Thesis--University of Oklahoma. / Bibliography: leaves 82-83.

Neste trabalho estudamos o aprendizado em uma classe específica de modelos probabilísticos conhecidos como modelos de Markov com variáveis de estado escondidas (em inglês, Hidden Markov Models ou HMMs). Primeiramente discutimos sua teoria básica e em seguida fazemos um estudo detalhado do comportamento de cinco diferentes algoritmos de aprendizado, dois deles já conhecidos na literatura e os outros três propostos por nós neste trabalho. Os cinco algoritmos estão descritos abaixo e são estudados na seqüência apresentada: Algoritmo de Baum-Welch (BW): consiste em um célebre algoritmo off-line obtido através da aplicação do algoritmo EM ao caso particular dos HMMs. Na literatura, é comum referir-se a ele pelo nome de Fórmulas de Reestimação de BaumWelch. Algoritmo de Baum-Welch On-line (BWO): versão on-line de BW proposta por nós. Algoritmo de Baldi-Chauvin (BC): algoritmo on-line proposto por Baldi e Chauvin em [5] onde uma representação do tipo softma:x é utilizada para as probabilidades dos HMMs e cujo objetivo é, a cada passo de iteração, maximizar a verossimilhança do modelo. Algoritmo Bayesiano On-line (BKL): algoritmo desenvolvido por nós baseado numa proposta de Opper [74], onde, após a atualização da distribuição de probabilidades do modelo a cada novo dado, projeta-se a densidade obtida em uma família paramétrica de distribuições tratáveis minimizando-se a distância de KullbackLeibler entre as duas. Algoritmo Posterior Média (PM): uma simplificação de BKL onde a projeção após a atualização é feita na distribuição posterior média. Para cada um dos algoritmos acima, obtemos curvas de aprendizado através de simulações onde utilizamos duas medidas distintas de erro de generalização: a distância de Kullback-Leibler (dKL) e a distância euclideana (d IND. E). Com exceção do algoritmo BW, que só pode ser utilizado em situações de aprendizado off-line, estudamos para todos os outros algoritmos as curvas de aprendizado tanto para a situação on-line quanto para a off-line. Comparamos as performances dos algoritmos entre si e discutimos os resultados obtidos mostrando que, apesar de um tempo de computação maior, o algoritmo bayesiano PM, proposto por nós, é superior aos outros algoritmos não-bayesianos quanto à generalização em situações de aprendizado estáticas e possui uma performance muito próxima do algoritmo bayesiano BKL. Fazemos, também, uma comparação entre os algoritmos PM e BC em situações de aprendizado variáveis com o tempo, com dados gerados artificialmente e em uma situação com dados reais, porém com um cenário simplificado, onde os utilizamos para prever o comportamento do índice da bolsa de valores de São Paulo (IBOVESPA), mostrando que, embora necessitem de um período longo de aprendizado, após essa fase inicial as previsões obtidas por esses algoritmos são surpreendentemente boas. Por fim, apresentamos uma discussão sobre aprendizado e quebra de simetria baseada nos estudos feitos. / In this work we study learning in a specific class of probabilistic models known as Hidden Markov Models (HMMs). First we discuss its basic theory and after we make a detailed study of the behavior of five different learning algorithms, two of them already known in the literature and the other three proposed by us in this work. The five algorithms are described below in the sequence they are presented in the thesis: Baum-Welch Algorithm(BW): consists of a renowed offline algorithm obtained by applying the EM-algorithm to the particular case of HMMs. Through the literature it is common to refer to it by the name Baum-Welch Reestimation Formulas. Baum-Welch Online Algorithm (BWO): online version of BW proposed by us. Baldi-Chauvin Algorithm (BC): online algorithm proposed by Baldi and Chauvin in [5] where a softmax representation for the probabilities of the HMMs is used and where the aim is to maximize the model likelihood at each iteration step. Online Bayesian Algorithm (BKL): an algorithm developed by us based on the work of Opper [74] where, after updating the probability distribution of the model with each new data, the obtained density is projected into a parametric family of tractable distributions minimizing the Kullback-Leibler distance between both. Mean Posterior Algorithm (PM): a simplification of BKL where the projection after the update is made on the mean posterior distribution. For each one of the above algorithms, we obtain learning curves by means of simulations where we use two distinct measures of generalization error: the Kullback-Leibler distance (dKL) and the Euclidian distance (dE). With exception of the BW algorithm, which can be used only in offline learning situations, we study for all the other algorithms the learning curves for both learning situations: online and offiine. We compare the performance of the algorithms with one another and discuss the results showing that, besides its larger computation time, the bayesian algorithm PM, proposed by us, is superior to the other non-bayesian algorithms with respect to the generalization in static learning situations and that it has a performance that is very close to the bayesian algorithm BKL. We also make a comparison between algorithms PM and BC in learning situations that change with time using artificially generated data and in one situation with real data, with a simplified scenario, where we use them to predict the behavior of the São Paulo Stock Market Index (BOVESPA) showing that, although they need a large learning period, after that initial phase the predictions obtained by both algorithms are surprisingly good. Finally, we present a discussion about learning and symmetry breaking based on the presented studies.

The purpose of this thesis is to propose some test statistics for testing the skewness and kurtosis parameters of a distribution, not limited to a normal distribution. Since a theoretical comparison is not possible, a simulation study has been conducted to compare the performance of the test statistics. We have compared both parametric methods (classical method with normality assumption) and non-parametric methods (bootstrap in Bias Corrected Standard Method, Efron’s Percentile Method, Hall’s Percentile Method and Bias Corrected Percentile Method). Our simulation results for testing the skewness parameter indicate that the power of the tests differs significantly across sample sizes, the choice of alternative hypotheses and methods we chose. For testing the kurtosis parameter, the simulation results suggested that the classical method performs well when the data are from both normal and beta distributions and bootstrap methods are useful for uniform distribution especially when the sample size is large.

