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Webster, Gregg. "Bayesian logistic regression models for credit scoring". Thesis, Rhodes University, 2011. http://hdl.handle.net/10962/d1005538.
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The Bayesian approach to logistic regression modelling for credit scoring is useful when there are data quantity issues. Data quantity issues might occur when a bank is opening in a new location or there is change in the scoring procedure. Making use of prior information (available from the coefficients estimated on other data sets, or expert knowledge about the coefficients) a Bayesian approach is proposed to improve the credit scoring models. To achieve this, a data set is split into two sets, “old” data and “new” data. Priors are obtained from a model fitted on the “old” data. This model is assumed to be a scoring model used by a financial institution in the current location. The financial institution is then assumed to expand into a new economic location where there is limited data. The priors from the model on the “old” data are then combined in a Bayesian model with the “new” data to obtain a model which represents all the available information. The predictive performance of this Bayesian model is compared to a model which does not make use of any prior information. It is found that the use of relevant prior information improves the predictive performance when the size of the “new” data is small. As the size of the “new” data increases, the importance of including prior information decreases
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Richmond, James Howard. "Bayesian Logistic Regression Models for Software Fault Localization". Case Western Reserve University School of Graduate Studies / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=case1326658577.
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Ozturk, Olcay. "Bayesian Semiparametric Models For Nonignorable Missing Datamechanisms In Logistic Regression". Master's thesis, METU, 2011. http://etd.lib.metu.edu.tr/upload/12613241/index.pdf.
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In this thesis, Bayesian semiparametric models for the missing data mechanisms of nonignorably missing covariates in logistic regression are developed. In the missing data literature, fully parametric approach is used to model the nonignorable missing data mechanisms. In that approach, a probit or a logit link of the conditional probability of the covariate being missing is modeled as a linear combination of all variables including the missing covariate itself. However, nonignorably missing covariates may not be linearly related with the probit (or logit) of this conditional probability. In our study, the relationship between the probit of the probability of the covariate being missing and the missing covariate itself is modeled by using a penalized spline regression based semiparametric approach. An efficient Markov chain Monte Carlo (MCMC) sampling algorithm to estimate the parameters is established. A WinBUGS code is constructed to sample from the full conditional posterior distributions of the parameters by using Gibbs sampling. Monte Carlo simulation experiments under different true missing data mechanisms are applied to compare the bias and efficiency properties of the resulting estimators with the ones from the fully parametric approach. These simulations show that estimators for logistic regression using semiparametric missing data models maintain better bias and efficiency properties than the ones using fully parametric missing data models when the true relationship between the missingness and the missing covariate has a nonlinear form. They are comparable when this relationship has a linear form.
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Kynn, Mary. "Eliciting Expert Knowledge for Bayesian Logistic Regression in Species Habitat Modelling". Queensland University of Technology, 2005. http://eprints.qut.edu.au/16041/.
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This research aims to develop a process for eliciting expert knowledge and incorporating this knowledge as prior distributions for a Bayesian logistic regression model. This work was motivated by the need for less data reliant methods of modelling species habitat distributions. A comprehensive review of the research from both cognitive psychology and the statistical literature provided specific recommendations for the creation of an elicitation scheme. These were incorporated into the design of a Bayesian logistic regression model and accompanying elicitation scheme. This model and scheme were then implemented as interactive, graphical software called ELICITOR created within the BlackBox Component Pascal environment. This software was specifically written to be compatible with existing Bayesian analysis software, winBUGS as an odd-on component. The model, elicitation scheme and software were evaluated through five case studies of various fauna and flora species. For two of these there were sufficient data for a comparison of expert and data-driven models. The case studies confirmed that expert knowledge can be quantified and formally incorporated into a logistic regression model. Finally, they provide a basis for a thorough discussion of the model, scheme and software extensions and lead to recommendations for elicitation research.
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Paz, Rosineide Fernando da. "Alternative regression models to beta distribution under bayesian approach". Universidade Federal de São Carlos, 2017. https://repositorio.ufscar.br/handle/ufscar/9146.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
The Beta distribution is a bounded domain distribution which has dominated the modeling the distribution of random variable that assume value between 0 and 1. Bounded domain distributions arising in various situations such as rates, proportions and index. Motivated by an analysis of electoral votes percentages (where a distribution with support on the positive real numbers was used, although a distribution with limited support could be more suitable) we focus on alternative distributions to Beta distribution with emphasis in regression models. In this work, initially we present the Simplex mixture model as a flexible model to modeling the distribution of bounded random variable then we extend the model to the context of regression models with the inclusion of covariates. The parameters estimation is discussed for both models considering Bayesian inference. We apply these models to simulated data sets in order to investigate the performance of the estimators. The results obtained were satisfactory for all the cases investigated. Finally, we introduce a parameterization of the L-Logistic distribution to be used in the context of regression models and we extend it to a mixture of mixed models.
A distribuição beta é uma distribuição com suporte limitado que tem dominado a modelagem de variáveis aleatórias que assumem valores entre 0 e 1. Distribuições com suporte limitado surgem em várias situações como em taxas, proporções e índices. Motivados por uma análise de porcentagens de votos eleitorais, em que foi assumida uma distribuição com suporte nos números reais positivos quando uma distribuição com suporte limitado seira mais apropriada, focamos em modelos alternativos a distribuição beta com enfase em modelos de regressão. Neste trabalho, apresentamos, inicialmente, um modelo de mistura de distribuições Simplex como um modelo flexível para modelar a distribuição de variáveis aleatórias que assumem valores em um intervalo limitado, em seguida estendemos o modelo para o contexto de modelos de regressão com a inclusão de covariáveis. A estimação dos parâmetros foi discutida para ambos os modelos, considerando o método bayesiano. Aplicamos os dois modelos a dados simulados para investigarmos a performance dos estimadores usados. Os resultados obtidos foram satisfatórios para todos os casos investigados. Finalmente, introduzimos a distribuição L-Logistica no contexto de modelos de regressão e posteriormente estendemos este modelo para o contexto de misturas de modelos de regressão mista.
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Zimmer, Zachary. "Predicting NFL Games Using a Seasonal Dynamic Logistic Regression Model". VCU Scholars Compass, 2006. http://scholarscompass.vcu.edu/etd_retro/97.
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The article offers a dynamic approach for predicting the outcomes of NFL games using the NFL games from 2002-2005. A logistic regression model is used to predict the probability that one team defeats another. The parameters of this model are the strengths of the teams and a home field advantage factor. Since it assumed that a team's strength is time dependent, the strength parameters were assigned a seasonal time series process. The best model was selected using all the data from 2002 through the first seven weeks of 2005. The last weeks of 2005 were used for prediction estimates.
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Fu, Shuting. "Bayesian Logistic Regression Model with Integrated Multivariate Normal Approximation for Big Data". Digital WPI, 2016. https://digitalcommons.wpi.edu/etd-theses/451.
