Many prior distributions are suggested for variance parameters in the hierarchical model. The “Non-informative” interval of the conjugate inverse-gamma prior might cause problems. I consider three priors – conjugate inverse-gamma, log-normal and truncated normal for the variance parameters and do the numerical analysis on Gelman’s 8-schools data. Then with the posterior draws, I compare the Bayesian credible intervals of parameters using the three priors. I use predictive distributions to do predictions and then discuss the differences of the three priors suggested. / text

Made available in DSpace on 2014-12-17T14:10:24Z (GMT). No. of bitstreams: 1 SheilaMQML_DISSERT.pdf: 1368501 bytes, checksum: 2c822b3639e0a0b07601b48174a835c9 (MD5) Previous issue date: 2011-03-29 / In this work we analyze the skin bioimpedance statistical distribution. We focus on the study of two distinct samples: the statistics of impedance of several points in the skin of a single individual and the statistics over a population (many individuals) but in a single skin point. The impedance data was obtained from the literature (Pearson, 2007). Using the Shapiro-Wilk test and the assymmetry test we conclude that the impedance of a population is better described by an assymetric and non-normal distribution. On the other side, the data concerning the individual impedance seems to follow a normal distribution. We have performed a goodnes of fitting test and the better distribution to fit the data of a population is the log-normal distribution. It is interesting to note that our result for skin impedance is in simtony with body impedance from the literature of electrical engeneering. Our results have an impact over the statistical planning and modelling of skin impedance experiments. Special attention we should drive to the treatment of outliers in this kind of dataset. The results of this work are important in the general discussion of low impedance of points of acupuncture and also in the problem of skin biopotentials used in equipments like the Electrodermal Screen Tests. / Neste trabalho analisamos a distribui??o estat?stica de bioimped?ncia de pele. Focamos o estudo sobre duas amostragens: a estat?stica da imped?ncia de v?rios pontos na pele em um ?nico indiv?duo e a estat?stica de um lugar espec?fico da pele em uma popula??o. Os dados de imped?ncia de pele foram obtidos da literatura (Pearson, 2007). A combina??o dos resultados do teste de Shapiro-Wilk e do Teste de Assimetria confirmam que os dados em uma popula??o s?o melhores modelados por uma distribui??o n?o normal e assim?trica. Outrossim, os dados referentes ? distribui??o de imped?ncia para um indiv?duo parecem seguir a uma distribui??o normal. Realizamos testes de ajustes de curva e a melhor distribui??o encontrada para ajustar o conjunto dos dados de imped?ncia de pele para uma popula??o foi a log-normal. ? interessante notar que este resultado est? em sintonia com medidas de imped?ncia corporal de humanos relatados na literatura de engenharia el?trica. Nossos resultados t?m um impacto no planejamento estat?stico e na modelagem de experimentos da imped?ncia da pele, especialmente no tratamento de outliers neste conjunto de dados. Este resultado ? importante n?o somente para a quest?o cl?ssica da suposta baixa imped?ncia dos pontos de acupuntura, mas, al?m disso, para o problema geral de medidas de biopotenciais sobre a pele usada em equipamentos do tipo Electrodermal Screen Tests.

The rapid growth in demand for cellular mobile communications and emerging fixed wireless access has created the need to increase system capacity through more efficient utilization of the frequency spectrum, and the need for better grade of service. In cellular systems, capacity improvement can be achieved by reducing co-channel interference. Several techniques have been proposed in literature for mitigating co-channel interference, such as adaptive antennas and power control. Also, by allocating transmitter power and communication channels efficiently (resource allocation), overall co-channel interference can be maintained below a desired maximum tolerable level, while maximizing the carried traffic of the system. This dissertation presents investigation results on the performance of base station adaptive antennas, power control and channel allocation, as techniques for capacity improvement. Several approaches are analyzed. Firstly, we study the combined use of adaptive antennas and fractional loading factor, in order to estimate the potential capacity improvement achieved by adaptive antennas. Next, an extensive simulation analysis of a cellular network is carried out aiming to investigate the complex interrelationship between power control, channel allocation and adaptive antennas. In the first part of this simulation analysis, the combined use of adaptive antennas, power control and reduced cluster size is analyzed in a cellular system using fixed channel allocation. In the second part, we analyze the benefits of combining adaptive antennas, dynamic channel allocation and power control. Two representative channel allocation algorithms are considered and analyzed regarding how efficiently they transform reduced co-channel interference into higher carried traffic. Finally, the spatial filtering capability of adaptive antennas is used to allow several users to share the same channel within the same cell. Several allocation algorithms combined with power control are analyzed. / Ph. D.

