Thesis (M.S. in Modeling, Virtual Environments, and Simulation (MOVES))--Naval Postgraduate School, June 2007. / Thesis Advisor(s): Christian Darken. "June 2007." Includes bibliographical references (p. 47). Also available in print.

X.-C. Lou, J.R. Rohlicek, P.G. Coxson, G.C. Verghese, A.S. Willsky. / Bibliography: leaves 5-6. / "March 1985."

Thesis (Ph. D.)--University of Washington, 2000. / Vita. Includes bibliographical references (p. 147-154).

Thesis (Ph. D.)--University of Texas Health Science Center at Houston, School of Public Health, 2008. / Source: Dissertation Abstracts International, Volume: 69-02, Section: B, page: 1086. Adviser: Wenyaw Chan. Includes bibliographical references.

The elderly living in smart homes can have their daily movement recorded and analyzed. Given the fact that different elders can have their own living habits, a methodology that can automatically identify their daily activities and discover their daily routines will be useful for better elderly care and support. In this thesis research, we focus on developing data mining algorithms for automatic detection of behavioral patterns from the trajectory data of an individual for activity identification, daily routine discovery, and activity prediction. The key challenges for the human activity analysis include the need to consider longer-range dependency of the sensor triggering events for activity modeling and to capture the spatio-temporal variations of the behavioral patterns exhibited by human. We propose to represent the trajectory data using a behavior-aware flow graph which is a probabilistic finite state automaton with its nodes and edges attributed with some local behavior-aware features. Subflows can then be extracted from the flow graph using the kernel k-means as the underlying behavioral patterns for activity identification. Given the identified activities, we propose a novel nominal matrix factorization method under a Bayesian framework with Lasso to extract highly interpretable daily routines. To better take care of the variations of activity durations within each daily routine, we further extend the Bayesian framework with a Markov jump process as the prior to incorporate the shift-invariant property into the model. For empirical evaluation, the proposed methodologies have been compared with a number of existing activity identification and daily routine discovery methods based on both synthetic and publicly available real smart home data sets with promising results obtained. In the thesis, we also illustrate how the proposed unsupervised methodology could be used to support exploratory behavior analysis for elderly care.

Orientador: José Gilberto Spasiani Rinaldi / Banca: Luiz Carlos Benini / Banca: Teresa Cristina Martins Dias / Resumo: As Cadeias de Markov são um instrumento poderosíssimo para previsão de eventos do futuro baseado apenas em um passado relativamente recente. São muito utilizadas nas situações mais diversas como na bolsa de valores, na fidelização de clientes, previsão do tempo, dentre outras. O objetivo principal deste trabalho é mostrar, em nível de Ensino Médio algumas interessantes aplicações, bem como estimular os alunos à pesquisa, coleta e processamento de dados, mostrando-nos o quanto a Matemática está presente no cotidiano de cada um deles / Abstract: The Markov Chains are a powerful tool for predicting future events based only on a relatively recent past. They are widely used in different situations such as on the stock exchange in customer loyalty, weather, among others. The main objective of this work is to show high school level in some interesting applications, as well as encourage students to research, collecting and processing data, showing us how mathematics is present in the daily life of each one of them / Mestre

