Statistics and Probability Commons^™

Threshold Models For Genome-Wide Association Mapping Of Familial Breast Cancer Incidence In Humans, Nasir Elmesmari

Electronic Theses and Dissertations

Breast cancer is the second most fatal cancer in the world and one of the most highly harmful cancers from which people suffer. Breast cancer studies have been able to uncover some knowledge about genetic susceptibility for familial breast cancer in humans. Hence, determining genetic factors may potentially help track the disease, as well as discover the cancer in early stages, or perhaps before it starts. In addition, this may allow early determination of possible treatment strategies which will make it easier to prevent the disease. In this context, it is important to determine whether the heritability of breast cancer …

Response Surface Methodology And Its Application In Optimizing The Efficiency Of Organic Solar Cells, Rajab Suliman

Electronic Theses and Dissertations

Response surface methodology (RSM) is a ubiquitous optimization approach used in a wide variety of scientific research studies. The philosophy behind a response surface method is to sequentially run relatively simple experiments or models in order to optimize a response variable of interest. In other words, we run a small number of experiments sequentially that can provide a large amount of information upon augmentation. In this dissertation, the RSM technique is utilized in order to find the optimum fabrication condition of a polymer solar cell that maximizes the cell efficiency. The optimal device performance was achieved using 10.25 mg/ml polymer …

Spatial And Spatiotemporal Modeling Of Epidemiological Data, Laxman Karki

Electronic Theses and Dissertations

This dissertation focuses on modeling approach for spatial and spatiotemporal data with epidemiological applications. Chapter one gives the general overview of spatial and spatiotemporal data and challenges in the statistical analysis of spatial and spatiotemporal data, and motivation and objectives of the study. Chapter two describes the regression models commonly used in spatial data analysis. Various types of regression methods such as OLS, GWR and MGWR were used to study the association between diabetes prevalence and socioeconomic and lifestyle factors on county level data of Midwestern United States. A new analysis workflow is purposed for regression analysis of spatial data. …

Development And Properties Of Kernel-Based Methods For The Interpretation And Presentation Of Forensic Evidence, Douglas Armstrong

Electronic Theses and Dissertations

The inference of the source of forensic evidence is related to model selection. Many forms of evidence can only be represented by complex, high-dimensional random vectors and cannot be assigned a likelihood structure. A common approach to circumvent this is to measure the similarity between pairs of objects composing the evidence. Such methods are ad-hoc and unstable approaches to the judicial inference process. While these methods address the dimensionality issue they also engender dependencies between scores when 2 scores have 1 object in common that are not taken into account in these models. The model developed in this research captures …

Approximate Statistical Solutions To The Forensic Identification Of Source Problem, Danica M. Ommen

Electronic Theses and Dissertations

Currently in forensic science, the statistical methods for solving the identification of source problems are inherently subjective and generally ad-hoc. The formal Bayesian decision framework provides the most statistically rigorous foundation for these problems to date. However, computing a solution under this framework, which relies on a Bayes Factor, tends to be computationally intensive and highly sensitive to the subjective choice of prior distributions for the parameters. Therefore, this dissertation aims to develop statistical solutions to the forensic identification of source problems which are less subjective, but which retain the statistical rigor of the Bayesian solution. First, this dissertation focuses …

U-Statistics For Characterizing Forensic Sufficiency Studies, Cami Fuglsby

Electronic Theses and Dissertations

One of the main metrics for deciding if a given forensic modality is useful across a broad spectrum of cases, within a given population, is the Random Match Probability (RMP), or the corresponding discriminating power. Traditionally, the RMP of a given modality is studied by comparing full `templates' and estimating the rate at which pairs of templates 'match' in a given population. This strategy leads to a natural U-statistic of degree two. However, in questioned document examination, the RMP is studied as a function of the amount of handwriting contained in the two documents being compared; turning the U-statistic into …