Algumas abordagens para o problema de Planejamento Ótimo da Operação de Sistemas Hidrotérmicos (POOSH) utilizam modelos estocásticos para representar as vazões afluentes dos reservatórios do sistema. Essas abordagens utilizam, em geral, técnicas de Programação Dinâmica Estocástica (PDE) para resolver o POOSH. Por outro lado, muitos autores têm defendido o uso dos modelos determinísticos ou, particularmente, a Programação Dinâmica Determinística (PDD) por representar de forma individualizada a interação entre as usinas hidroelétricas do sistema. Nesse contexto, esta dissertação tem por objetivo comparar o desempenho da solução do POOSH obtida via PDD com a solução obtida pela PDE, que emprega um modelo Markoviano periódico, com distribuição condicional Log-Normal Truncada para representar as vazões. Além disso, é realizada a análise com abordagem bayesiana, no modelo de vazões, para estimação dos parâmetros e previsões das vazões afluentes. Comparamos as performances simulando a operação das usinas hidroelétricas de Furnas e Sobradinho, considerando séries de vazões geradas artificialmente / Some approaches for problem of Optimal Operation Planning of Hydrothermal Systems (OOPHS) use stochastic models to represent the inflows in the reservoirs that compose the system. These approaches typically use the Stochastic Dynamic Programming (SDP) to solve the OOPHS. On the other hand, many authors defend the use of deterministic models and, particularly, the Deterministic Dynamic Programming (DDP) since it individually represents the interaction between the hydroelectric plants. In this context, this dissertation aims to compare the performance of the OOPHS solution obtained via DDP with the one given by SDP, which employs a periodic Markovian model with conditional Truncated Log-Normal distribution to represent the inflows. Furthermore, it is performed a bayesian approach analysis, in the inflow model, for estimating the parameters and forecasting the inflows. We have compared the performances of the DDP and SDP solutions by simulating the hydroelectric plants of Furnas and Sobradinho, employing artificially generated series