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The analysis of big data is of great interest today, and this comes with challenges of improving precision and efficiency in estimation and prediction. We study binary data with covariates from numerous small areas, where direct estimation is not reliable, and there is a need to borrow strength from the ensemble. This is generally done using Bayesian logistic regression, but because there are numerous small areas, the exact computation for the logistic regression model becomes challenging. Therefore, we develop an integrated multivariate normal approximation (IMNA) method for binary data with covariates within the Bayesian paradigm, and this procedure is assisted by the empirical logistic transform. Our main goal is to provide the theory of IMNA and to show that it is many times faster than the exact logistic regression method with almost the same accuracy. We apply the IMNA method to the health status binary data (excellent health or otherwise) from the Nepal Living Standards Survey with more than 60,000 households (small areas). We estimate the proportion of Nepalese in excellent health condition for each household. For these data IMNA gives estimates of the household proportions as precise as those from the logistic regression model and it is more than fifty times faster (20 seconds versus 1,066 seconds), and clearly this gain is transferable to bigger data problems.
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Schoergendorfer, Angela. "BAYESIAN SEMIPARAMETRIC GENERALIZATIONS OF LINEAR MODELS USING POLYA TREES". UKnowledge, 2011. http://uknowledge.uky.edu/gradschool_diss/214.
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In a Bayesian framework, prior distributions on a space of nonparametric continuous distributions may be defined using Polya trees. This dissertation addresses statistical problems for which the Polya tree idea can be utilized to provide efficient and practical methodological solutions.
One problem considered is the estimation of risks, odds ratios, or other similar measures that are derived by specifying a threshold for an observed continuous variable. It has been previously shown that fitting a linear model to the continuous outcome under the assumption of a logistic error distribution leads to more efficient odds ratio estimates. We will show that deviations from the assumption of logistic error can result in great bias in odds ratio estimates. A one-step approximation to the Savage-Dickey ratio will be presented as a Bayesian test for distributional assumptions in the traditional logistic regression model. The approximation utilizes least-squares estimates in the place of a full Bayesian Markov Chain simulation, and the equivalence of inferences based on the two implementations will be shown. A framework for flexible, semiparametric estimation of risks in the case that the assumption of logistic error is rejected will be proposed.
A second application deals with regression scenarios in which residuals are correlated and their distribution evolves over an ordinal covariate such as time. In the context of prediction, such complex error distributions need to be modeled carefully and flexibly. The proposed model introduces dependent, but separate Polya tree priors for each time point, thus pooling information across time points to model gradual changes in distributional shapes. Theoretical properties of the proposed model will be outlined, and its potential predictive advantages in simulated scenarios and real data will be demonstrated.
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Tang, Zhongwen. "LOF of logistic GEE models and cost efficient Bayesian optimal designs for nonlinear combinations of parameters in nonlinear regression models". Diss., Manhattan, Kan. : Kansas State University, 2008. http://hdl.handle.net/2097/1011.
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Dikshit, Anubhav. "Omnichannel path to purchase : Viability of Bayesian Network as Market Attribution Models". Thesis, Linköpings universitet, Filosofiska fakulteten, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-165443.
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Market attribution is the problem of interpreting the influence of advertisements onthe user’s decision process. Market attribution is a hard problem, and it happens to be asignificant reason for Google’s revenue. There are broadly two types of attribution models- data-driven and heuristics.This thesis focuses on the data driven attribution modeland explores the viability of using Bayesian Network as market attribution models andbenchmarks the performance against a logistic regression. The data used in this thesiswas prepossessed using undersampling technique. Furthermore, multiple techniques andalgorithms to learn and train Bayesian Network are explored and evaluated.For the given dataset, it was found that Bayesian Network can be used for market at-tribution modeling and that its performance is better than the baseline logistic model. Keywords: Market Attribution Model, Bayesian Network, Logistic Regression.
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Ortega, Villa Ana Maria. "Semiparametric Varying Coefficient Models for Matched Case-Crossover Studies". Diss., Virginia Tech, 2015. http://hdl.handle.net/10919/64181.
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Semiparametric modeling is a combination of the parametric and nonparametric models in which some functions follow a known form and some others follow an unknown form. In this dissertation we made contributions to semiparametric modeling for matched case-crossover data.
In matched case-crossover studies, it is generally accepted that the covariates on which a case and associated controls are matched cannot exert a confounding effect on independent predictors included in the conditional logistic regression model. Any stratum effect is removed by the conditioning on the fixed number of sets of the case and controls in the stratum. However, some matching covariates such as time, and/or spatial location often play an important role as an effect modification. Failure to include them makes incorrect statistical estimation, prediction and inference. Hence in this dissertation, we propose several approaches that will allow the inclusion of time and spatial location as well as other effect modifications such as heterogeneous subpopulations among the data.
To address modification due to time, three methods are developed: the first is a parametric approach, the second is a semiparametric penalized approach and the third is a semiparametric Bayesian approach. We demonstrate the advantage of the one stage semiparametric approaches using both a simulation study and an epidemiological example of a 1-4 bi-directional case-crossover study of childhood aseptic meningitis with drinking water turbidity.
To address modifications due to time and spatial location, two methods are developed: the first one is a semiparametric spatial-temporal varying coefficient model for a small number of locations. The second method is a semiparametric spatial-temporal varying coefficient model, and is appropriate when the number of locations among the subjects is medium to large. We demonstrate the accuracy of these approaches by using simulation studies, and when appropriate, an epidemiological example of a 1-4 bi-directional case-crossover study.
Finally, to explore further effect modifications by heterogeneous subpopulations among strata we propose a nonparametric Bayesian approach constructed with Dirichlet process priors, which clusters subpopulations and assesses heterogeneity. We demonstrate the accuracy of our approach using a simulation study, as well a an example of a 1-4 bi-directional case-crossover study.Ph. D.
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Diniz, Márcio Augusto. "Modelos bayesianos semi-paramétricos para dados binários". Universidade de São Paulo, 2015. http://www.teses.usp.br/teses/disponiveis/45/45133/tde-02112015-013658/.
