Statistics and Probability Commons^™

Toward Uncharted Territory Of Cellular Heterogeneity: Advances And Applications Of Single-Cell Rna-Seq, Brandon Lieberman, Meena Kusi, Chia Nung Hung, Chih Wei Chou, Ning He, Yen Yi Ho, Josephine A. Taverna, Tim H.M. Huang, Chun Liang Chen

Faculty Publications

Among single-cell analysis technologies, single-cell RNA-seq (scRNA-seq) has been one of the front runners in technical inventions. Since its induction, scRNA-seq has been well received and undergone many fast-paced technical improvements in cDNA synthesis and amplification, processing and alignment of next generation sequencing reads, differentially expressed gene calling, cell clustering, subpopulation identification, and developmental trajectory prediction. scRNA-seq has been exponentially applied to study global transcriptional profiles in all cell types in humans and animal models, healthy or with diseases, including cancer. Accumulative novel subtypes and rare subpopulations have been discovered as potential underlying mechanisms of stochasticity, differentiation, proliferation, tumorigenesis, and …

Analyzing Electronic Health Records With Time-To-Event Endpoints: Propensity Scores And Semiparametric Approaches, Jonathan W. Yu

Theses and Dissertations

For analyzing large electronic health records (EHR) with time-to-event endpoints, such as in kidney transplantation, a major challenge is to provide an accurate risk analyses, while accounting for a multitude of epidemiological and statistical complexities. Motivated by a right-censored kidney transplantation EHR dataset derived from the United Network of Organ Sharing (UNOS), this dissertation, through a culmination of two interrelated yet distinctly different projects, focuses on developments of novel statistical procedures and methodologies to address some pressing issues arising in EHR-based research. In the first project, we aim to decouple the causal effects of treatments (here, studying subgroups, such as …

Parametric, Nonparametric, And Semiparametric Linear Regression In Classical And Bayesian Statistical Quality Control, Chelsea L. Jones

Theses and Dissertations

Statistical process control (SPC) is used in many fields to understand and monitor desired processes, such as manufacturing, public health, and network traffic. SPC is categorized into two phases; in Phase I historical data is used to inform parameter estimates for a statistical model and Phase II implements this statistical model to monitor a live ongoing process. Within both phases, profile monitoring is a method to understand the functional relationship between response and explanatory variables by estimating and tracking its parameters. In profile monitoring, control charts are often used as graphical tools to visually observe process behaviors. We construct a …

Bayesian Techniques For Relating Genetic Polymorphisms To Diffusion Tensor Images Of Cocaine Users, Tmader Alballa

Theses and Dissertations

Past investigations utilizing Diffusion Tensor Imaging (DTI) have demonstrated that cocaine use disorder (CUD) yields white matter changes. We proposed three Bayesian techniques in order to explore the relationship between Fractional Anisotropy (FA), genetic data, and years of cocaine use (YCU). CUD participants exhibit abnormality in different areas of the brain versus non-drug using controls, which is measured by DTI. This dissertation is motivated by a neuroimaging genetic study in cocaine dependence, which found that there were relationships between several genes such as GAD and 5-HT₂R and CUD subjects.

In the first chapter, there is background on the …

Bias Of Rank Correlation Under A Mixture Model, Russell Land

College of Graduate Studies: Theses & Dissertations

This thesis project will analyze the bias in mixture models when contaminated data is present. Specifically, we will analyze the relationship between the bias and the mixing proportion, p, for the rank correlation methods Spearman’s Rho and Kendall’s Tau. We will first look at the history of the two non-parametric rank correlation methods and the sample and population definitions will be introduced. Copulas will be introduced to show a few ways we can define these correlation methods. After that, mixture models will be defined and the main theorem will be stated and proved. As an example, we will apply this …

การเปรียบเทียบประสิทธิภาพของการประมาณค่าของพารามิเตอร์ด้วยวิธีลาสโซและวิธีการคัดเลือกชุดข้อมูลย่อยที่ดีที่สุดในการวิเคราะห์การถดถอยเชิงเส้นสำหรับข้อมูลที่มีมิติสูง, วรัญญา บุตรบุรี

Chulalongkorn University Theses and Dissertations (Chula ETD)