Made available in DSpace on 2015-03-26T13:32:04Z (GMT). No. of bitstreams: 1 texto completo.pdf: 569181 bytes, checksum: 1b525772884dca74fcef6c9c8033aaa5 (MD5) Previous issue date: 2008-09-05 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Reburning caused by Phytophthora infestansis is characterized as an aggressive disease of great destructive impact, capable of limiting or even hindering the economic cultivation of the tomato plant under conditions of high humidity and low temperatures. In view of the problems reburning can cause to tomato plant crops, this work aimed to: 1) fit models to describe the progress of the disease and form groups of tomato accesses with similar curves; 2) estimate data referring to the number of days to reach 5% severity of the disease, by means of inverse regression; 3) fit survival curves by means of the Kaplan-Meier estimator for the access groups and compare them by means of the Logrank test;4)fit survival curves by means of probabilistic models and compare these curves with Kaplan Meir´s non-parametric technique. Using tomato reburning real data, it was possible to fit the exponential model (Y = y0 exp (rX)) to describe the disease s progress. The means of the parameter estimates were submitted to grouping analysis using the centroid method, generating 10 access groups. Time up to 5% of the disease was calculated via inverse regression. Non-parametric techniques were used to estimate survival function by means of the Kaplan-Meier´s estimator to compare the survival curves by the Logrank test .The survival function was also fit using the probabilistic models, exponential Weibull and Log-normal, respectively, which were compared by means of the verisimilitude ratio test (VRT), considering the generalized Gamma model, as a general case for these models. The methodology applied allowed fitting the exponential model to describe tomato plant reburning progress and to regroup the accesses studied in the 10 groups. The access BGH-6 obtained a smaller disease progress than the others, thus characterizing its higher resistance to the disease; An inverse regression allowed time estimation up to the occurrence of 5% of the severity of the tomato plant reburning. The Kaplan-Meier ´s non-parametric technique allowed estimating the survival curves of the tomato plant accesses belonging to the groups 1, 2, 4, 6 and 8. Utilizing the Logrank test, it could be concluded that most two-by-two comparisons were significant (p<0.05), except in the comparisons of groups 2x4, 4x8 and 6x8. The use of the probabilistic models, exponential Weibull and Log-normal allowed estimating the survival curves of groups 2, 4, 6 and 8, except for group 4, to which the Weibull model was not adequate. Comparing the probabilistic models with the non-parametric technique, the curves of the probabilistic models of groups 2 and 4 presented satisfactory results, compared to the curve estimated by Kaplan-Meier. / A requeima causada por Phytophthora infestans caracteriza-se por ser uma doença agressiva e de grande impacto destrutivo, podendo limitar ou até mesmo impedir o cultivo econômico do tomateiro sob condições de alta umidade e baixas temperaturas. Diante dos problemas que a requeima pode provocar às lavouras de tomate, este trabalho teve por objetivos: 1) ajustar modelos para descrever o progresso da doença e formar grupos de acessos de tomateiro com curvas semelhantes; 2) estimar dados referentes ao número de dias até atingir 5% de severidade da doença, por meio de regressão inversa; 3) ajustar curvas de sobrevivência por meio do estimador de Kaplan-Meier para grupos de acessos e compará-las mediante o uso do teste Logrank; 4) ajustar curvas de sobrevivência por meio de modelos probabilísticos e compará-las com a técnica não-paramétrica de Kaplan-Meier. Utilizando dados reais sobre a requeima do tomateiro, foi possível ajustar o modelo exponencial (Y = y0 exp (rX)) para descrever o progresso da doença. As médias das estimativas dos parâmetros foram submetidas à análise de agrupamento pelo método Centróide, o que gerou 10 grupos de acessos, sendo o tempo até a incidência de 5% da doença calculado via regressão inversa. Foram utilizadas técnicas não-paramétricas para estimar a função de sobrevivência por meio do estimador de Kaplan-Meier e para comparar as curvas de sobrevivência pelo teste Logrank. Foi também ajustada a função de sobrevivência, empregando-se os modelos probabilísticos Exponencial, Weibull e Log-normal, os quais foram comparados por meio do Teste da Razão da Verossimilhança (TRV), considerando-se o modelo Gama generalizado por ser caso geral para esses modelos. A metodologia utilizada permitiu ajustar o modelo Exponencial para descrever o progresso da requeima do tomateiro e agrupar os acessos estudados em 10 grupos. O acesso BGH-6 sofreu um progresso de doença menor que os demais, caracterizando-se, assim, sua maior resistência à enfermidade. A regressão inversa possibilitou estimar o tempo até a ocorrência de 5% da severidade da requeima do tomateiro. Pela técnica não-paramétrica de Kaplan-Meier, foi possível estimar as curvas de sobrevivência dos acessos de tomateiro pertencentes aos grupos 1, 2, 4, 6 e 8. Utilizando o teste Logrank, pode-se concluir que a maioria das comparações duas a duas foi significativa (p<0,05), exceto nas comparações dos grupos 2x4, 4x8 e 6x8. O uso dos modelos probabilísticos Exponencial, Weibull e Log-normal possibilitou a estimação das curvas de sobrevivência nos grupos 2, 4, 6 e 8, exceto no grupo 4, em que o modelo Weibull não foi adequado. Comparando os modelos probabilísticos com a técnica não-paramétrica, as curvas dos modelos probabilísticos dos grupos 2 e 4 apresentaram ajustes satisfatórios com relação à curva estimada por Kaplan-Meier.

Algumas abordagens para o problema de Planejamento Ótimo da Operação de Sistemas Hidrotérmicos (POOSH) utilizam modelos estocásticos para representar as vazões afluentes dos reservatórios do sistema. Essas abordagens utilizam, em geral, técnicas de Programação Dinâmica Estocástica (PDE) para resolver o POOSH. Por outro lado, muitos autores têm defendido o uso dos modelos determinísticos ou, particularmente, a Programação Dinâmica Determinística (PDD) por representar de forma individualizada a interação entre as usinas hidroelétricas do sistema. Nesse contexto, esta dissertação tem por objetivo comparar o desempenho da solução do POOSH obtida via PDD com a solução obtida pela PDE, que emprega um modelo Markoviano periódico, com distribuição condicional Log-Normal Truncada para representar as vazões. Além disso, é realizada a análise com abordagem bayesiana, no modelo de vazões, para estimação dos parâmetros e previsões das vazões afluentes. Comparamos as performances simulando a operação das usinas hidroelétricas de Furnas e Sobradinho, considerando séries de vazões geradas artificialmente / Some approaches for problem of Optimal Operation Planning of Hydrothermal Systems (OOPHS) use stochastic models to represent the inflows in the reservoirs that compose the system. These approaches typically use the Stochastic Dynamic Programming (SDP) to solve the OOPHS. On the other hand, many authors defend the use of deterministic models and, particularly, the Deterministic Dynamic Programming (DDP) since it individually represents the interaction between the hydroelectric plants. In this context, this dissertation aims to compare the performance of the OOPHS solution obtained via DDP with the one given by SDP, which employs a periodic Markovian model with conditional Truncated Log-Normal distribution to represent the inflows. Furthermore, it is performed a bayesian approach analysis, in the inflow model, for estimating the parameters and forecasting the inflows. We have compared the performances of the DDP and SDP solutions by simulating the hydroelectric plants of Furnas and Sobradinho, employing artificially generated series