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Este trabalho propõe modelos Bayesiano semi-paramétricos para dados binários. O primeiro modelo é uma mistura em escala que permite lidar com discrepâncias relacionadas a curtose do modelo Logístico. É uma extensão relevante a partir do que já foi proposto por Basu e Mukhopadhyay (2000) ao possibilitar a interpretação da distribuição a priori dos parâmetros através de razões de chances. O segundo modelo usufrui da mistura em escala em conjunto com a transformação proposta por \\Yeo e Johnson (2000) possibilitando que a curtose assim como a assimetria sejam ajustadas e um parâmetro informativo de assimetria seja estimado. Esta transformação é muito mais apropriada para lidar com valores negativos do que a transformação de Box e Cox (1964) utilizada por Guerrero e Johnson (1982) e é mais simples do que o modelo proposto por Stukel (1988). Por fim, o terceiro modelo é o mais geral entre todos e consiste em uma mistura de posição e escala tal que possa descrever curtose, assimetria e também bimodalidade. O modelo proposto por Newton et al. (1996), embora, seja bastante geral, não permite uma interpretação palpável da distribuição a priori para os pesquisadores da área aplicada. A avaliação dos modelos é realizada através de medidas de distância de probabilidade Cramér-von Mises, Kolmogorov-Smirnov e Anderson-Darling e também pelas Ordenadas Preditivas Condicionais.This work proposes semi-parametric Bayesian models for binary data. The first model is a scale mixture that allows handling discrepancies related to kurtosis of Logistic model. It is a more interesting extension than has been proposed by Basu e Mukhopadyay (1998) because this model allows the interpretation of the prior distribution of parameters using odds ratios. The second model enjoys the scale mixture together with the scale transformation proposed by Yeo and Johnson (2000) modeling the kurtosis and the asymmetry such that a parameter of asymmetry is estimated. This transformation is more appropriate to deal with negative values than the transformation of Box e Cox (1964) used by Guerrero e Johnson (1982) and simpler than the model proposed by Stukel (1988). Finally, the third model is the most general among all and consists of a location-scale mixture that can describe kurtosis and skewness also bimodality. The model proposed by Newton et al (1996), although general, does not allow a tangible interpretation of the a priori distribution for reseachers of applied area. The evaluation of the models is performed through distance measurements of distribution of probabilities Cramer-von Mises Kolmogorov-Smirnov and Anderson-Darling and also the Conditional Predictive sorted.
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Mendonça, Tiago Silva. "Modelos de regressão logística clássica, Bayesiana e redes neurais para Credit Scoring". Universidade Federal de São Carlos, 2008. https://repositorio.ufscar.br/handle/ufscar/4535.
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Previous issue date: 2008-02-15Important advances have been achieved in the granting of credit, however, the problem of identifying good customers for the granting of credit does not provide a definitive solution. Several techniques were presented and are being developed, each presents its characteristics, advantages and disadvantages as to their discrimination power, robustness, ease of implementation and possibility of interpretation. This work presents three techniques for the classification of defaults in models of Credit Score, Classical Logistic Regression, Bayesian Logistic Regression with no prior information and Artificial Neural Networks with a few different architectures. The main objective of the study is to compare the performance of these techniques in the identification of customers default. For this, four metrics were used for comparison of models: predictive capacity, ROC Curve, Statistics of Kolmogorov Smirnov and capacity of hit models. Two data bases were used, an artificial bank and a real bank. The database was constructed artificially based on an article by Breiman that generates the explanatory variables from a multivariate normal distribution and the actual database used is a problem with Credit Score of a financial institution that operates in the retail Brazilian market more than twenty years.
Importantes avanços vêm sendo conquistados na área de concessão de crédito, não obstante, o problema de identificação de bons clientes para a concessão de crédito não apresenta uma solução definitiva. Diversas técnicas foram apresentadas e vêm sendo desenvolvidas, cada uma apresenta suas características, com vantagens e desvantagens no tocante ao seu poder de discriminação, robustez, facilidade de implementação e possibilidade de interpretação. Este trabalho apresenta três técnicas para a classificação de inadimplência em modelos de Credit Score, Regressão Logística Clássica, Regressão Logística Bayesiana com priori não informativa e Redes Neurais Artificiais com algumas diferentes arquiteturas. O objetivo principal do trabalho é comparar o desempenho destas técnicas na identificação de clientes inadimplentes. Para isto, Foram utilizadas quatro métricas para a comparação dos modelos: Capacidade Preditiva, Curva ROC, Estatística de Kolmogorov Smirnov e a Capacidade de Acerto dos modelos. Dois bancos de dados foram utilizados, um banco artificial e um banco real. O banco de dados artificial foi construído baseado em um artigo de Breiman que gera as variáveis explicativas a partir de uma distribuição normal multivariada e o banco de dados real utilizado trata-se de um problema de Credit Score de uma instituição financeira que atua no mercado varejista brasileiro há mais de vinte anos.
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Karcher, Cristiane. "Redes Bayesianas aplicadas à análise do risco de crédito". Universidade de São Paulo, 2009. http://www.teses.usp.br/teses/disponiveis/3/3142/tde-25052009-162507/.
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Modelos de Credit Scoring são utilizados para estimar a probabilidade de um cliente proponente ao crédito se tornar inadimplente, em determinado período, baseadas em suas informações pessoais e financeiras. Neste trabalho, a técnica proposta em Credit Scoring é Redes Bayesianas (RB) e seus resultados foram comparados aos da Regressão Logística. As RB avaliadas foram as Bayesian Network Classifiers, conhecidas como Classificadores Bayesianos, com seguintes tipos de estrutura: Naive Bayes, Tree Augmented Naive Bayes (TAN) e General Bayesian Network (GBN). As estruturas das RB foram obtidas por Aprendizado de Estrutura a partir de uma base de dados real. Os desempenhos dos modelos foram avaliados e comparados através das taxas de acerto obtidas da Matriz de Confusão, da estatística Kolmogorov-Smirnov e coeficiente Gini. As amostras de desenvolvimento e de validação foram obtidas por Cross-Validation com 10 partições. A análise dos modelos ajustados mostrou que as RB e a Regressão Logística apresentaram desempenho similar, em relação a estatística Kolmogorov- Smirnov e ao coeficiente Gini. O Classificador TAN foi escolhido como o melhor modelo, pois apresentou o melhor desempenho nas previsões dos clientes maus pagadores e permitiu uma análise dos efeitos de interação entre variáveis.Credit Scoring Models are used to estimate the insolvency probability of a customer, in a period, based on their personal and financial information. In this text, the proposed model for Credit Scoring is Bayesian Networks (BN) and its results were compared to Logistic Regression. The BN evaluated were the Bayesian Networks Classifiers, with structures of type: Naive Bayes, Tree Augmented Naive Bayes (TAN) and General Bayesian Network (GBN). The RB structures were developed using a Structure Learning technique from a real database. The models performance were evaluated and compared through the hit rates observed in Confusion Matrix, Kolmogorov-Smirnov statistic and Gini coefficient. The development and validation samples were obtained using a Cross-Validation criteria with 10-fold. The analysis showed that the fitted BN models have the same performance as the Logistic Regression Models, evaluating the Kolmogorov-Smirnov statistic and Gini coefficient. The TAN Classifier was selected as the best BN model, because it performed better in prediction of bad customers and allowed an interaction effects analysis between variables.
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Williams, Alison Kay. "The influence of probability of detection when modeling species occurrence using GIS and survey data". Diss., Virginia Tech, 2000. http://hdl.handle.net/10919/11129.
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I compared the performance of habitat models created from data of differing reliability. Because the reliability is dependent on the probability of detecting the species, I experimented to estimate detectability for a salamander species. Based on these estimates, I investigated the sensitivity of habitat models to varying detectability.
Models were created using a database of amphibian and reptile observations at Fort A.P. Hill, Virginia, USA. Performance was compared among modeling methods, taxa, life histories, and sample sizes. Model performance was poor for all methods and species, except for the carpenter frog (Rana virgatipes). Discriminant function analysis and ecological niche factor analysis (ENFA) predicted presence better than logistic regression and Bayesian logistic regression models. Database collections of observations have limited value as input for modeling because of the lack of absence data. Without knowledge of detectability, it is unknown whether non-detection represents absence.
