Computer models or simulators are becoming increasingly common in many fields in science and engineering, powered by the phenomenal growth in computer hardware over the past decades. Many of these simulators implement a particular mathematical model as a deterministic computer code, meaning that running the simulator again with the same input gives the same output. Often running the code involves some computationally expensive tasks, such as solving complex systems of partial differential equations numerically. When simulator runs become too long, it may limit their usefulness. In order to overcome time or budget constraints by making the most out of limited computational resources, a statistical methodology has been proposed, known as the "Design and Analysis of Computer Experiments". The main idea is to run the expensive simulator only at a relatively few, carefully chosen design points in the input space, and based on the outputs construct an emulator (statistical model) that can emulate (predict) the output at new, untried locations at a fraction of the cost. This approach is useful provided that we can measure how much the predictions of the cheap emulator deviate from the real response surface of the original computer model. One way to quantify emulator error is to construct pointwise prediction bands designed to envelope the response surface and make assertions that the true response (simulator output) is enclosed by these envelopes with a certain probability. Of course, to be able to make such probabilistic statements, one needs to introduce some kind of randomness. A common strategy that we use here is to model the computer code as a random function, also known as a Gaussian stochastic process. We concern ourselves with smooth response surfaces and use the Gaussian covariance function that is ideal in cases when the response function is infinitely differentiable. In this thesis, we propose Fast Bayesian Inference (FBI) that is both computationally efficient and can be implemented as a black box. Simulation results show that it can achieve remarkably accurate prediction uncertainty assessments in terms of matching coverage probabilities of the prediction bands and the associated reparameterizations can also help parameter uncertainty assessments. / Science, Faculty of / Statistics, Department of / Graduate

The Dirichlet process is perhaps the most popular prior used in the nonparametric Bayesian inference. This prior which is placed on the space of probability distributions has conjugacy property and asymptotic consistency. In this thesis, our concentration is on applying this nonparametric Bayesian inference on the Tukey depth and Tukey median. Due to the complexity of the distribution of Tukey median, we use this nonparametric Bayesian inference, namely the Lo’s bootstrap, to approximate the distribution of the Tukey median. We also compare our results with the Efron’s bootstrap and Rubin’s bootstrap. Furthermore, the existing asymptotic theory for the Tukey median is reviewed. Based on these existing results, we conjecture that the bootstrap sample Tukey median converges to the same asymp- totic distribution and our simulation supports the conjecture that the asymptotic consistency holds.

Orientador: Laura Leticia Ramos Rifo / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-26T15:05:12Z (GMT). No. of bitstreams: 1 Tasca_GustavoHenrique_M.pdf: 979052 bytes, checksum: bb1371bb1b8626882cebcf01550bb823 (MD5) Previous issue date: 2015 / Resumo: Neste trabalho, estudamos métodos de inferência bayesiana para distribuições de cauda longa, que não envolvam o cálculo da função de verossimilhança. Inicialmente, apresentamos uma análise das propriedades de distribuições de cauda pesada e seus casos particulares, como as famílias de distribuições de cauda longa, subexponenciais e de variação regular. Apresentamos algumas estatísticas e seus comportamentos amostrais, a fim de desenvolvermos medidas de diagnóstico. Para obtenção de inferências a posteriori, discutimos o método ABC de mínima entropia e outros algoritmos para verificação e seleção de modelos, que não utilizam o cálculo da função de verossimilhança. Introduzimos um novo algoritmo para seleção de modelos baseado na distribuição preditiva a posteriori, cujos resultados são validados através de simulações e análises de dados reais relacionados à hidrologia / Abstract: In this work, we study Bayesian inference methods for long-tailed distributions that don't involve the evaluation of the likelihood function. Initially, we present an analysis of the properties of heavy-tailed distributions and particular cases, as long-tailed, subexponencial and regular variation families. Some statistics are presented and their sampling behavior studied, in order to develop diagnostic measures. For obtaining posterior inferences, we discuss the minimum entropy ABC and others likelihood-free algorithms, aiming model checking and model selection. We introduce a new model selection algorithm based on the posterior predictive distribution, the results of which are validated through simulations and real data related to river flow / Mestrado / Estatistica / Mestre em Estatística

