With the development of DNA microarray technology, scientists can now measure the expression levels of thousands of genes (features or genomic biomarkers) simultaneously in one single experiment. Robust and accurate gene selection methods are required to identify differentially expressed genes across different samples for disease diagnosis or prognosis. The problem of identifying significantly differentially expressed genes can be stated as follows: Given gene expression measurements from an experiment of two (or more)conditions, find a subset of all genes having significantly different expression levels across these two (or more) conditions. Analysis of genomic data is challenging due to high dimensionality of data and low sample size. Currently several mathematical and statistical methods exist to identify significantly differentially expressed genes. The methods typically focus on gene by gene analysis within a parametric hypothesis testing framework. In this study, we propose three flexible procedures for analyzing microarray data. In the first method we propose a parametric method which is based on a flexible distribution, Generalized Logistic Distribution of Type II (GLDII), and an approximate likelihood ratio test (ALRT) is developed. Though the method considers gene-by-gene analysis, the ALRT method with distributional assumption GLDII appears to provide a favourable fit to microarray data. In the second method we propose a test statistic for testing whether area under receiver operating characteristic curve (AUC) for each gene is greater than 0.5 allowing different variances for each gene. This proposed method is computationally less intensive and can identify genes that are reasonably stable with satisfactory prediction performance. The third method is based on comparing two AUCs for a pair of genes that is designed for selecting highly correlated genes in the microarray datasets. We propose a nonparametric procedure for selecting genes with expression levels correlated with that of a ``seed" gene in microarray experiments. The test proposed by DeLong et al. (1988) is the conventional nonparametric procedure for comparing correlated AUCs. It uses a consistent variance estimator and relies on asymptotic normality of the AUC estimator. Our proposed method includes DeLong's variance estimation technique in comparing pair of genes and can identify genes with biologically sound implications. In this thesis, we focus on the primary step in the gene selection process, namely, the ranking of genes with respect to a statistical measure of differential expression. We assess the proposed approaches by extensive simulation studies and demonstrate the methods on real datasets. The simulation study indicates that the parametric method performs favorably well at any settings of variance, sample size and treatment effects. Importantly, the method is found less sensitive to contaminated by noise. The proposed nonparametric methods do not involve complicated formulas and do not require advanced programming skills. Again both methods can identify a large fraction of truly differentially expressed (DE) genes, especially if the data consists of large sample sizes or the presence of outliers. We conclude that the proposed methods offer good choices of analytical tools to identify DE genes for further biological and clinical analysis.

Thesis (Ph. D.)--Carleton University, 2004. / Includes bibliographical references (p. 175-179). Also available in electronic format on the Internet.

Thesis (M. Sc.)--Carleton University, 2008. / Includes bibliographical references (p. 57-62). Also available in electronic format on the Internet.

Generally the primary goal of randomized clinical trials (RCT) is to make comparisons among two or more treatments hence clinical investigators require the most appropriate treatment allocation procedure to yield reliable results regardless of whether the ultimate data suggest a clinically important difference between the treatments being studied. Although recommended by many researchers, the utilization of minimization has been seldom reported in randomized trials mainly because of the controversy surrounding the statistical efficiency in detecting treatment effect and its complexity in implementation. Methods: A SAS simulation code was designed for allocating patients into two different treatment groups. Categorical prognostic factors were used together with multi-level response variables and demonstration of how simulation of data can help to determine the power of the minimization technique was carried out using ordinal logistic regression models. Results: Several scenarios were simulated in this study. Within the selected scenarios, increasing the sample size significantly increased the power of detecting the treatment effect. This was contrary to the case when the probability of allocation was decreased. Power did not change when the probability of allocation given that the treatment groups are balanced was increased. The probability of allocation { } k P was seen to be the only one with a significant effect on treatment balance. Conclusion: Maximum power can be achieved with a sample of size 300 although a small sample of size 200 can be adequate to attain at least 80% power. In order to have maximum power, the probability of allocation should be fixed at 0.75 and set to 0.5 if the treatment groups are equally balanced.

<p>Censoring arises quite often in lifetime data. Its presence may be planned or unplanned. In this project, we demonstrate progressive Type-II right censoring when the underlying distribution is log-logistic. The objective is to discuss inferential methods for the unknown parameters of the distribution based on the maximum likelihood estimation method. The Newton-Raphson method is proposed as a numerical technique to solve the pertinent non-linear equations. In addition, confidence intervals for the unknown parameters are constructed based on (i) asymptotic normality of the maximum likelihood estimates, and (ii) percentile bootstrap resampling technique. A Monte Carlo simulation study is conducted to evaluate the performance of the methods of inference developed here. Some illustrative examples are also presented.</p> / Master of Science (MSc)