To estimate detectability, I experimented with red-backed salamanders (Plethodon cinereus) using daytime, cover-object searches and nighttime, visual surveys. Salamanders were maintained in enclosures (n = 124) assigned to four treatments, daytime__low density, daytime__high density, nighttime__low density, and nighttime__high density. Multiple observations of each enclosure were made. Detectability was higher using daytime, cover-object searches (64%) than nighttime, visual surveys (20%). Detection was also higher in high-density (49%) versus low-density enclosures (35%).
Because of variation in detectability, I tested model sensitivity to the probability of detection. A simulated distribution was created using functions relating habitat suitability to environmental variables from a landscape. Surveys were replicated by randomly selecting locations (n = 50, 100, 200, or 500) and determining whether the species was observed, based on the probability of detection (p = 40%, 60%, 80%, or 100%). Bayesian logistic regression and ENFA models were created for each sample. When detection was 80 __ 100%, Bayesian predictions were more correlated with the known suitability and identified presence more accurately than ENFA.
Probability of detection was variable among sampling methods and effort. Models created from presence/absence data were sensitive to the probability of detection in the input data. This stresses the importance of quantifying detectability and using presence-only modeling methods when detectability is low. If planning for sampling as an input for suitability modeling, it is important to choose sampling methods to ensure that detection is 80% or higher.Ph. D.
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Selig, Katharina [Verfasser], Donna P. [Akademischer Betreuer] Ankerst, Pamela A. [Gutachter] Shaw y Donna P. [Gutachter] Ankerst. "Bayesian information criterion approximations for model selection in multivariate logistic regression with application to electronic medical records / Katharina Selig ; Gutachter: Pamela A. Shaw, Donna P. Ankerst ; Betreuer: Donna P. Ankerst". München : Universitätsbibliothek der TU München, 2020. http://d-nb.info/1211476367/34.
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Allan, Michelle L. "Measuring Skill Importance in Women's Soccer and Volleyball". Diss., CLICK HERE for online access, 2009. http://contentdm.lib.byu.edu/ETD/image/etd2809.pdf.
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Rashid, Mamunur. "Inference on Logistic Regression Models". Bowling Green State University / OhioLINK, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1214165101.
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Batchelor, John Stephen. "Trauma scoring models using logistic regression". Thesis, University College London (University of London), 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.418022.
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Xiang, Fei. "Bayesian consistency for regression models". Thesis, University of Kent, 2012. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.587522.
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Bayesian consistency is an important issue in the context of non- parametric problems. The posterior consistency is a validation of a Bayesian approach and guarantees the posterior mass accumulates around the true density, which" is unknown in most circumstances, as the number of observations goes to infinity. This thesis mainly considers the consistency for nonparametric regression models over both random and non random covariates. The techniques to achieve consistency under random covariates are similar to that derived in Walker (2003, 2004) which is designed for the consistency of independent and identically distributed variables. We contribute a new idea to deal with the supremum metric over covariates when the regression model is with non random covariates. That is, if a regression density is away from the true density in the Hellinger sense, then there is a covariate, whose value is picked from a specific design, such that the density indexed by this value is also away from the true density. As a result, the posterior concentrates in the supremum Hellinger neighbourhood of the real model under conditions on the prior such as the Kullback-Leibler property and the summability of the square rooted prior mass on Hellinger covering balls. Furthermore, the predictive is also shown to be consistent and we illustrate our results on a normal mean regression function and demonstrate the usefulness of a model based on piecewise constant functions. We also investigate conditions under which a piecewise density model is consistent.
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Williams, Ulyana P. "On Some Ridge Regression Estimators for Logistic Regression Models". FIU Digital Commons, 2018. https://digitalcommons.fiu.edu/etd/3667.
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The purpose of this research is to investigate the performance of some ridge regression estimators for the logistic regression model in the presence of moderate to high correlation among the explanatory variables. As a performance criterion, we use the mean square error (MSE), the mean absolute percentage error (MAPE), the magnitude of bias, and the percentage of times the ridge regression estimator produces a higher MSE than the maximum likelihood estimator. A Monto Carlo simulation study has been executed to compare the performance of the ridge regression estimators under different experimental conditions. The degree of correlation, sample size, number of independent variables, and log odds ratio has been varied in the design of experiment. Simulation results show that under certain conditions, the ridge regression estimators outperform the maximum likelihood estimator. Moreover, an empirical data analysis supports the main findings of this study. This thesis proposed and recommended some good ridge regression estimators of the logistic regression model for the practitioners in the field of health, physical and social sciences.
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Wang, Jie. "Incorporating survey weights into logistic regression models". Digital WPI, 2013. https://digitalcommons.wpi.edu/etd-theses/267.
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Incorporating survey weights into likelihood-based analysis is a controversial issue because the sampling weights are not simply equal to the reciprocal of selection probabilities but they are adjusted for various characteristics such as age, race, etc. Some adjustments are based on nonresponses as well. This adjustment is accomplished using a combination of probability calculations. When we build a logistic regression model to predict categorical outcomes with survey data, the sampling weights should be considered if the sampling design does not give each individual an equal chance of being selected in the sample. We rescale these weights to sum to an equivalent sample size because the variance is too small with the original weights. These new weights are called the adjusted weights. The old method is to apply quasi-likelihood maximization to make estimation with the adjusted weights. We develop a new method based on the correct likelihood for logistic regression to include the adjusted weights. In the new method, the adjusted weights are further used to adjust for both covariates and intercepts. We explore the differences and similarities between the quasi-likelihood and the correct likelihood methods. We use both binary logistic regression model and multinomial logistic regression model to estimate parameters and apply the methods to body mass index data from the Third National Health and Nutrition Examination Survey. The results show some similarities and differences between the old and new methods in parameter estimates, standard errors and statistical p-values.
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McGlothlin, Anna E. Stamey James D. Seaman John Weldon. "Logistic regression with misclassified response and covariate measurement error a Bayesian approach /". Waco, Tex. : Baylor University, 2007. http://hdl.handle.net/2104/5101.
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Roberts, Brook R. "Measuring NAVSPASUR sensor performance using logistic regression models". Thesis, Monterey, California. Naval Postgraduate School, 1992. http://hdl.handle.net/10945/23952.
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Weng, Yu. "Maximum Likelihood Estimation of Logistic Sinusoidal Regression Models". Thesis, University of North Texas, 2013. https://digital.library.unt.edu/ark:/67531/metadc407796/.
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We consider the problem of maximum likelihood estimation of logistic sinusoidal regression models and develop some asymptotic theory including the consistency and joint rates of convergence for the maximum likelihood estimators. The key techniques build upon a synthesis of the results of Walker and Song and Li for the widely studied sinusoidal regression model and on making a connection to a result of Radchenko. Monte Carlo simulations are also presented to demonstrate the finite-sample performance of the estimators
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Kang, An. "Online Bayesian nonparametric mixture models via regression". Thesis, University of Kent, 2018. https://kar.kent.ac.uk/66306/.