[pt] O principal objetivo desta dissertação é realizar a previsão da reserva IBNR. Para isto foi desenvolvido um modelo estatístico de distribuições combinadas que busca uma adequada representação dos dados. A reserva IBNR, sigla em inglês para Incurred But Not Reported, representa o montante que as seguradoras precisam ter para pagamentos de sinistros atrasados, que já ocorreram no passado, mas ainda não foram avisados à seguradora até a data presente. Dada a importância desta reserva, diversos métodos para estimação da reserva IBNR já foram propostos. Um dos métodos mais utilizado pelas seguradoras é o Método Chain Ladder, que se baseia em triângulos run-off, que é o agrupamento dos dados conforme data de ocorrência e aviso de sinistro. No entanto o agrupamento dos dados faz com que informações importantes sejam perdidas. Esta dissertação baseada em outros artigos e trabalhos que consideram o não agrupamento dos dados, propõe uma nova modelagem para os dados não agrupados. O modelo proposto combina a distribuição do atraso no aviso da ocorrência, representada aqui pela distribuição log-normal truncada (pois só há informação até a última data observada); a distribuição da quantidade total de sinistros ocorridos num dado período, modelada pela distribuição Poisson; e a distribuição do número de sinistros ocorridos em um dado período e avisados até a última data observada, que será caracterizada por uma distribuição Binomial. Por fim, a quantidade de sinistros IBNR foi estimada por método e pelo Chain Ladder e avaliou-se a capacidade de previsão de ambos. Apesar da distribuição de atrasos do modelo proposto se adequar bem aos dados, o modelo proposto obteve resultados inferiores ao Chain Ladder em termos de previsão. / [en] The main objective of this dissertation is to predict the IBNR reserve. For this, it was developed a statistical model of combined distributions looking for a new distribution that fits the data well. The IBNR reserve, short for Incurred But Not Reported, represents the amount that insurers need to have to pay for the claims that occurred in the past but have not been reported until the present date. Given the importance of this reserve, several methods for estimating this reserve have been proposed. One of the most used methods for the insurers is the Chain Ladder, which is based on run-off triangles; this is a format of grouping the data according to the occurrence and the reported date. However this format causes the lost of important information. This dissertation, based on other articles and works that consider the data not grouped, proposes a new model for the non-aggregated data. The proposed model combines the delay in the claim report distribution represented by a log normal truncated (because there is only information until the last observed date); the total amount of claims incurred in a given period modeled by a Poisson distribution and the number of claims occurred in a certain period and reported until the last observed date characterized by a binomial distribution. Finally, the IBNR reserve was estimated by this method and by the chain ladder and the prediction capacity of both methods will be evaluated. Although the delay distribution seems to fit the data well, the proposed model obtained inferior results to the Chain Ladder in terms of forecast.

This thesis considers statistical issues in source localization from the received signal strength (RSS) measurements at sensor locations, under the practical assumption of log-normal shadowing. Distance information of source from sensor locations can be estimated from RSS measurements and many algorithms directly use powers of distances to localize the source, even though distance measurements are not directly available. The first part of the thesis considers the statistical analysis of distance estimation from RSS measurments. We show that the underlying problem is inefficient and there is only one unbiased estimator for this problem and its mean square error (MSE) grows exponentially with noise power. Later, we provide the linear minimum mean square error (MMSE) estimator whose bias and MSE are bounded in noise power. The second part of the thesis establishes an isomorphism between estimates of differences between squares of distances and the source location. This is used to completely characterize the class of unbiased estimates of the source location and to show that their MSEs grow exponentially with noise powers. Later, we propose an estimate based on the linear MMSE estimate of distances that has error variance and bias that is bounded in the noise variance.