A Kernel Based Approach To Determine Atypicality, Austin O'Brien

Electronic Theses and Dissertations

This dissertation outlines the development and use for a new probabilistic measure for categorization, referred to as atypicality. Given a set of known source objects, we can create a corresponding set of similarity scores between them. Assuming the set of scores has a normal distribution, we can estimate its parameters. Then, we can introduce new trace objects to the problem, and compute similarity scores for them. The main goal of the atypicality score is to determine if the new trace objects are similar to the source objects. To do this, we bootstrap many new scores using the estimated parameters (from …

Comparative Study Of The Distribution Of Repetitive Dna In Model Organisms, Mohamed K. Aburweis

Electronic Theses and Dissertations

Repetitive DNA elements are abundant in the genome of a wide range of organisms. In mammals, repetitive elements comprise about 40-50% of the total genomes. However, their biological functions remain largely unknown. Analysis of their abundance and distribution may shed some light on how they affect genome structure, function, and evolution. We conducted a detailed comparative analysis of repetitive DNA elements across ten different eukaryotic organisms, including chicken (G. gallus), zebrafish (D. rerio), Fugu (T. rubripes), fruit fly (D. melanogaster), and nematode worm (C. elegans), along with five mammalian organisms: human (H. sapiens), mouse (M. musculus), cow (B. taurus), rat …

Development Of Computational Techniques For Regulatory Dna Motif Identification Based On Big Biological Data, Jinyu Yang

Electronic Theses and Dissertations

Accurate regulatory DNA motif (or motif) identification plays a fundamental role in the elucidation of transcriptional regulatory mechanisms in a cell and can strongly support the regulatory network construction for both prokaryotic and eukaryotic organisms. Next-generation sequencing techniques generate a huge amount of biological data for motif identification. Specifically, Chromatin Immunoprecipitation followed by high throughput DNA sequencing (ChIP-seq) enables researchers to identify motifs on a genome scale. Recently, technological improvements have allowed for DNA structural information to be obtained in a high-throughput manner, which can provide four DNA shape features. The DNA shape has been found as a complementary factor …

Memory Properties Of Transformations Of Linear Processes And Symmetric Gini Correlation, Yongli Sang

Electronic Theses and Dissertations

A large class of time series processes can be modeled by linear processes, including a subset of the fractional ARIMA process. Transformation of linear processes is one of the most popular topics in univariate time-series analysis in recent years. In this dissertation, we study the memory properties of transformations of linear processes. Our results show that the transformations of short-memory time series still have short-memory and the transformation of long-memory time series may have different weaker memory parameters which depend on the power rank of the transformation. In particular, we provide the memory parameters of the FARIMA (p,d,q) processes. As …

A Multi-Indexed Logistic Model For Time Series, Xiang Liu

Electronic Theses and Dissertations

In this thesis, we explore a multi-indexed logistic regression (MILR) model, with particular emphasis given to its application to time series. MILR includes simple logistic regression (SLR) as a special case, and the hope is that it will in some instances also produce significantly better results. To motivate the development of MILR, we consider its application to the analysis of both simulated sine wave data and stock data. We looked at well-studied SLR and its application in the analysis of time series data. Using a more sophisticated representation of sequential data, we then detail the implementation of MILR. We compare …

Tornado Density And Return Periods In The Southeastern United States: Communicating Risk And Vulnerability At The Regional And State Levels, Michelle Bradburn

Electronic Theses and Dissertations

Tornado intensity and impacts vary drastically across space, thus spatial and statistical analyses were used to identify patterns of tornado severity in the Southeastern United States and to assess the vulnerability and estimated recurrence of tornadic activity. Records from the Storm Prediction Center's tornado database (1950-2014) were used to estimate kernel density to identify areas of high and low tornado frequency at both the regional- and state-scales. Return periods (2-year, 5-year, 10-year, 25-year, 50-year, and 100-year) were calculated at both scales as well using a composite score that included EF-scale magnitude, injury counts, and fatality counts. Results showed that the …