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Sensors are widely used in modern industrial systems as well as consumer devices, such as food production, energy transportation and nuclear power plant. The sensors of interest in this project from an engineering company are associated with industrial control systems, where high precision is the dominant concern. Due to manufacturing variation, sensors manufactured from the same production line are non-identical. Therefore, each sensor needs to be characterised via parameter estimation to achieve a high precision or accuracy before sending to the end users. The classical linear regression model has been adopted in current industry procedure, which requires a certain number of measurements per device to achieve the required level of accuracy. The aim of the project is, under guarantee of the required level of accuracy, to use the available information and advanced statistical models to reduce the number of measurements needed per sensor, and hence reduce both costs and time for the characterisation process. To achieve this, a Bayesian linear model with Dirichlet process mixture prior (BL-DPMP) is proposed, where the Bayesian linear regression presents the relationship between the response variable and the covariates demonstrated to be appropriate by the company, and the regression coefficients are modelled by a Dirichlet process mixture (DPM) model. The idea here is to apply the DPM model to the historical information from similar sensors to provide adequate prior information to the linear regression model in order to compensate the current characterising sensor with block missing measurements, at the same time to maintain the required level of accuracy. The slice sampling scheme based on the full conditional posteriors of hyperparameters is used to update the parameters in the DPM model. Also, a generalised Dirichlet process mixture regression model is proposed with a data-driven prediction procedure to deal with the considered situation. By reducing the number of measurements required per sensor, we could drastically reduce the characterisation period. However, two proposed approaches are quite computationally intensive, which counteract the time saved from collecting a fewer number of measurements. Hence, there is a clearly pressing need for dramatically faster alternatives. A hybrid Variational Bayes (HVB) procedure following a greedy searching scheme is proposed, which can dramatically reduce the computational time, at the same time provide highly accurate approximations of the exact posterior distributions. The ultimate goal of this project is to implement the proposed advanced statistical model in the production line, where the model can be executed within seconds (online). An optimal permutation sequential (OPS) algorithm for the DPM model is proposed, which differs from MCMC algorithms. The idea is to draw approximate independent and identically distributed samples from the posterior distribution of the latent allocations, and to draw samples from the weights and locations conditional on the allocations. Hence, independent draws are taken from the posterior distribution, which allow us to take independent samples from the predictive distribution. The OPS algorithm requires only a single run which the computational costs of a few seconds. We present examples to show model performance on simulated and real datasets. It is worth noting that the proposed Bayesian linear model with Dirichlet process mixture prior together with the OPS algorithm is under the testing stage of being implemented in our industrial partner's production line. This research acts as the underpinning work and contributes to a potential impact case for the Research Excellence Framework (REF) 2021.
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Lin, Shan. "Simultaneous confidence bands for linear and logistic regression models". Thesis, University of Southampton, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.443030.
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Jia, Yan. "Optimal experimental designs for two-variable logistic regression models". Diss., This resource online, 1996. http://scholar.lib.vt.edu/theses/available/etd-06062008-152028/.
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Lund, Anton. "Two-Stage Logistic Regression Models for Improved Credit Scoring". Thesis, KTH, Skolan för datavetenskap och kommunikation (CSC), 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-160551.
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This thesis has investigated two-stage regularized logistic regressions applied on the credit scoring problem. Credit scoring refers to the practice of estimating the probability that a customer will default if given credit. The data was supplied by Klarna AB, and contains a larger number of observations than many other research papers on credit scoring. In this thesis, a two-stage regression refers to two staged regressions were the some kind of information from the first regression is used in the second regression to improve the overall performance. In the best performing models, the first stage was trained on alternative labels, payment status at earlier dates than the conventional. The predictions were then used as input to, or to segment, the second stage. This gave a gini increase of approximately 0.01. Using conventional scorecutoffs or distance to a decision boundary to segment the population did not improve performance.Denna uppsats har undersökt tvåstegs regulariserade logistiska regressioner för att estimera credit score hos konsumenter. Credit score är ett mått på kreditvärdighet och mäter sannolikheten att en person inte betalar tillbaka sin kredit. Data kommer från Klarna AB och innehåller fler observationer än mycket annan forskning om kreditvärdighet. Med tvåstegsregressioner menas i denna uppsats en regressionsmodell bestående av två steg där information från det första steget används i det andra steget för att förbättra den totala prestandan. De bäst presterande modellerna använder i det första steget en alternativ förklaringsvariabel, betalningsstatus vid en tidigare tidpunkt än den konventionella, för att segmentera eller som variabel i det andra steget. Detta gav en giniökning på approximativt 0,01. Användandet av enklare segmenteringsmetoder så som score-gränser eller avstånd till en beslutsgräns visade sig inte förbättra prestandan.
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Wang, Junhua. "Large-Sample Logistic Regression with Latent Covariates in a Bayesian Networking Context". TopSCHOLAR®, 2009. http://digitalcommons.wku.edu/theses/103.
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We considered the problem of predicting student retention using logistic regression when the most important covariates such as the college variables are latent, but the network structure is known. This network structure specifies the relationship between pre-college to college variables and then from college to student retention variables. Based on this structure, we developed three estimators, examined their large-sample properties, and evaluated their empirical efficiencies using WKU student retention database. Results show that while the hat estimator is expected to be most efficient, the tilde estimator was shown to be more efficient than the check method. This increased efficiency suggests that utilizing the network information can improve our predictions.
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Marjerison, William M. "Bayesian Logistic Regression with Spatial Correlation: An Application to Tennessee River Pollution". Digital WPI, 2006. https://digitalcommons.wpi.edu/etd-theses/1115.
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"We analyze data (length, weight and location) from a study done by the Army Corps of Engineers along the Tennessee River basin in the summer of 1980. The purpose is to predict the probability that a hypothetical channel catfish at a location studied is toxic and contains 5 ppm or more DDT in its filet. We incorporate spatial information and treate it separetely from other covariates. Ultimately, we want to predict the probability that a catfish from the unobserved location is toxic. In a preliminary analysis, we examine the data for observed locations using frequentist logistic regression, Bayesian logistic regression, and Bayesian logistic regression with random effects. Later we develop a parsimonious extension of Bayesian logistic regression and the corresponding Gibbs sampler for that model to increase computational feasibility and reduce model parameters. Furthermore, we develop a Bayesian model to impute data for locations where catfish were not observed. A comparison is made between results obtained fitting the model to only observed data and data with missing values imputed. Lastly, a complete model is presented which imputes data for missing locations and calculates the probability that a catfish from the unobserved location is toxic at once. We conclude that length and weight of the fish have negligible effect on toxicity. Toxicity of these catfish are mostly explained by location and spatial effects. In particular, the probability that a catfish is toxic decreases as one moves further downstream from the source of pollution."
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Brezger, Andreas. "Bayesian P-Splines in Structured Additive Regression Models". Diss., lmu, 2005. http://nbn-resolving.de/urn:nbn:de:bvb:19-39420.