งานวิจัยครั้งนี้มีวัตถุประสงค์เพื่อเปรียบเทียบประสิทธิภาพของวิธีการประมาณค่าพารามิเตอร์สำหรับข้อมูลที่มีมิติสูงด้วยทั้งหมด 5 วิธี ได้แก่ วิธี L0Learn, L0L2Learn, L1, A-L1 และวิธี A-L1L2 โดยการเปรียบเทียบประสิทธิภาพจะเปรียบเทียบใน 2 ด้าน คือ 1) เปรียบเทียบประสิทธิภาพด้านการพยากรณ์ ซึ่งวัดจากค่าคลาดเคลื่อนการทำนาย (MSE) และ 2) ความถูกต้องในการคัดเลือกตัวแปรอิสระเข้าสู่ตัวแบบ ซึ่งพิจารณาจากของค่า Precision Recall และค่า AUC ข้อมูลที่มีมิติสูงที่ใช้ในการศึกษาครั้งนี้ได้จากการจำลอง โดยกำหนดให้ในแต่ละชุดข้อมูลประกอบด้วยจำนวนค่าสังเกต 100 ค่าสังเกต (n = 100) และมีตัวแปรอิสระจำนวน 100 ตัว (p = 1000) โดยตัวแปรอิสระมีการแจกแจงแบบปรกติหลายตัวแปรซึ่งมีความสัมพันธ์กันแบบยกกำลัง (Exponential Correlation) 3 ระดับคือ 0, 0.5 และ 0.9 ค่าความคลาดเคลื่อนสุ่มขึ้นอยู่กับอัตราส่วนสัญญาณต่อสัญญาณรบกวน (SNR) ซึ่งมี 6 ระดับคือ 0.1, 0.5, 1, 5, 10, และ 20 โดยจำลองข้อมูลจำนวน 100 ชุดในแต่ละสถานการณ์ จากการวัดประสิทธิภาพจากค่าเฉลี่ยของข้อมูลทั้ง 100 ชุด ผลการเปรียบเทียบประสิทธิภาพด้านการพยากรณ์พบว่า เมื่อข้อมูลมีค่า SNR ต่ำและตัวแปรอิสระมีความสัมพันธ์กันน้อยถึงปานกลาง วิธี L1 จะมีประสิทธิภาพสูงที่สุด ตามด้วยวิธี L0L2Leran วิธี L0Learn วิธี A-L1L2 และวิธี A-L1 ตามลำดับ แต่เมื่อข้อมูลมีค่า SNR เพิ่มสูงขึ้นและในขณะเดียวกันตัวแปรอิสระมีความสัมพันธ์กันมากขึ้นวิธี A-L1 และวิธี A-L1L2 จะมีประสิทธิภาพสูงที่สุด ตามด้วยวิธี L1 วิธี L0L2Leran วิธี L0Learn ตามลำดับ ส่วนผลการเปรียบเทียบประสิทธิภาพด้านการคัดเลือกตัวแปรเข้าสู่ตัวแบบ เมื่อพิจารณาจากค่าเฉลี่ยของค่า Precision …

Methods For Developing A Machine Learning Framework For Precise 3d Domain Boundary Prediction At Base-Level Resolution, Spiro C. Stilianoudakis

Theses and Dissertations

High-throughput chromosome conformation capture technology (Hi-C) has revealed extensive DNA looping and folding into discrete 3D domains. These include Topologically Associating Domains (TADs) and chromatin loops, the 3D domains critical for cellular processes like gene regulation and cell differentiation. The relatively low resolution of Hi-C data (regions of several kilobases in size) prevents precise mapping of domain boundaries by conventional TAD/loop-callers. However, high resolution genomic annotations associated with boundaries, such as CTCF and members of cohesin complex, suggest a computational approach for precise location of domain boundaries.