Semicontinuous data consist of a combination of a point-mass at zero and a positive skewed distribution. This type of non-negative data distribution is found in data from many fields, but presents unique challenges for analysis. Specifically, these data cannot be analyzed using positive distributions, but distributions that are unbounded are also likely a poor fit. Two-part models incorporate both the zero values from semicontinuous data and the positive continuous values. In this dissertation, we compare zero-inflated gamma (ZIG) and zero-inflated log-normal (ZILN) two-part models. For both of these models, the probability that an outcome is non-zero is modeled via logistic regression. Then the distribution of the non-zero outcomes is modeled via gamma regression with a log-link for ZIG regression and via log-normal regression for ZILN. In this dissertation we propose tests which combine the two parts of the ZIG and ZILN models in meaningful ways for performing a two group comparison. Then we compare these tests in terms of observed Type 1 error rates and power levels under both correctly specified and misspecified ZIG and ZILN models. Tests falling under two main hypotheses are examined. First, we look at two-part tests which come from a two-part hypothesis of no difference between the two groups in terms of the probability of non-zero values and in terms of the the mean of the non-zero values. The second type of tests are mean-based tests. These combine the two parts of the model in ways related to the overall group means of the semicontinuous variable. When not adjusting for covariates, two tests are developed based on a difference of means (DM) and a ratio of means (RM). When adjusting for covariates, tests using mean-based hypotheses are developed which marginalize over the values of the adjusting covariates. Under the adjusting framework, two ratio of means statistics are proposed and examined, an average of the subject specific ratio of means (RMSS) and a ratio of the marginal group means (RMMAR). Simulations are used to compare Type 1 error and power for these tests and standard two group comparison tests. Simulation results show that when ZIG and ZILN models are misspecified and the coefficient of variation (CoV) and/or sample size is large, there are differences in Type 1 error and power results between the misspecified and correctly specified models. Specifically, when ZILN data with high CoV or sample size are analyzed as ZIG, Type 1 error rates are prohibitively high. On the other hand, when ZIG data are analyzed as ZILN under these scenarios, power levels are much lower for ZILN analyses than for ZIG analyses. Examination of Q-Q plots show, however, that in these settings, distinguishing between ZIG and ZILN data can be relatively straightforward. When the coefficient of variation is small it is harder to distinguish between ZIG and ZILN models, but the differences between Type 1 error rates and power levels for misspecified or correctly specified models is also slight. Finally, we use the proposed methods to analyze a data set involving Parkinson's disease (PD) and driving. A number of these methods show that PD subjects exhibit poorer lane keeping ability than control subjects.

The design of clinical trials is one of the important problems in medical statistics. Its main purpose is to determine the methodology and the sample size required of a testing study to examine the safety and efficacy of drugs. It is also a part of the Food and Drug Administration approval process. In this thesis, we first study the comparison of the efficacy of drugs in clinical trials. We focus on the two-sample comparison of proportions to investigate testing strategies based on two-stage design. The properties and advantages of the procedures from the proposed testing designs are demonstrated by numerical results, where comparison with the classical method is made under the same sample size. A real example discussed in Cardenal et al. (1999) is provided to explain how the methods may be used in practice. Some figures are also presented to illustrate the pattern changes of the power functions of these methods. In addition, the proposed procedure is also compared with the Pocock (1997) and O¡¦Brien and Fleming (1979) tests based on the standardized statistics. In the second part of this work, the operating room scheduling problem is considered, which is also important in medical studies. The national health insurance system has been conducted more than ten years in Taiwan. The Bureau of National Health Insurance continues to improve the national health insurance system and try to establish a reasonable fee ratio for people in different income ranges. In accordance to the adjustment of the national health insurance system, hospitals must pay more attention to control the running cost. One of the major hospital's revenues is generated by its surgery center operations. In order to maintain financial balance, effective operating room management is necessary. For this topic, this study focuses on the model fitting of operating times and operating room scheduling. Log-normal and mixture log-normal distributions are identified to be acceptable statistically in describing these operating times. The procedure is illustrated through analysis of thirteen operations performed in the gynecology department of a major teaching hospital in southern Taiwan. The best fitting distributions are used to evaluate performances of some operating combinations on daily schedule, which occurred in real data. The fitted distributions are selected through certain information criteria and bootstrapping the log-likelihood ratio test. Moreover, we also classify the operations into three different categories as well as three stages for each operation. Then based on the classification, a strategy of efficient scheduling is proposed. The benefits of rescheduling based on the proposed strategy are compared with the original scheduling observed.