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Konrath, Susanne. "Bayesian regularization in regression models for survival data". Diss., Ludwig-Maximilians-Universität München, 2013. http://nbn-resolving.de/urn:nbn:de:bvb:19-159745.
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This thesis is concerned with the development of flexible continuous-time survival models based on the accelerated failure time (AFT) model for the survival time and the Cox relative risk (CRR) model for the hazard rate. The flexibility concerns on the one hand the extension of the predictor to take into account simultaneously for a variety of different forms of covariate effects. On the other hand, the often too restrictive parametric assumptions about the survival distribution are replaced by semiparametric approaches that allow very flexible shapes of survival distribution. We use the Bayesian methodology for inference. The arising problems, like e. g. the penalization of high-dimensional linear covariate effects, the smoothing of nonlinear effects as well as the smoothing of the baseline survival distribution, are solved with the application of regularization priors tailored for the respective demand.
The considered expansion of the two survival model classes enables to deal with various challenges arising in practical analysis of survival data. For example the models can deal with high-dimensional feature spaces (e. g. gene expression data), they facilitate feature selection from the whole set or a subset of the available covariates and enable the simultaneous modeling of any type of nonlinear covariate effects for covariates that should always be included in the model. The option of the nonlinear modeling of covariate effects as well as the semiparametric modeling of the survival time distribution enables furthermore also a visual inspection of the linearity assumptions about the covariate effects or accordingly parametric assumptions about the survival time distribution.
In this thesis it is shown, how the p>n paradigm, feature relevance, semiparametric inference for functional effect forms and the semiparametric inference for the survival distribution can be treated within a unified Bayesian framework. Due the option to control the amount of regularization of the considered priors for the linear regression coefficients, there is no need to distinguish conceptionally between the cases p<=n and p>n. To accomplish the desired regularization, the regression coefficients are associated with shrinkage, selection or smoothing priors. Since the utilized regularization priors all facilitate a hierarchical representation, the resulting modular prior structure, in combination with adequate independence assumptions for the prior parameters, enables to establish a unified framework and the possibility to construct efficient MCMC sampling schemes for joint shrinkage, selection and smoothing in flexible classes of survival models. The Bayesian formulation enables therefore the simultaneous estimation of all parameters involved in the models as well as prediction and uncertainty statements about model specification.
The presented methods are inspired from the flexible and general approach for structured additive regression (STAR) for responses from an exponential family and CRR-type survival models. Such systematic and flexible extensions are in general not available for AFT models. An aim of this work is to extend the class of AFT models in order to provide such a rich class of models as resulting from the STAR approach, where the main focus relies on the shrinkage of linear effects, the selection of covariates with linear effects together with the smoothing of nonlinear effects of continuous covariates as representative of a nonlinear modeling. Combined are in particular the Bayesian lasso, the Bayesian ridge and the Bayesian NMIG (a kind of spike-and-slab prior) approach to regularize the linear effects and the P-spline approach to regularize the smoothness of the nonlinear effects and the baseline survival time distribution. To model a flexible error distribution for the AFT model, the parametric assumption for the baseline error distribution is replaced by the assumption of a finite Gaussian mixture distribution. For the special case of specifying one basis mixture component the estimation problem essentially boils down to estimation of log-normal AFT model with STAR predictor. In addition, the existing class of CRR survival models with STAR predictor, where also baseline hazard rate is approximated by a P-spline, is expanded to enable the regularization of the linear effects with the mentioned priors, which broadens further the area of application of this rich class of CRR models. Finally, the combined shrinkage, selection and smoothing approach is also introduced to the semiparametric version of the CRR model, where the baseline hazard is unspecified and inference is based on the partial likelihood.
Besides the extension of the two survival model classes the different regularization properties of the considered shrinkage and selection priors are examined. The developed methods and algorithms are implemented in the public available software BayesX and in R-functions and the performance of the methods and algorithms is extensively tested by simulation studies and illustrated through three real world data sets.
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Koutsourelis, Antonios. "Bayesian extreme quantile regression for hidden Markov models". Thesis, Brunel University, 2012. http://bura.brunel.ac.uk/handle/2438/7071.
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The main contribution of this thesis is the introduction of Bayesian quantile regression for hidden Markov models, especially when we have to deal with extreme quantile regression analysis, as there is a limited research to inference conditional quantiles for hidden Markov models, under a Bayesian approach. The first objective is to compare Bayesian extreme quantile regression and the classical extreme quantile regression, with the help of simulated data generated by three specific models, which only differ in the error term’s distribution. It is also investigated if and how the error term’s distribution affects Bayesian extreme quantile regression, in terms of parameter and confidence intervals estimation. Bayesian extreme quantile regression is performed by implementing a Metropolis-Hastings algorithm to update our parameters, while the classical extreme quantile regression is performed by using linear programming. Moreover, the same analysis and comparison is performed on a real data set. The results provide strong evidence that our method can be improved, by combining MCMC algorithms and linear programming, in order to obtain better parameter and confidence intervals estimation. After improving our method for Bayesian extreme quantile regression, we extend it by including hidden Markov models. First, we assume a discrete time finite state-space hidden Markov model, where the distribution associated with each hidden state is a) a Normal distribution and b) an asymmetric Laplace distribution. Our aim is to explore the number of hidden states that describe the extreme quantiles of our data sets and check whether a different distribution associated with each hidden state can affect our estimation. Additionally, we also explore whether there are structural changes (breakpoints), by using break-point hidden Markov models. In order to perform this analysis we implement two new MCMC algorithms. The first one updates the parameters and the hidden states by using a Forward-Backward algorithm and Gibbs sampling (when a Normal distribution is assumed), and the second one uses a Forward-Backward algorithm and a mixture of Gibbs and Metropolis-Hastings sampling (when an asymmetric Laplace distribution is assumed). Finally, we consider hidden Markov models, where the hidden state (latent variables) are continuous. For this case of the discrete-time continuous state-space hidden Markov model we implement a method that uses linear programming and the Kalman filter (and Kalman smoother). Our methods are used in order to analyze real interest rates by assuming hidden states, which represent different financial regimes. We show that our methods work very well in terms of parameter estimation and also in hidden state and break-point estimation, which is very useful for the real life applications of those methods.
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Tüchler, Regina. "Bayesian Variable Selection for Logistic Models Using Auxiliary Mixture Sampling". Department of Statistics and Mathematics, WU Vienna University of Economics and Business, 2006. http://epub.wu.ac.at/984/1/document.pdf.
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The paper presents an Markov Chain Monte Carlo algorithm for both variable and covariance selection in the context of logistic mixed effects models. This algorithm allows us to sample solely from standard densities, with no additional tuning being needed. We apply a stochastic search variable approach to select explanatory variables as well as to determine the structure of the random effects covariance matrix. For logistic mixed effects models prior determination of explanatory variables and random effects is no longer prerequisite since the definite structure is chosen in a data-driven manner in the course of the modeling procedure. As an illustration two real-data examples from finance and tourism studies are given. (author's abstract)Series: Research Report Series / Department of Statistics and Mathematics
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Crixell, JoAnna Christine Seaman John Weldon Stamey James D. "Logistic regression with covariate measurement error in an adaptive design a Bayesian approach /". Waco, Tex. : Baylor University, 2008. http://hdl.handle.net/2104/5229.