Multilevel Models For Longitudinal Data, Aastha Khatiwada

Electronic Theses and Dissertations

Longitudinal data arise when individuals are measured several times during an ob- servation period and thus the data for each individual are not independent. There are several ways of analyzing longitudinal data when different treatments are com- pared. Multilevel models are used to analyze data that are clustered in some way. In this work, multilevel models are used to analyze longitudinal data from a case study. Results from other more commonly used methods are compared to multilevel models. Also, comparison in output between two software, SAS and R, is done. Finally a method consisting of fitting individual models for each …

Propensity Score Based Methods For Estimating The Treatment Effects Based On Observational Studies., Younathan Abdia

Electronic Theses and Dissertations

This dissertation consists of two interconnected research projects. The first project was a study of propensity scores based statistical methods for estimating the average treatment effect (ATE) and the average treatment effect among treated (ATT) when there are two treatment groups. The ATE is defined as the mean of the individual causal effects in the whole population, while ATT is defined as the treatment effect for the treated population. Propensity score based statistical methods, such as matching, regression, stratification, inverse probability weighting (IPW), and doubly robust (DR) methods were used to estimate the ATE and ATT. Simulation studies and case …

Spatio-Temporal Analysis Of Point Patterns, Abdul-Nasah Soale

Electronic Theses and Dissertations

In this thesis, the basic tools of spatial statistics and time series analysis are applied to the case study of the earthquakes in a certain geographical region and time frame. Then some of the existing methods for joint analysis of time and space are described and applied. Finally, additional research questions about the spatial-temporal distribution of the earthquakes are posed and explored using statistical plots and models. The focus in the last section is in the relationship between number of events per year and maximum magnitude and its effect on how clustered the spatial distribution is and the relationship between …

Newsvendor Models With Monte Carlo Sampling, Ijeoma W. Ekwegh

Electronic Theses and Dissertations

Newsvendor Models with Monte Carlo Sampling by Ijeoma Winifred Ekwegh The newsvendor model is used in solving inventory problems in which demand is random. In this thesis, we will focus on a method of using Monte Carlo sampling to estimate the order quantity that will either maximizes revenue or minimizes cost given that demand is uncertain. Given data, the Monte Carlo approach will be used in sampling data over scenarios and also estimating the probability density function. A bootstrapping process yields an empirical distribution for the order quantity that will maximize the expected profit. Finally, this method will be used …

Some Contributions To Nonparametric And Semiparametric Inference For Clustered And Multistate Data., Sandipan Dutta

Electronic Theses and Dissertations

This dissertation is composed of research projects that involve methods which can be broadly classified as either nonparametric or semiparametric. Chapter 1 provides an introduction of the problems addressed in these projects, a brief review of the related works that have done so far, and an outline of the methods developed in this dissertation. Chapter 2 describes in details the first project which aims at developing a rank-sum test for clustered data where an outcome from group in a cluster is associated with the number of observations belonging to that group in that cluster. Chapter 3 proposes the use of …

Takens Theorem With Singular Spectrum Analysis Applied To Noisy Time Series, Thomas K. Torku

Electronic Theses and Dissertations

The evolution of big data has led to financial time series becoming increasingly complex, noisy, non-stationary and nonlinear. Takens theorem can be used to analyze and forecast nonlinear time series, but even small amounts of noise can hopelessly corrupt a Takens approach. In contrast, Singular Spectrum Analysis is an excellent tool for both forecasting and noise reduction. Fortunately, it is possible to combine the Takens approach with Singular Spectrum analysis (SSA), and in fact, estimation of key parameters in Takens theorem is performed with Singular Spectrum Analysis. In this thesis, we combine the denoising abilities of SSA with the Takens …

A Log Rank Test For Clustered Data Under Informative Within-Cluster Group Size., Mary Elizabeth Gregg

Electronic Theses and Dissertations

The log rank test is a popular nonparametric test for comparing the marginal survival distribution of two groups. When data are organized within clusters and the size of clusters or the distribution of group membership within a cluster is related to an outcome of interest, traditional methods of data analysis can be biased. In this thesis, we develop a within-cluster group weighted log rank test to compare marginal survival time distributions between groups from clustered data, correcting for cluster size and intra-cluster group size informativeness. The performance of this new test is compared with the unweighted and cluster-weighted log rank …

