DNA methylation plays a key role in disease analysis, especially for studies that compare known large scale differences in CpG sites, such as cancer/normal studies or between-tissues studies. However, before any analysis can be done, data normalization and preprocessing of methylation data are required. A useful data preprocessing pipeline for large scale comparisons is Functional Normalization (FunNorm), (Fortin et al., 2014) implemented in the minfi package in R. In FunNorm, the univariate quantiles of the methylated and unmethylated signal values in the raw data are used to preprocess the data. However, although FunNorm has been shown to outperform other preprocessing and data normalization processes for these types of studies, it does not account for the correlation between the methylated and unmethylated signals into account; the focus of this paper is to improve upon FunNorm by taking this correlation into account. The concept of a bivariate quantile is used in this study as an attempt to take the correlation between the methylated and unmethylated signals into consideration. From the bivariate quantiles found, the partial least squares method is then used on these quantiles in this preprocessing. The raw datasets used for this research were collected from the European Molecular Biology Laboratory - European Bioinformatics Institute (EMBL-EBI) website. The results from this preprocessing algorithm were then compared and contrasted to the results from FunNorm. Drawbacks, limitations and future research are then discussed. / Thesis / Master of Science (MSc)

In this thesis, first we replace the condition X ¡Ø y in Huang and Su (2000) by X ¡Ù y and give necessary and sufficient conditions such that there exists a random variable X satisfying that E(g(X)| X ¡Ø y)=h(y) f(y )/ F(y), " y Î CX, where CX is the support of X.Next, we investigate necessary and sufficient conditions such that h(y)=E(g(X) | X ¡Ø y ), for a given function h and extend these results to bivariate case.

Let (X, Y) be bivariate normal random vectors which represent the responses as a result of Treatment 1 and Treatment 2. The statistical inference about the bivariate normal distribution parameters involving missing data with both treatment samples is considered. Assuming the correlation coefficient ρ of the bivariate population is known, the MLE of population means and variance (ξ, η, and σ2) are obtained. Inferences about these parameters are presented. Procedures of constructing confidence interval for the difference of population means ξ – η and testing hypothesis about ξ – η are established. The performances of the new estimators and testing procedure are compared numerically with the method proposed in Looney and Jones (2003) on the basis of extensive Monte Carlo simulation. Simulation studies indicate that the testing power of the method proposed in this thesis study is higher.

With evidence of increasing hurricane risks in Georgia Coastal Area (GCA) and Virginia in the U.S. Southeast and elsewhere, understanding intended evacuation behavior is becoming more and more important for community planners. My research investigates intended evacuation behavior due to hurricane risks, a behavioral survey of the six counties in GCA under the direction of two social scientists with extensive experience in survey research related to citizen and household response to emergencies and disasters. Respondents gave answers whether they would evacuate under both voluntary and mandatory evacuation orders. Bivariate probit models are used to investigate the subjective belief structure of whether or not the respondents are concerned about the hurricane, and the intended probability of evacuating as a function of risk perception, and a lot of demographic and socioeconomic variables (e.g., gender, military, age, length of residence, owning vehicles).

Let S31(?) be the bivariate C1-cubic spline space over a triangulated quadrangulation ?. In this paper, an explicit representation of a locally supported basis of S31(?) is given using the interpolation conditions at vertices.

This paper is concerned with a study of approximation order and construction of locally supported elements for the space S41 (Δ) of Cl quartic pp (piecewise polynomial) functions on a triangulation Δ of a connected polygonal domain Ω in R2. It is well known that, when Δ is a three-directional mesh Δ(1), the order of approximation of S41(Δ(1)) is only 4, not 5. Though a local Clough-Tocher refinement procedure of an arbitrary triangulation A yields the optimal (fifth) order of approximation from the space S41(Δ) (see [1]), it needs more data points in addition to the vertex set of the triangulation A. In this paper, we will introduce a particular mixed three-directional mesh Δ(3)) and construct so-called mixed three-directional elements. We prove that the space S41(Δ(3)) achieves its optimal-order of approximation by constructing an interpolation scheme using mixed three-directional elements.

The Poisson distribution is commonly used in analyzing count data, and many insurance companies are interested in studying the related risk models and ruin probability theory. Over the past century, many different bivariate models have been developed in the literature. The bivariate Poisson distribution was first introduced by Campbell (1934) for modelling bivariate accident data. However, in some situations, a given dataset may possess over-dispersion compared to Poisson distribution which moti- vated researchers to develop alternative models to handle such situations. In this regard, Minkova and Balakrishnan (2014a) developed the Type I bivariate Polya- Aeppli distribution by using compounding with Geometric random variables and the trivariate reduction method. Inference for this Type I bivariate Polya-Aeppli distribution is the topic of this thesis. The parameters in a model are used to describe and summarize a given sample within a specific distribution. So, their estimation becomes important and the goal of estimation theory is to seek a method to find estimators for the parameters of interest that have some good properties. There exist many methods of finding estimators such as Method of Moments, Bayesian estimators, Least Squares, and Maximum Likelihood Estimators (MLEs). Each method of estimation has its own strength and weakness (Casella and Berger (2008)). Minkova and Balakrishnan (2014a) discussed the moment estimation of the parameters of the Type I bivariate Polya-Aeppli dis- tribution. In this thesis, we develop the likelihood inference for this model. A simulation study is carried out with various parameter settings. The obtained results show that the MLEs require more computational time compared to Moment estimation. However, Method of Moments (MoM) did not result in good estimates for all the simulation settings. In terms of mean squared error and bias, we observed that MLEs performed, in most of the settings, better than MoM. Finally, we apply the Type I bivariate Polya-Aeppli model to a real dataset containing the frequencies of railway accidents in two subsequent six year periods. We also carry out some hypothesis tests using the Wald test statistic. From these results, we conclude that the two variables belong to the same univariate Polya-Aeppli distribution but are correlated. / Thesis / Master of Science (MSc)