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Truong, Alfred Kar Yin. "Fast growing and interpretable oblique trees via logistic regression models". Thesis, University of Oxford, 2009. http://ora.ox.ac.uk/objects/uuid:e0de0156-da01-4781-85c5-8213f5004f10.
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The classification tree is an attractive method for classification as the predictions it makes are more transparent than most other classifiers. The most widely accepted approaches to tree-growth use axis-parallel splits to partition continuous attributes. Since the interpretability of a tree diminishes as it grows larger, researchers have sought ways of growing trees with oblique splits as they are better able to partition observations. The focus of this thesis is to grow oblique trees in a fast and deterministic manner and to propose ways of making them more interpretable. Finding good oblique splits is a computationally difficult task. Various authors have proposed ways of doing this by either performing stochastic searches or by solving problems that effectively produce oblique splits at each stage of tree-growth. A new approach to finding such splits is proposed that restricts attention to a small but comprehensive set of splits. Empirical evidence shows that good oblique splits are found in most cases. When observations come from a small number of classes, empirical evidence shows that oblique trees can be grown in a matter of seconds. As interpretability is the main strength of classification trees, it is important for oblique trees that are grown to be interpretable. As the proposed approach to finding oblique splits makes use of logistic regression, well-founded variable selection techniques are introduced to classification trees. This allows concise oblique splits to be found at each stage of tree-growth so that oblique trees that are more interpretable can be directly grown. In addition to this, cost-complexity pruning ideas which were developed for axis-parallel trees have been adapted to make oblique trees more interpretable. A major and practical component of this thesis is in providing the oblique.tree package in R that allows casual users to experiment with oblique trees in a way that was not possible before.
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Shavdia, Dewang. "Septic shock : providing early warnings through multivariate logistic regression models". Thesis, Massachusetts Institute of Technology, 2007. http://hdl.handle.net/1721.1/42338.
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Includes bibliographical references (leaves 87-89).Thesis (M. Eng.)--Harvard-MIT Division of Health Sciences and Technology, 2007.
(cont.) The EWS models were then tested in a forward, casual manner on a random cohort of 500 ICU patients to mimic the patients' stay in the unit. The model with the highest performance achieved a sensitivity of 0.85 and a positive predictive value (PPV) of 0.70. Of the 35 episodes of hypotension despite fluid resuscitation present in the random patient dataset, the model provided early warnings for 29 episodes with a mean early warning time of 582 ± 355 minutes.
Early goal-directed therapy (EGDT) in severe sepsis and septic shock has shown to provide substantial benefits in patient outcomes. However, these preventive therapeutic interventions are contingent upon an early detection or suspicion of the underlying septic etiology. Detection of sepsis in the early stages can be difficult, as the initial pathogenesis can occur while the patient is still displaying normal vital signs. This study focuses on developing an early warning system (EWS) to provide clinicians with a forewarning of an impending hypotensive crisis-thus allowing for EGDT intervention. Research was completed in three main stages: (1) generating an annotated septic shock dataset, (2) constructing multivariate logistic regression EWS models using the annotated dataset, and (3) testing the EWS models in a forward, causal manner on a random cohort of patients to simulate performance in a real-life ICU setting. The annotated septic shock dataset was created using the Multi-parameter Intelligent Monitoring for Intensive Care II (MIMIC II) database. Automated pre-annotations were generated using search criteria designed to identify two patient types: (1) sepsis patients who do not progress to septic shock, and (2) sepsis patient who progress to septic shock. Currently, manual review by expert clinicians to verify the pre-annotations has not been completed. Six separate EWS models were constructed using the annotated septic shock dataset. The multivariate logistic regression EWS models were trained to differentiate between 107 high-risk sepsis patients of whom 39 experienced a hypotensive crisis and 68 who remained stable. The models were tested using 7-fold cross validation; the mean area under the receiver operating characteristic (ROC) curve for the best model was 0.940 ± 0.038.
by Dewang Shavdia.
M.Eng.
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Berrett, Candace. "Bayesian Probit Regression Models for Spatially-Dependent Categorical Data". The Ohio State University, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=osu1285076512.
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Pan, Tianshu. "Using the multivariate multilevel logistic regression model to detect DIF a comparison with HGLM and logistic regression DIF detection methods /". Diss., Connect to online resource - MSU authorized users, 2008.
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Thesis (PH. D.)--Michigan State University. Measurement and Quantitative Methods, 2008.Title from PDF t.p. (viewed on Sept. 8, 2009) Includes bibliographical references (p. 85-89). Also issued in print.
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Mo, Lijia. "Examining the reliability of logistic regression estimation software". Diss., Kansas State University, 2010. http://hdl.handle.net/2097/7059.
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Doctor of PhilosophyDepartment of Agricultural Economics
Allen M. Featherstone
Bryan W. Schurle
The reliability of nine software packages using the maximum likelihood estimator for the logistic regression model were examined using generated benchmark datasets and models. Software packages tested included: SAS (Procs Logistic, Catmod, Genmod, Surveylogistic, Glimmix, and Qlim), Limdep (Logit, Blogit), Stata (Logit, GLM, Binreg), Matlab, Shazam, R, Minitab, Eviews, and SPSS for all available algorithms, none of which have been previously tested. This study expands on the existing literature in this area by examination of Minitab 15 and SPSS 17. The findings indicate that Matlab, R, Eviews, Minitab, Limdep (BFGS), and SPSS provided consistently reliable results for both parameter and standard error estimates across the benchmark datasets. While some packages performed admirably, shortcomings did exist. SAS maximum log-likelihood estimators do not always converge to the optimal solution and stop prematurely depending on starting values, by issuing a ``flat" error message. This drawback can be dealt with by rerunning the maximum log-likelihood estimator, using a closer starting point, to see if the convergence criteria are actually satisfied. Although Stata-Binreg provides reliable parameter estimates, there is no way to obtain standard error estimates in Stata-Binreg as of yet. Limdep performs relatively well, but did not converge due to a weakness of the algorithm. The results show that solely trusting the default settings of statistical software packages may lead to non-optimal, biased or erroneous results, which may impact the quality of empirical results obtained by applied economists. Reliability tests indicate severe weaknesses in SAS Procs Glimmix and Genmod. Some software packages fail reliability tests under certain conditions. The finding indicates the need to use multiple software packages to solve econometric models.
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Burton, Sarah L. "Logistic regression models and their application in medical discrimination and diagnosis". Thesis, University of Sheffield, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.364332.
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Volinsky, Christopher T. "Bayesian model averaging for censored survival models /". Thesis, Connect to this title online; UW restricted, 1997. http://hdl.handle.net/1773/8944.
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Hills, Susan. "The parametrisation of statistical models". Thesis, University of Nottingham, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.329850.
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Bin, Muhd Noor Nik Nooruhafidzi. "Statistical modelling of ECDA data for the prioritisation of defects on buried pipelines". Thesis, Brunel University, 2017. http://bura.brunel.ac.uk/handle/2438/16392.