Cheung, Kwan Wing. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (p. 115-124). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.v / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Motivation --- p.1 / Chapter 1.2 --- Contributions --- p.7 / Chapter 1.3 --- Findings --- p.8 / Chapter 1.4 --- Structure of the Thesis --- p.10 / Chapter 2 --- Beer Logistics in China --- p.12 / Chapter 2.1 --- The Logistics and Supply Chain in China --- p.12 / Chapter 2.2 --- Beer in China --- p.22 / Chapter 2.2.1 --- The Expanding Market --- p.22 / Chapter 2.2.2 --- The Multi-tiered Supply Chain --- p.22 / Chapter 2.2.3 --- Reverse Logistics --- p.25 / Chapter 2.2.4 --- Manual Demand and Inventory Manage- ment --- p.26 / Chapter 2.2.5 --- Retail Fees and Value Chains --- p.28 / Chapter 2.2.6 --- Packaging --- p.30 / Chapter 2.3 --- The Wholesaler --- p.31 / Chapter 2.3.1 --- High Service Quality under Fierce Com- petition --- p.31 / Chapter 2.3.2 --- Use of Vans --- p.33 / Chapter 2.3.3 --- Delivery Problem of Wholesalers --- p.35 / Chapter 3 --- Literature Review --- p.37 / Chapter 3.1 --- Beer Logistics in China --- p.37 / Chapter 3.2 --- Modelling Delivery Problems --- p.39 / Chapter 3.3 --- Applications of the Vehicle Routing Problem --- p.42 / Chapter 3.4 --- Heuristics and Metaheuristics --- p.43 / Chapter 3.5 --- Round up --- p.45 / Chapter 4 --- Problem Definition --- p.48 / Chapter 4.1 --- Problem Definition --- p.48 / Chapter 4.2 --- Assumptions --- p.53 / Chapter 5 --- Problem Formulation --- p.55 / Chapter 5.1 --- Introduction --- p.55 / Chapter 5.2 --- Notations --- p.58 / Chapter 5.2.1 --- Indices --- p.58 / Chapter 5.2.2 --- Parameters --- p.58 / Chapter 5.2.3 --- Decision Variables --- p.59 / Chapter 5.3 --- Mixed Integer Programming Model --- p.60 / Chapter 5.3.1 --- The Model --- p.60 / Chapter 5.3.2 --- Descriptions --- p.61 / Chapter 5.3.3 --- Complexity and Polynomial Number of Con- straints --- p.66 / Chapter 6 --- Solution Methodology --- p.69 / Chapter 6.1 --- Input Parameters --- p.69 / Chapter 6.2 --- Finding the Optimal Solution --- p.70 / Chapter 6.2.1 --- By CPLEX Optimization Package --- p.70 / Chapter 6.2.2 --- Problems of Using Optimization Packages --- p.72 / Chapter 6.2.3 --- Observations of Some Optimal Solutions --- p.74 / Chapter 6.3 --- Heuristics Development --- p.77 / Chapter 6.3.1 --- Solution Strategies --- p.77 / Chapter 6.3.2 --- Evaluation of the Strategy Combinations --- p.84 / Chapter 6.3.3 --- Best Combinations --- p.90 / Chapter 6.3.4 --- Final Heuristic --- p.92 / Chapter 7 --- Computational Results --- p.94 / Chapter 7.1 --- Methodology --- p.94 / Chapter 7.2 --- Results of Using the Final Heuristic --- p.95 / Chapter 7.3 --- Computational Time --- p.99 / Chapter 8 --- Managerial Insights --- p.102 / Chapter 8.1 --- Practical Issues --- p.102 / Chapter 8.2 --- Managerial Insights --- p.105 / Chapter 9 --- Future Work and Conclusion --- p.109 / Chapter 9.1 --- Future Work --- p.109 / Chapter 9.2 --- Conclusion --- p.112 / Bibliography --- p.115

The multinomial logit model (MNL) possesses a latent variable representation in terms of random variables following a multivariate logistic distribution. Based on multivariate finite mixture approximations of the multivariate logistic distribution, various data-augmented Metropolis-Hastings algorithms are developed for a Bayesian inference of the MNL model.

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.

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.

Dans cette thèse, nous traitons essentiellement des problèmes de lot sizing en désassemblage avec une structure de produits à désassembler à deux niveaux sans composants communs. Nous traitons deux problèmes différents. Dans le premier problème, nous considérons un seul produit et la contribution porte sur le développement de deux modèles de programmation en nombres entiers. Le premier modèle est considéré sans ventes perdues où toutes les demandes doivent être satisfaites, et le deuxième est considéré avec ventes perdues où les demandes peuvent ne pas être satisfaites. Pour la résolution de ce problème, nous développons d’abord une approche analytique permettant de calculer les stocks de surplus (avant la résolution du problème) à la fin de l’horizon de planification. Ensuite, nous adaptons trois heuristiques connues pour leurs performances et largement utilisées dans le problème lot sizing en production « Silver Meal, Part Period Balancing et Least Unit Cost ». Dans le deuxième problème, nous considérons plusieurs produits avec contrainte de capacité et la contribution porte sur l’extension des deux modèles précédents. Le premier est également considéré sans ventes perdues et le deuxième avec ventes perdues. En ce qui concerne la résolution de ce problème et compte tenu de sa complexité, un algorithme génétique est d’abord proposé. Ensuite, afin d’améliorer cet algorithme, nous intégrons une heuristique Fix-and-Optimize dans ce dernier tout en proposant une approche hybride. Finalement, des tests sont effectués sur de nombreuses instances de la littérature afin de montrer l’efficacité et les limites de chaque approche de résolution / In this thesis, we mainly deal with lot sizing problems by disassembling with a structure of products to disassemble with two levels and without commonality components. We treat two different problems. In the first problem, we consider a single product whose contribution focuses on developing the two programming models integers. The first model is considered without lost sales where all demands must be satisfied, and the second one is considered with lost sales where demands may not be met. To solve this problem, we first develop an analytical approach to calculate the surplus stocks (before solving the problem) at the end of the planning horizon. Then we adapt three heuristics known for their performance and widely used in the lot sizing problem of production "Silver Meal, Part Period Balancing and Least Unit Cost". In the second problem, we consider a number of products with capacity constraint, and the contribution relates to the extension of the two previous models. The first is considered without lost sales and the second with lost sales. Regarding the resolution of this problem and given its complexity, a genetic algorithm is first proposed. Then, to improve this algorithm, we integrate a Fix-and-Optimize heuristic in the latter while offering a hybrid approach. Finally, various tests are performed on different literature instances to demonstrate the effectiveness and limitations of each solving approach