Integrated Analysis Of Mirna/Mrna Expression And Gene Methylation Using Sparse Canonical Correlation Analysis., Dake Yang

Electronic Theses and Dissertations

MicroRNAs (miRNAs) are a large number of small endogenous non-coding RNA molecules (18-25 nucleotides in length) which regulate expression of genes post-transcriptionally. While a variety of algorithms exist for determining the targets of miRNAs, they are generally based on sequence information and frequently produce lists consisting of thousands of genes. Canonical correlation analysis (CCA) is a multivariate statistical method that can be used to find linear relationships between two data sets, and here we apply CCA to find the linear combination of differentially expressed miRNAs and their corresponding target genes having maximal negative correlation. Due to the high dimensionality, sparse …

Propensity Score Methods : A Simulation And Case Study Involving Breast Cancer Patients., John Craycroft

Electronic Theses and Dissertations

Observational data presents unique challenges for analysis that are not encountered with experimental data resulting from carefully designed randomized controlled trials. Selection bias and unbalanced treatment assignments can obscure estimations of treatment effects, making the process of causal inference from observational data highly problematic. In 1983, Paul Rosenbaum and Donald Rubin formalized an approach for analyzing observational data that adjusts treatment effect estimates for the set of non-treatment variables that are measured at baseline. The propensity score is the conditional probability of assignment to a treatment group given the covariates. Using this score, one may balance the covariates across treatment …

Semi-Parametric Methods For Personalized Treatment Selection And Multi-State Models., Chathura K. Siriwardhana

Electronic Theses and Dissertations

This dissertation contains three research projects on personalized medicine and a project on multi-state modelling. The idea behind personalized medicine is selecting the best treatment that maximizes interested clinical outcomes of an individual based on his or her genetic and genomic information. We propose a method for treatment assignment based on individual covariate information for a patient. Our method covers more than two treatments and it can be applied with a broad set of models and it has very desirable large sample properties. An empirical study using simulations and a real data analysis show the applicability of the proposed procedure. …

Inference For A Zero-Inflated Conway-Maxwell-Poisson Regression For Clustered Count Data., Hyoyoung Choo-Wosoba

Electronic Theses and Dissertations

This dissertation is directed toward developing a statistical methodology with applications of the Conway-Maxwell-Poisson (CMP) distribution (Conway, R. W., and Maxwell, W. L., 1962) to count data. The count data for this dissertation exhibit three different characteristics: clustering, zero inflation, and dispersion. Clustering suggests that observations within clusters are correlated, and the zero inflation phenomenon occurs when the data exhibit excessive zero counts. Dispersion implies that the mean is greater/smaller than the variance unlike a Poisson distribution. The dissertation starts with an introduction of inference for a zero-inflated clustered count data in the first chapter. Then, it presents novel methodologies …

A Descriptive Study Of The Effect Of Payer Source On Multiple Longitudinal Outcome Measures Within The Tbi Model Systems National Database Using Longitudinal Hlm Analyses, Melissa Carole Hofmann

Electronic Theses and Dissertations

Using longitudinal data from the TBIMS ND, this study utilized a longitudinal hierarchical linear modeling approach to describe the effect of primary payer source on individual level change in outcomes including the FIM and DRS. To facilitate the use of parametric statistics, Rasch-transformed FIM and DRS scores were utilized; thus approaching an interval level of measurement. The FIM was separated into 3 separate cognitive, mobility, and self-care subscales. In this way, rehabilitation professionals including speech, physical, and occupational therapists for this TBI sample could reference results to inform current clinical practice.