Recentemente, Guiol, Machado e Schinazi propuseram um modelo estocástico para a evolução de espécies. Nesse modelo, as intensidades de nascimentos de novas espécies e de ocorrências de extinções são invariantes ao longo do tempo. Ademais, no instante de nascimento de uma nova espécie, a mesma é rotulada com um número aleatório gerado de uma distribuição absolutamente contínua. Toda vez que ocorre uma extinção, apenas uma espécie morre - a com o menor número vinculado. Quando a intensidade com que surgem novas espécies é maior que a com que ocorrem extinções, existe um valor crítico f_c tal que todas as espécies rotuladas com números menores que f_c morrerão quase certamente depois de um tempo aleatório finito, e as rotuladas com números maiores que f_c terão probabilidades positivas de se tornarem perpétuas. No entanto, espécies menos aptas continuam a aparecer durante o processo evolutivo e não há a garantia do surgimento de uma espécie imortal. Consideramos um caso particular do modelo de Guiol, Machado e Schinazi e abordamos estes dois últimos pontos. Caracterizamos o processo pontual limite vinculado às espécies na fase subcrítica do modelo e discorremos sobre a existência de espécies imortais. / Recently, Guiol, Machado and Schinazi proposed a stochastic model for species evolution. In this model, births and deaths of species occur with intensities invariant over time. Moreover, at the time of birth of a new species, it is labeled with a random number sampled from an absolutely continuous distribution. Each time there is an extinction event, exactly one existing species disappears: that with the smallest number. When the birth rate is greater than the extinction rate, there is a critical value f_c such that all species that come with number less than f_c will almost certainly die after a finite random time, and those with numbers higher than f_c survive forever with positive probability. However, less suitable species continue to appear during the evolutionary process and there is no guarantee the emergence of an immortal species. We consider a particular case of Guiol, Machado and Schinazi model and approach these last two points. We characterize the limit point process linked to species in the subcritical phase of the model and discuss the existence of immortal species.

In this thesis, we investigate the estimation problem and inference problem for the complex models. Two major categories of complex models are emphasized by us, one is generalized linear models, the other is time series models. For the generalized linear models, we consider one fundamental problem about sure screening for interaction terms in ultra-high dimensional feature space; for time series models, an important model assumption about Markov property is considered by us. The first part of this thesis illustrates the significant interaction pursuit problem for ultra-high dimensional models with two-way interaction effects. We propose a simple sure screening procedure (SSI) to detect significant interactions between the explanatory variables and the response variable in the high or ultra-high dimensional generalized linear regression models. Sure screening method is a simple, but powerful tool for the first step of feature selection or variable selection for ultra-high dimensional data. We investigate the sure screening properties of the proposal method from theoretical insight. Furthermore, we indicate that our proposed method can control the false discovery rate at a reasonable size, so the regularized variable selection methods can be easily applied to get more accurate feature selection in the following model selection procedures. Moreover, from the viewpoint of computational efficiency, we suggest a much more efficient algorithm-discretized SSI (DSSI) to realize our proposed sure screening method in practice. And we also investigate the properties of these two algorithms SSI and DSSI in simulation studies and apply them to some real data analyses for illustration. For the second part, our concern is the testing of the Markov property in time series processes. Markovian assumption plays an extremely important role in time series analysis and is also a fundamental assumption in economic and financial models. However, few existing research mainly focused on how to test the Markov properties for the time series processes. Therefore, for the Markovian assumption, we propose a new test procedure to check if the time series with beta-mixing possesses the Markov property. Our test is based on the Conditional Distance Covariance (CDCov). We investigate the theoretical properties of the proposed method. The asymptotic distribution of the proposed test statistic under the null hypothesis is obtained, and the power of the test procedure under local alternative hypothesizes have been studied. Simulation studies are conducted to demonstrate the finite sample performance of our test.

Report to Hydrology Laboratory, Office of Hydrology, National Weather Service, NOAH, Dept. of Commerce, Contract 6 -35229 / The value of a forecast system in preventing urban property damage depends on the accuracy of the forecasts, the time at which they are received, the response by the floodplain dweller and the êfficacy of that response. A systems model of the overall flood forecast -response system is developed. Evaluation of the system is accomplished by a decision theoretic methodology. A case study is done for Milton, Pennsylvania, which evaluates the present system and potential changes to it. It is concluded that the sequential nature of the forecast sequence must be considered in modeling the flood forecast -response system if a meaningful evaluation of the economic value of the system is to be obtained. Methodology for obtaining the parameterization of the model from the available data is given. Computer programs have been written to handle a good portion of the calculations. While more work is needed on obtaining accurate parameterization of certain parts of the model, such as the actual response to forecasts; use of the procedures and programs as they now stand produces reasonable evaluations.

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