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Buried pipelines are vulnerable to the threat of corrosion. Hence, they are normally coated with a protective coating to isolate the metal substrate from the surrounding environment with the addition of CP current being applied to the pipeline surface to halt any corrosion activity that might be taking place. With time, this barrier will deteriorate which could potentially lead to corrosion of the pipe. The External Corrosion Direct Assessment (ECDA) methodology was developed with the intention of upholding the structural integrity of pipelines. Above ground indirect inspection techniques such as the DCVG which is an essential part of an ECDA, is commonly used to determine coating defect locations and measure the defect's severity. This is followed by excavation of the identified location for further examination on the extent of pipeline damage. Any coating or corrosion defect found at this stage is repaired and remediated. The location of such excavations is determined by the measurements obtained from the DCVG examination in the form of %IR and subjective inputs from experts which bases their justification on the environment and the physical characteristics of the pipeline. Whilst this seems to be a straight forward process, the factors that comes into play which gave rise to the initial %IR is not fully understood. The lack of understanding with the additional subjective inputs from the assessors has led to unnecessary excavations being conducted which has put tremendous financial strain on pipeline operators. Additionally, the threat of undiscovered defects due to the erroneous nature of the current method has the potential to severely compromise the pipeline's safe continual operation. Accurately predicting the coating defect size (TCDA) and interpretation of the indication signal (%IR) from an ECDA is important for pipeline operators to promote safety while keeping operating cost at a minimum. Furthermore, with better estimates, the uncertainty from the DCVG indication is reduced and the decisions made on the locations of excavation is better informed. However, ensuring the accuracy of these estimates does not come without challenges. These challenges include (1) the need of proper methods for large data analysis from indirect assessment and (2) uncertainty about the probability distribution of quantities. Standard mean regression models e.g. the OLS, were used but fail to take the skewness of the distributions involved into account. The aim of this thesis is thus, to come up with statistical models to better predict TCDA and to interpret the %IR from the indirect assessment of an ECDA more precisely. The pipeline data used for the analyses is based on a recent ECDA project conducted by TWI Ltd. for the Middle Eastern Oil Company (MEOC). To address the challenges highlighted above, Quantile Regression (QR) was used to comprehensively characterise the underlying distribution of the dependent variable. This can be effective for example, when determining the different effect of contributing variables towards different sizes of TCDA (different quantiles). Another useful advantage is that the technique is robust to outliers due to its reliance on absolute errors. With the traditional mean regression, the effect of contributing variables towards other quantiles of the dependent variable is ignored. Furthermore, the OLS involves the squaring of errors which makes it less robust to outliers. Other forms of QR such as the Bayesian Quantile Regression (BQR) which has the advantage of supplementing future inspection projects with prior data and the Logistic Quantile Regression (LQR) which ensures the prediction of the dependent variable is within its specified bounds was applied to the MEOC dataset. The novelty of research lies in the approaches (methods) taken by the author in producing the models highlighted above. The summary of such novelty includes: * The use of non-linear Quantile Regression (QR) with interacting variables for TCDA prediction. * The application of a regularisation procedure (LASSO) for the generalisation of the TCDA prediction model.* The usage of the Bayesian Quantile Regression (BQR) technique to estimate the %IR and TCDA. * The use of Logistic Regression as a guideline towards the probability of excavation * And finally, the use of Logistic Quantile Regression (LQR) in ensuring the predicted values are within bounds for the prediction of the %IR and POPD. Novel findings from this thesis includes: * Some degree of relationship between the DCVG technique (%IR readings) and corrosion dimension. The results of the relationship between TCDA and POPD highlights a negative trend which further supports the idea that %IR has some relation to corrosion. * Based on the findings from Chapter 4, 5 and 6 suggests that corrosion activity rate is more prominent than the growth of TCDA at its median depth. It is therefore suggested that for this set of pipelines (those belonging to MEOC) repair of coating defects should be done before the coating defect has reached its median size. To the best of the Author's knowledge, the process of employing such approaches has never been applied before towards any ECDA data. The findings from this thesis also shed some light into the stochastic nature of the evolution of corrosion pits. This was not known before and is only made possible by the usage of the approaches highlighted above. The resulting models are also of novelty since no previous model has ever been developed based on the said methods. The contribution to knowledge from this research is therefore the greater understanding of relationship between variables stated above (TCDA, %IR and POPD). With this new knowledge, one has the potential to better prioritise location of excavation and better interpret DCVG indications. With the availability of ECDA data, it is also possible to predict the magnitude of corrosion activity by using the models developed in this thesis. Furthermore, the knowledge gained here has the potential to translate into cost saving measures for pipeline operators while ensuring safety is properly addressed.
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Fréchette, Luc A. "Development of urban traffic models using a Bayesian regression approach". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1996. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp04/mq22112.pdf.
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Frechette, Luc A. Carleton University Dissertation Engineering Civil and Environmental. "Development of urban traffic models using a Bayesian regression approach". Ottawa, 1996.
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Lamba, Binu. "Performance of ordinal logistic regression models under conditions of pooling adjacent categories". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp04/mq28600.pdf.
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Konis, Kjell Peter. "Linear programming algorithms for detecting separated data in binary logistic regression models". Thesis, University of Oxford, 2007. http://ora.ox.ac.uk/objects/uuid:8f9ee0d0-d78e-4101-9ab4-f9cbceed2a2a.
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This thesis is a study of the detection of separation among the sample points in binary logistic regression models. We propose a new algorithm for detecting separation and demonstrate empirically that it can be computed fast enough to be used routinely as part of the fitting process for logistic regression models. The parameter estimates of a binary logistic regression model fit using the method of maximum likelihood sometimes do not converge to finite values. This phenomenon (also known as monotone likelihood or infinite parameters) occurs because of a condition among the sample points known as separation. There are two classes of separation. When complete separation is present among the sample points, iterative procedures for maximizing the likelihood tend to break down, when it would be clear that there is a problem with the model. However, when quasicomplete separation is present among the sample points, the iterative procedures for maximizing the likelihood tend to satisfy their convergence criterion before revealing any indication of separation. The new algorithm is based on a linear program with a nonnegative objective function that has a positive optimal value when separation is present among the sample points. We compare several approaches for solving this linear program and find that a method based on determining the feasibility of the dual to this linear program provides a numerically reliable test for separation among the sample points. A simulation study shows that this test can be computed in a similar amount of time as fitting the binary logistic regression model using the method of iteratively reweighted least squares: hence the test is fast enough to be used routinely as part of the fitting procedure. An implementation of our algorithm (as well as the other methods described in this thesis) is available in the R package safeBinaryRegression.
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Weng, Chin-Fang. "Fixed versus mixed parameterization in logistic regression models application to meta-analysis /". College Park, Md.: University of Maryland, 2008. http://hdl.handle.net/1903/8985.
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Thesis (M.A.) -- University of Maryland, College Park, 2008.Thesis research directed by: Dept. of Mathematics. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.