Orientador: Helio Fiori de Castro / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica / Made available in DSpace on 2018-08-28T11:56:54Z (GMT). No. of bitstreams: 1 Tyminski_NataliaCezaro_M.pdf: 6550021 bytes, checksum: 3fb888c14fc5d24d29f7f155d0e4f2b0 (MD5) Previous issue date: 2015 / Resumo: As unidades geradoras de energia das usinas são formadas por turbinas e turbo-geradores, que são exemplos típicos de máquinas rotativas. Essas maquinas são componentes críticos, pois são essenciais à geração de energia. Sabendo que a análise dinâmica de máquinas rotativas é uma tarefa complexa envolvendo diversos parâmetros a serem analisados, sua realização não deve considerar apenas o rotor, pois seu comportamento dinâmico é influenciado pela interação com os demais componentes do mesmo sistema. O comportamento dinâmico de uma máquina rotativa é, geralmente, representado por um modelo determinístico. Entretanto, sistemas rotativos reais possuem características estocásticas, visto que os inúmeros parâmetros de projetos possuem incertezas inerentes à fabricação e, principalmente, às condições de operações. Desta forma, modelos estocásticos são uma opção importante para representação de sistemas rotativos na fase de projeto, onde se podem prever os efeitos da variação dos parâmetros de projeto. O tema em foco nesta dissertação de mestrado é a aplicação de Inferência Bayesiana para ajustar um modelo de sistema rotativo. Neste trabalho foram analisadas as incertezas nos parâmetros de projeto de um sistema rotativo, e a partir das incertezas obtidas foi possível obter a resposta estocástica do sistema. A primeira analise considera as incertezas dos parâmetros relacionados ao eixo; como o modulo de elasticidade, a massa especifica do material e o coeficiente de proporcionalidade a matriz de rigidez. Na segunda análise, os parâmetros escolhidos foram os parâmetros de desbalanceamento; ângulo de fase, momento de desbalanceamento e posição axial. Em uma terceira abordagem, foi analisado parâmetros dos mancais hidrodinâmicos, folga radial do mancal e temperatura do óleo lubrificante. A partir das incertezas dos referidos parâmetros, foi possível analisar a propagação de incertezas desses parâmetros no cálculo da posição do eixo no mancal e dos coeficientes dinâmicos dos mancais hidrodinâmicos / Abstract: Energy generation plants rely on units such as turbines and turbo-generators, which are common examples of rotating machines. These machines are critical components in these units, once they are essential to the energy generation. The dynamic analysis of rotating machines is a complex task including several parameters to be considered. This analysis requires taking the rotor into account but also the other components, which affect the dynamic behavior of the system. The dynamic behavior of rotating machines is usually represented by a deterministic model. Although, real rotating system have stochastic characteristics once that the parameters on project have uncertainties. In this way, stochastic models are an important option for the representation of these systems, and it's possible predict the variation's parameters. This study aims the application of Bayesian Inference for model updating on rotating systems. The uncertainties of rotating machines parameters were analyzed, and the system stochastic response was obtained. The first analyzed considers the uncertainties of the beam parameters, as the Young¿s modulus, and the proportionality coefficient to the stiffness matrix. In the second analysis, the selected parameters were the unbalance parameters; phase angle, unbalance moment and axial position. In a third approach, it was analyzed parameters of journal bearings, clearance radial and lubricating oil temperature. From the uncertainties of these parameters, it was possible to analyze the propagation of uncertainties of these parameters, to calculate the center line position in the bearing, and the dynamic coefficients of journal bearings / Mestrado / Mecanica dos Sólidos e Projeto Mecanico / Mestra em Engenharia Mecânica

During the last decade, a new trend in medicine is transforming the nature of healthcare from reactive to proactive. This new paradigm is changing into a personalized medicine where the prevention, diagnosis, and treatment of disease is focused on individual patients. This paradigm is known as P4 medicine. Among other key benefits, P4 medicine aspires to detect diseases at an early stage and introduce diagnosis to stratify patients and diseases to select the optimal therapy based on individual observations and taking into account the patient outcomes to empower the physician, the patient, and their communication. This paradigm transformation relies on the availability of complex multi-level biomedical data that are increasingly accurate, since it is possible to find exactly the needed information, but also exponentially noisy, since the access to that information is more and more challenging. In order to take advantage of this information, an important effort is being made in the last decades to digitalize medical records and to develop new mathematical and computational methods for extracting maximum knowledge from patient records, building dynamic and disease-predictive models from massive amounts of integrated clinical and biomedical data. This requirement enables the use of computer-assisted Clinical Decision Support Systems for the management of individual patients. The Clinical Decision Support System (CDSS) are computational systems that provide precise and specific knowledge for the medical decisions to be adopted for diagnosis, prognosis, treatment and management of patients. The CDSS are highly related to the concept of evidence-based medicine since they infer medical knowledge from the biomedical databases and the acquisition protocols that are used for the development of the systems, give computational support based on evidence for the clinical practice, and evaluate the performance and the added value of the solution for each specific medical problem. / Tortajada Velert, S. (2012). Incremental Learning approaches to Biomedical decision problems [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/17195 / Palancia

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This thesis presents three emerging computational methods: machine learning, gradient-free optimization, and Bayesian modelling. Each method is showcased in its ability to enable energy savings in new and existing buildings when paired with dynamic energy models. Machine learning algorithms provide rapid computational speed increases when used as surrogate models, supporting early-stage designs of buildings. Genetic algorithms support the design of complex interacting systems in a reduced amount of effort. Finally, Bayesian modelling can be leveraged to incorporate uncertainty in building energy model calibration. These methods are all readily available and user-friendly, and can be incorporated into current engineering workflows. / Graduate

The Bayesian approach to probability and statistics is described, a brief history of Bayesianism is related, differences between Bayesian and Frequentist schools of statistics are defined, protential applications are investigated, and a literature survey is presented in the form of a machine-sort card file. Bayesian thought is increasing in favor among statisticians because of its ability to attack problems that are unassailable from the Frequentist approach. It should become more popular among practitioners because of the flexibility it allows experimenters and the ease with which prior knowledge can be combined with experimental data. (82 pages)