We developed preciseTAD, an optimized machine learning framework that leverages a random …

The Relevance Of Credit Risk In The Determination Of Commercial Banks’ Profitability: Evidence From Ghana, Godwin Kwabla Ekpe

Graduate Research Theses & Dissertations

Existing empirical literature on the relationship between credit risk and bank’s profitability is replete with mixed results. This research investigates the probable effect of credit risk on banks’ profitability by examining the nature of the relationship between two measures of credit risk (Loss provisioning rate and Actual provisioning charge rate) and two measures ofprofitability (Return on assets and Return on Equity). The investigation is conducted using data on the Ghanaian banking industry. Various modeling techniques are used to fit the data, including frequentist beta regression and Bayesian beta regression models. The results across all models suggest negative linear relationship between …

Traffic Fatality Rate Prediction Based On Deep Neural Network And Bayesian Neural Network, Yiqun Hu

Graduate Research Theses & Dissertations

There have been numerous studies on traffic accidents and their fatality rate. For this challenging machine learning regression problem, Neural Networks (NNs) have produced state-of-the-art data. Despite their success, they are often used in a fre- quentist scheme, which means they cannot account for uncertainty in their forecasts. BNNs are comprised of a Probabilistic Model and a Neural Network. The aim of such a design is to bring together the benefits of Neural Networks and stochastic modeling. Neural networks have the ability to approximate continuous functions uni- versally. Statistical models allow for the direct definition of a model with known …

A Time Series Analysis Approach To Forecasting Covid-19 Cases And Deaths: An Analysis Of Covid-19 Data In Colombia, Andrea Jackson-Sagredo

Graduate Research Theses & Dissertations

The novel Coronavirus, known as COVID-19 is a highly contagious and transmissible infectious disease that has taken a toll throughout the entire world for over a year. The inner workings and long term effects of COVID-19 continue to be misunderstood. While COVID-19 has impacted all countries tremendously, Latin American countries and specifically Colombia have been impacted significantly by the virus. This thesis investigates the potential to forecast COVID-19 cases and deaths using Time Series Analysis methods and models for the South American country of Colombia. Time series analysis on Colombian COVID-19 data begins with data processing on a data set …

Stochastic Infection In Network Models With Applications To Pollution Analysis, Alexander Thor Wold

Graduate Research Theses & Dissertations

The continued adoption and escalation of commercial surface extraction techniques threatens to contaminate adjacent river networks across the coal mining landscape. We look to simulate the movement of this pollution across connected graph structures using stochastic block model methodologies, fueled from work and theory derived from exponential random graph models. We begin our study by applying our virtual experiment to the motivating material, later offering an exhaustive walk through of the simulation itself. Afterwards, we present our findings and their implications to water pollution analysis, emphasizing a need for this research and expanding on some inferential statistics left for later …

The Simulation Extrapolation Method With Differential Measurement Error, Dominic Partipilo

Graduate Research Theses & Dissertations

Most of statistical theory operates under the assumption that the true values of covariates have been measured correctly, but it is not always possible to obtain the true values of these covariates. A common issue, specifically in regression models, is that predictors are misclassified or measured with systematic measurement error. There have been many methods developed for handling measurement error, specifically in the case where measurement error is nondifferential, where the measurement error can be treated as independent from the covariates. The frequentist method known as simulation extrapolation (SIMEX) is one of these methods that specifically handles the case for …

Optimization Of Dynamic Objective Functions Using Path Integrals, Paramahansa Pramanik

Graduate Research Theses & Dissertations

Path integrals are used to find an optimal strategy for a firm under a Walrasian system. We define dynamic optimal strategies and develop an integration method to capture all non-additive non-convex strategies. We also show that the method can solve the non-linear case, for example Merton-Garman-Hamiltonian system, which the traditional Pontryagin maximum principle cannot solve in closed form. Furthermore, we assume that the strategy space and time are inseparable with respect to a contract. Under this assumption we show that the strategy spacetime is a dynamic curved Liouville-like 2-brane quantum gravity surface under asymmetric information and that traditional Euclidean geometry …

Methods For High-Dimensional Spatial Data: Dimension Reduction And Covariance Approximation, Paul May

Electronic Theses and Dissertations

In spatial statistics, because quantities are correlated based on their relative positions in space, data is modeled as a single realization of a multivariate stochastic process. Spatial data can be high-dimensional either through a large number of observed variables per location, or through a large number of observed locations. The two are often handled differently, with the former addressed through dimension reduction and the latter addressed through appropriate modeling of the spatial correlation between locations. The main body of this dissertation is a three-part work. Parts 2 and 3 pertain to the "many variables" problem, proposing novel methods of dimension …

Statistical And Machine Learning Approaches To Depressive Disorders Among Adults In The United States: From Factor Discovery To Prediction Evaluation, Minhwa Lee

Senior Independent Study Theses

According to the National Institutes of Mental Health (NIMH), depressive disorders (or major depression) are considered one of the most common and serious health risks in the United States. Our study focuses on extracting non-medical factors of depressive disorders diagnosis, such as overall health states, health risk behaviors, demography, and healthcare access, using the Behavioral Risk Factor Surveillance System (BRFSS) data set collected by the Centers for Disease Control and Prevention (CDC) in 2018.