A diagnostic test identifies patients according to their disease status. Different meta-analytic models for diagnostic test accuracy studies have been developed to synthesize the sensitivity and specificity of the test. Because of the likely correlation between the sensitivity and specificity of a test, modeling the two parameters using a bivariate model is desirable. Historically, the logit transformation has been used to model sensitivity and specificity pairs from multiple studies as a bivariate normal. In this thesis, we propose two transformations, the arcsine square root and the Freeman-Tukey double arcsine transformation, in the context of a bivariate random-effects model to meta-analyze diagnostic test accuracy studies. We evaluated the performance of the three transformations (the commonly used logit and the proposed transformations) using an extensive simulation study in terms of bias, root mean square error and coverage probability. We illustrate the methods using three real data sets. The simulation study results showed that, for smaller sample size and higher values of sensitivity and specificity, the proposed transformations are less biased, have smaller root mean square error and better coverage probability than the standard logit transformation regardless of the number of studies. On the other hand, for large sample sizes, the usual logit transformation is less biased and has better coverage probability regardless of the true values of sensitivity, specificity and number of studies. However, when the sample size is large, the logit transformation has better root mean square error for moderate and large number of studies. The point estimates of the two parameters, sensitivity & specificity, from the methods using the three real data sets follow patterns similar to those reported by our simulation. / Thesis / Master of Science (MSc)

The research examines the effect of commuting on stress for both motorized and non-motorized commuters and understanding how they cope with it. Understanding this effect can be helpful for decision-makers in the economy, transportation planning, and demographics studies to promote a safe and peaceful experience of travel for all the commuters in the community by designing better transportation systems and developing infrastructure of alternative modes like walking. Moreover, understanding the emotional states of individuals during their journeys and how they navigate and manage the commuting stress feeling, can be beneficial for decision-makers to enhance commuting experiences and feelings. To this end, a bivariate ordinal model was adopted, allowing for an analysis of stress factors and their interactions with key exploratory variables, including income, age, and choice of transportation mode. Interestingly, the results obtained from the context of Santiago, Chile, a region characterized by a predominance of middle and low-income populations according to the research findings, revealed intriguing patterns. The study found that commuting stress influences people in different ways regarding their age. Moreover, commuting stress at higher levels decreases at elevated age levels. This trend remains steady as commuters gain higher economic status and have access to alternative modes of transportation beyond public means. Policymakers and transportation planners should consider the complex interplay of the following clusters according to the result of this research to improve commuting experiences. The first encompasses factors such as income status, choice among different modes of transportation, and age. The second pertains to commuting stress and the importance of stress from commuters' viewpoint. A salient example of the consequence of this interplay, is evident in the research, where normalization a coping strategy implying eliminating some aspects of travel, is employed, showcasing both potential advantages and drawbacks. The findings suggest that promoting active travel options could contribute to a happier commuting experience, emphasizing the importance of understanding coping mechanisms across different commuter groups for the design of effective policies. The implications of these findings extend to the domain of transportation system planning and urban development. By shedding light on the challenges caused by commuting stress and highlighting effective coping mechanisms, this research holds the potential to understand how people deal with commuting stress during their regular trips. Furthermore, the gained insights can inform urban planning initiatives and facilitate the commuting experience by considering commuters' experiences and the associated factors. Ultimately, the integration of these insights into policies and practices has the capacity to cultivate sustainable and resilient communities, which thrive even when facing the inevitable stresses associated with daily commuting. This research makes a two-fold contribution. First, it compiles an extensive array of data including socio-demographics, health metrics, feelings and emotions, built environment, and work commute-related details, all presented in a comprehensive and reproducible data package format. Subsequently, the study delves into the commuting stress analysis and identifies the various coping strategies employed by commuters. The data used for the analysis have been derived from the demographics and health information sections of the dataset. Serving as a reproducible data package, it provides a robust foundation for future research endeavours. Future researchers can have access to the data set as an open source data set allowing them to understand the representativeness of this data package and enable them to replicate various stages where needed. / Thesis / Master of Science (MSc) / Nowadays commuting as a daily travel mostly between work and home is considered as an inevitable part of modern lifestyle. This experience has been indicated to be a source of stress and anxiety as numerous studies have already revealed. Understanding commuting patterns and travel behaviour is important for analyzing stress-related issues, consequences and coping strategies. As @koslowsky2013commuting have mentioned, this is also beneficial to have a perception of commuting patterns, modes of transportation, road congestion and so on for commuting network planning from scratch. Using the relevant stress commuting variables such as experienced stress and assigned importance to this stress can help to this end. This research aimed at providing a comprehensive and reproducible data package of travel behaviour and other aspects of the urban commuting experience of respondents in Santiago, Chile. Each component of this data package serves different aspects for future research such as using demographic information in travel demand modelling, health-related information for improving health, well-being and safety in transportation planning, reasons and planning decisions information for origin-destination modelling, and so on. The research also has been focused on an integrated list of variables chosen from the demographic and health information sections of the data package. This list helps to identify how commuters interact with experiencing stress during their travels. This research also contributes to addressing commuting stress by identifying relevant variables, then figuring out the affected groups and analyzing their coping strategies.

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