The diploma paper is devoted to verification the application of SPC methods and performs evaluation of statistical stability and process eligibility of steel stampings in the real production process. In the second part is the author of the paper trying to design the optimal form of SPC methods for its use in a specified manufacturing process.

The aim of this thesis is creating a web application that allows dataset import and analyzing data with use of statistical methods. The application uses a user access that allows multiple number of persons manipulate with a single dataset, as well as interact with each other. Data is stored on a remote server and application is accessible from any computer that is connected to the Internet. The application is created in PHP programming language with use of MySQL database system, and user interface is built in HTML language with use of CSS styles. All parts of application are stored on an attached CD in form of text files. In addition to the web application, a part of the thesis is also a text output, which contains a theoretical part in form of description of the chosen statistical analysis methods, and a practical part containing list of application's functions, data model's description and demonstration of data analysis options on specific examples.

Poisson process is a common model for count data. However, a global Poisson model is inadequate for sparse data such as the marked salmon recovery data that have huge extraneous variations and noise. An empirical Bayes model, which enables information to be aggregated to overcome the lack of information from data in individual cells, is thus developed to handle these data. The method fits a local parametric Poisson model to describe the variation at each sampling period and incorporates this approach with a conventional local smoothing technique to remove noise. Finally, the overdispersion relative to the Poisson model is modelled by mixing these locally smoothed, Poisson models in an appropriate way. This method is then applied to the marked salmon data to obtain the overall patterns and the corresponding credibility intervals for the underlying trend in the data. / Science, Faculty of / Statistics, Department of / Graduate

In this thesis, I explore in two essays how to augment thin historical purchase data with other sources of information using Bayesian and probabilistic machine learning frameworks to better infer customers' preferences and their future behavior. In the first essay, I posit that firms can better manage recently-acquired customers by using the information from acquisition to inform future demand preferences for those customers. I develop a probabilistic machine learning model based on Deep Exponential Families to relate multiple acquisition characteristics with individual level demand parameters, and I show that the model is able to capture flexibly non-linear relationships between acquisition behaviors and demand parameters. I estimate the model using data from a retail context and show that firms can better identify which new customers are the most valuable. In the second essay, I explore how to combine the information collected through the customer journey—search queries, clicks and purchases; both within-journeys and across journeys—to infer the customer’s preferences and likelihood of buying, in settings in which there is thin purchase history and where preferences might change from one purchase journey to another. I propose a non-parametric Bayesian model that combines these different sources of information and accounts for what I call context heterogeneity, which are journey-specific preferences that depend on the context of the specific journey. I apply the model in the context of airline ticket purchases using data from one of the largest travel search websites and show that the model is able to accurately infer preferences and predict choice in an environment characterized by very thin historical data. I find strong context heterogeneity across journeys, reinforcing the idea that treating all journeys as stemming from the same set of preferences may lead to erroneous inferences.

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The general problem considered in this thesis is to determine an optimum strategy for deciding how to allocate the observations in each stage of a multi-stage experimental procedure between two binomial populations (e.g., the numbers of successes for two drugs) on the basis of the results of previous stages. After all of the stages of the experiment have been performed, one must make the terminal decision of which of the two populations has the higher probability of success. The optimum strategy is to be optimum relative to a given loss function; and a prior distribution, or weighting function, for the probabilities of success for the two populations is assumed. Two general classes of loss functions are considered, and it is assumed that the total number of observations in each stage is fixed prior to the experiment. In order to find the optimum strategy a method of analysis called extensive-form analysis is used. This is essentially a method for enumerating all the possible outcomes and corresponding strategies and choosing the optimum strategy for a given outcome. However, it is found that this method of analysis is much too long for all but small examples even when a digital computer is used. Because of this difficulty two alternative procedures, which are approximations to extensive-form analysis, are proposed. In the stage-by-stage procedure one assumes that at each stage he is at the last stage of his multi-stage procedure and allocates his observations to each of the two populations accordingly. It is shown that this is equivalent to assuming at each stage one has a one stage procedure. In the approximate procedure one (approximately) minimizes the posterior variance of the difference of the probabilities of success for the two populations at each stage. The computations for this procedure are quite simple to perform. The stage-by-stage procedure for the case that the two populations are normal with known variance rather than binomial is considered. It is then shown that the approximate procedure can be derived as an approximation to the stage-by- stage procedure when normal approximations to binomial distributions are used. The three procedures are compared with each other and with equal division of the observations in several examples by the computation of the probability of making the correct terminal decision for various values of the population parameters (the probabilities of success}. It is assumed in these computations that the prior distributions of the population parameters are rectangular distributions and that the loss functions are symmetric} i.e., the losses are as great for one wrong terminal decision as they are for the other. These computations show that, for the examples studied, there is relatively little loss in using the stage-by-stage procedure rather than extensive-form analysis and relatively little gain in using the approximate procedure instead of equal division of the observations. However, there is a relatively large loss in using the approximate procedure rather than the stage-by-stage procedure when the population parameters are close to 0 or 1. At first it is assumed there are a fixed number of stages in the experiment, but later in the thesis this restriction is weakened to the restriction that only the maximum number of stages possible in the experiment is fixed and the experiment can be stopped at any stage before the last possible stage is reached. Stopping rules for the stage-by- stage and the approximate procedures are then derived. / Ph. D.