing adaptive nonparametric Bayes approaches for learning low-dimensional structures underlying higher-dimensional objects e.g. a high-dimensional regression function supported on a lower dimensional space, closed curves representing the boundaries of shapes in 2D images and closed surfaces located on or near the point cloud data. Characterizing the distribution of these objects has a tremendous impact in several application areas ranging from tumor tracking for targeted radiation therapy, to classifying cells in the brain, to model based methods for 3D animation and so on. </p><p> </p><p> The first three chapters are devoted to Bayesian nonparametric theory and modeling in unconstrained Euclidean spaces e.g. mean regression and density regression, the next two focus on Bayesian modeling of manifolds e.g. closed curves and surfaces, and the final one on nonparametric Bayes spatial point pattern data modeling when the sampling locations are informative of the outcomes.</p> / Dissertation

<p>The immune system is constantly faced with the daunting task of protecting the host from a large number of ever-evolving pathogens. In vertebrates, the immune response results from the interplay of two cellular systems: the innate immunity and the adaptive immunity. In the past decades, dendritic cells have emerged as major players in the modulation of the immune response, being one of the primary links between these two branches of the immune system.</p><p>Dendritic cells are pathogen-sensing cells that alert the rest of the immune system of the presence of infection. The signals sent by dendritic cells result in the recruitment of the appropriate cell types and molecules required for effectively clearing the infection. A question of utmost importance in our understanding of the immune response and our ability to manipulate it in the development of vaccines and therapies is: "How do dendritic cells translate the various cues they perceive from the environment into different signals that specifically activate the appropriate parts of the immune system that result in an immune response streamlined to clear the given pathogen?"</p><p>Here we have developed computational and statistical methods aimed to address specific aspects of this question. In particular, understanding how dendritic cells ultimately modulate the immune response requires an understanding of the subtleties of their maturation process in response to different environmental signals. Hence, the first part of this dissertation focuses on elucidating the changes in the transcriptional</p><p>program of dendritic cells in response to the detection of two common pathogen- associated molecules, LPS and CpG. We have developed a method based on Langevin and Dirichlet processes to model and cluster gene expression temporal data, and have used it to identify, on a large scale, genes that present unique and common transcriptional behaviors in response to these two stimuli. Additionally, we have also investigated a different, but related, aspect of dendritic cell modulation of the adaptive immune response. In the second part of this dissertation, we present a method to predict peptides that will bind to MHC molecules, a requirement for the activation of pathogen-specific T cells. Together, these studies contribute to the elucidation of important aspects of dendritic cell biology.</p> / Dissertation

<p>Our interest is the risk assessment of rare natural hazards, such as</p><p>large volcanic pyroclastic flows. Since catastrophic consequences of</p><p>volcanic flows are rare events, our analysis benefits from the use of</p><p>a computer model to provide information about these events under</p><p>natural conditions that may not have been observed in reality.</p><p>A common problem in the analysis of computer experiments, however, is the high computational cost associated with each simulation of a complex physical process. We tackle this problem by using a statistical approximation (emulator) to predict the output of this computer model at untried values of inputs. Gaussian process response surface is a technique commonly used in these applications, because it is fast and easy to use in the analysis.</p><p>We explore several aspects of the implementation of Gaussian process emulators in a Bayesian context. First, we propose an improvement for the implementation of the plug-in approach to Gaussian processes. Next, we also evaluate the performance of a spatial model for large data sets in the context of computer experiments.</p><p>Computer model data can also be combined to field observations in order to calibrate the emulator and obtain statistical approximations to the computer model that are closer to reality. We present an application where we learn the joint distribution of inputs from field data and then bind this auxiliary information to the emulator in a calibration process.</p><p>One of the outputs of our computer model is a surface of maximum volcanic flow height over some geographical area. We show how the topography of the volcano area plays an important role in determining the shape of this surface, and we propose methods</p><p>to incorporate geophysical information in the multivariate analysis of computer model output.</p> / Dissertation