Results indicated that FIM and DRS trajectories were best …

A Comparison Between Propensity Score Matching, Weighting, And Stratification In Multiple Treatment Groups: A Simulation Study, Priyalatha Govindasamy

Electronic Theses and Dissertations

The application of propensity score techniques (matching, stratification, and weighting) with multiple treatment levels are similar to those used in binary groups. However, given that the application of propensity scores in multiple treatment groups is new, factors affecting the performance of matching, stratification, and weighting in multiple treatment groups are less explored. Therefore, this study was conducted to determine the performance of different propensity score techniques with multiple treatment groups under various circumstances. Specifically, the study focused on examining how the three propensity score corrective techniques perform in estimating treatment effects under (1) overt and (2) hidden types of selection …

A Comparison Of Latent Class Analysis And The Mixture Rasch Model: A Cross-Cultural Comparison Of 8th Grade Mathematics Achievement In The Fourth International Mathematics And Science Study (Timss-2011), Turker Toker

Electronic Theses and Dissertations

This study provides a comparison of the results of latent class analysis (LCA) and mixture Rasch model (MRM) analysis using data from the Trends in International Mathematics and Science Study - 2011 (TIMSS-2011) with a focus on the 8th-grade mathematics section. The research study focuses on the comparison of LCA with Mplus version 7.31 and MRM with WinMira 2011 to determine if results obtained differ when the assumed psychometric model differs. Also, a log-linear analysis was conducted to understand the interactions between latent classes identified by LCA and MRM. The data set used in the study was from four diverse …

Identifying Data Centers From Satellite Imagery, Adam Buskirk

Electronic Theses and Dissertations

We develop two different descriptors which can be utilized to describe satellite imagery. The first, the differential-magnitude and radius descriptor, describes a scene by computing the directional gradient of the scene with respect to a vector field whose solutions are circles around a pixel to be described, and then counts pixels in a descriptor matrix according to the magnitude of this gradient and the distance at which this magnitude occurs. The second, the radial Fourier descriptor, extracts from the scene a sequence of annuloid sectors, and uses this to approximate the behavior of the image on a circle around the …

On Variable Bandwidth Kernel Density And Regression Estimation, Janet Nakarmi

Electronic Theses and Dissertations

We study the ideal variable bandwidth kernel density estimator introduced by McKay (1993) and the plug-in practical version of the variable bandwidth kernel density estimator with two sequences of bandwidths as in Ginè and Sang (2013).We estimate the variance of the variable bandwidth kernel density estimator. Based on the exact formula of the bias and the variance of the variable bandwidth kernel density estimator, we develop the optimal bandwidth selection of the true variable bandwidth kernel density estimator. Furthermore, we present the central limit theorem of the true variable bandwidth kernel density estimator. We also propose a new variable bandwidth …

Anatomy, Implant Selection And Placement Influence Spine Mechanics Associated With Total Disc Replacement, Justin F.M. Hollenbeck

Electronic Theses and Dissertations

Through aging and injury, the intervertebral disc of the lumbar spine can undergo degeneration, leading to collapse of the vertebrae and low back pain, a symptom that affects half the adult population in any given year. In an effort to reduce low back pain, total disc replacement treatment removes the degenerated disc, restores natural height and lordosis of the segment, and preserves motion at the joint. Patient anatomy, implant selection, and implant placement play significant roles in a patient's outcomes after total disc replacement surgery. Thus, the objective of the work presented in this thesis was to develop a suite …

Predicting Intraday Financial Market Dynamics Using Takens' Vectors; Incorporating Causality Testing And Machine Learning Techniques, Abubakar-Sadiq Bouda Abdulai

Electronic Theses and Dissertations

Traditional approaches to predicting financial market dynamics tend to be linear and stationary, whereas financial time series data is increasingly nonlinear and non-stationary. Lately, advances in dynamical systems theory have enabled the extraction of complex dynamics from time series data. These developments include theory of time delay embedding and phase space reconstruction of dynamical systems from a scalar time series. In this thesis, a time delay embedding approach for predicting intraday stock or stock index movement is developed. The approach combines methods of nonlinear time series analysis with those of causality testing, theory of dynamical systems and machine learning (artificial …