We set the two objectives of our study about depressive disorders diagnosis in the United States as follows. First, we aim to utilize machine learning algorithms …

An Evaluation Of The Performance Of Proc Arima's Identify Statement: A Data-Driven Approach Using Covid-19 Cases And Deaths In Florida, Fahmida Akter Shahela

Electronic Theses and Dissertations, 2020-2023

Understanding data on novel coronavirus (COVID-19) pandemic, and modeling such data over time are crucial for decision making at managing, fighting, and controlling the spread of this emerging disease. This thesis work looks at some aspects of exploratory analysis and modeling of COVID-19 data obtained from the Florida Department of Health (FDOH). In particular, the present work is devoted to data collection, preparation, description, and modeling of COVID-19 cases and deaths reported by FDOH between March 12, 2020, and April 30, 2021. For modeling data on both cases and deaths, this thesis utilized an autoregressive integrated moving average (ARIMA) times …

Impact Of Case Management On Childhood Lead Exposure In Marion County, Indiana, Maliki Yacouba

Walden Dissertations and Doctoral Studies

The Centers for Disease Control and Prevention recently declared that no amount of childhood blood lead level (BLL) is safe. The purpose of this quantitative study with a retrospective cohort design was to evaluate the effectiveness of case management intervention on children diagnosed with elevated BLL (EBLL; ≥ 5 μg/dL) in Marion, County, Indiana. The health belief model was used as the theoretical foundation for the study. A data set of 160 lead exposure case management records was analyzed to find whether: (a) BLL at post-case-management time significantly differ from BLL at baseline (b) BLL at post-case-management time is affected …

A Model For Inhalation Of Infectious Aerosol Contaminants In An Aircraft Passenger Cabin, Bert A. Silich

International Journal of Aviation, Aeronautics, and Aerospace

Aerosol contamination of an aircraft cabin by infectious passengers is a concern of passengers, aircrew and the aviation industry. This may be especially important during a pandemic, such as COVID-19, where the full extent of aerosol transmission is not well understood. A statistical method to determine the number of infectious passengers on board along with a mathematical model estimating the contaminant concentration of aerosols in the cabin and the number of inhaled infectious particles by passengers is presented. An example is used to demonstrated how the results can be estimated during normal operations and emergency conditions with malfunctions of the …

Prognostic Modeling Of Recovery Following Stem Cell Transplantation, Brielle A. Forsthoffer

Theses and Dissertations

Predicting the trajectory of lymphoid recovery following myeloablative hematopoietic stem cell transplantation (SCT) can help guide subsequent therapeutic decisions, since poor recovery has been associated with graft-versus-host disease (GVHD), relapse and mortality. Previous attempts at classifying patients depended on absolute criteria being set prior to modeling absolute lymphocyte counts (ALCs) over time. Having an empirical clinical decision support tool for objectively determining the trajectory an individual might take during their recovery would be advantageous. We propose using growth-based trajectory modeling (GBTM) and growth mixture modeling (GMM), which utilize machine learning algorithms to empirically identify latent groupings of data. Due to …

Bayesian Experimental Design For Bayesian Hierarchical Models With Differential Equations For Ecological Applications, Rebecca Atanga

Theses and Dissertations

Ecologists are interested in the composition of species in various ecosystems. Studying population dynamics can assist environmental managers in making better decisions for the environment. Traditionally, the sampling of species has been recorded on a regular time frequency. However, sampling can be an expensive process due to financial and physical constraints. In some cases the environments are threatening, and ecologists prefer to limit their time collecting data in the field. Rather than convenience sampling, a statistical approach is introduced to improve data collection methods for ecologists by studying the dynamics associated with populations of interest. Population models including the logistic …