Statistics and Probability Commons^™

Limit Theorems For L-Functions In Analytic Number Theory, Asher Roberts

Dissertations, Theses, and Capstone Projects

We use the method of Radziwill and Soundararajan to prove Selberg’s central limit theorem for the real part of the logarithm of the Riemann zeta function on the critical line in the multivariate case. This gives an alternate proof of a result of Bourgade. An upshot of the method is to determine a rate of convergence in the sense of the Dudley distance. This is the same rate Selberg claims using the Kolmogorov distance. We also achieve the same rate of convergence in the case of Dirichlet L-functions. Assuming the Riemann hypothesis, we improve the rate of convergence by using …

An Application Of An In-Depth Advanced Statistical Analysis In Exploring The Dynamics Of Depression, Sleep Deprivation, And Self-Esteem, Muslihat Gaffari

Electronic Theses and Dissertations

Depression, intertwined with sleep deprivation and self-esteem, presents a significant challenge to mental health worldwide. The research shown in this paper employs advanced statistical methodologies to unravel the complex interactions among these factors. Through log-linear homogeneous association, multinomial logistic regression, and generalized linear models, the study scrutinizes large datasets to uncover nuanced patterns and relationships. By elucidating how depression, sleep disturbances, and self-esteem intersect, the research aims to deepen understanding of mental health phenomena. The study clarifies the relationship between these variables and explores reasons for prioritizing depression research. It evaluates how statistical models, such as log-linear, multinomial logistic regression, …

Quasi – Monte Carlo Estimation For Functional Generalized Linear Mixed Models, Ruvini Jayamaha

Waldo Library Student Exhibits

Functional Data Analysis (FDA) is a topic of growing interest in the Statistics community. The data in FDA are smooth curves or surfaces in time or space which can be conceptualized as functions.

We propose a Functional Generalized Linear Mixed Model (FGLMM) to fit EEG data and estimate the parameters using Quasi-Monte Carlo Method.

This proposed model deals with non-Gaussian scalar response, functional predictor, and random effects. We relax the assumption of link and variance functions.

Examining The Interaction Between Calcium Supplement Use, Demographics, And Lifestyle Factors On Bone Health Of Women, Vix J. Talbot

University Honors Theses

Osteoporosis is a condition which poses a significant health threat, particularly among women during the menopause transition, where accelerated bone loss increases fracture risk. Calcium supplementation has been shown to be an important intervention to mitigate bone mineral density (BMD) decline during this and other periods of life. However, the efficacy of calcium supplementation is influenced by various individual factors, including demographics and lifestyle habits. This study investigates the interaction between calcium supplement use, and several interaction terms on bone health in women. Multiple linear regression analysis is employed to assess the impact of these factors on BMD. Data from …

On Limiting Distributions For Eigenvalue Spectra Of Sample Correlation Matrices From Heavy-Tailed Populations: Literature Review, Sachini Sandhareka Wijesundara

Major Papers

This major paper offers an extensive review of literature concerning the limiting distributions for the eigenvalue spectrum of sample correlation matrices from a p-dimensional population, where both the dimension p and the sample size n grow to infinity. The study systematically categorizes the reviewed literature based on underlying assumptions regarding the data characteristics. Specifically, it examines several distinct cases: the independent and identically distributed (i.i.d) case with finite fourth moments, the i.i.d case with infinite fourth moments, the i.i.d case with infinite second moments, and scenarios where rows and columns of the data are linearly dependent. Additionally, the major paper …

Big Two And N-Card Poker Probabilities, Brian Wu, Chai Wah Wu

Communications on Number Theory and Combinatorial Theory

Between the poker hands of straight, flush, and full house, which hand is more common? In standard 5-card poker, the order from most common to least common is straight, flush, full house. The same order is true for 7-card poker such as Texas hold'em. However, is the same true for n-card poker for larger n? We study the probability of obtaining these various hands for n-card poker for various values of n≥5. In particular, we derive closed expressions for the probabilities of flush, straight and full house and show that the probability of a flush is less than a straight …

Scale Of Harm: Estimating The Prevalence Of Online Sexual Exploitation Of Children In The Philippines, Ben Brewster

SMU Human Trafficking Data Conference

No abstract provided.

Gender-Based Service Quality Evaluation Of Multimodal Public Transportation In Dki Jakarta, Mohammad Owais, Jachrizal Sumabrata, Nahry Yusuf

Smart City

In DKI Jakarta, despite the extensive infrastructure development, there has been a significant decline in the usage of public transportation. This can be attributed to the inadequate quality of the services provided. Various studies have highlighted the significance of evaluating the quality of service in public transportation to ensure passenger satisfaction and attract new users. However, there is no agreement on the most effective methodology and suitable indicators for conducting such analyses. In addition, there is a growing recognition of the importance of promoting gender equality in multimodal public transportation (MMPT) and understanding gender differences and perceptions of MMPT services. …

(R2073) Analysis Of Mmap/Ph(1), Ph(2)/1 Preemptive Priority Queueing Model With Single Vacation, Repair And Impatient Customers, S. Meena, G. Ayyappan

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we analyse a single server preemptive priority queue with phase-type vacation and repair, feedback, working breakdown, close-down and impatient customers. Customers arrive according to the Marked Markovian Arrival Process and their service time according to Phase-type distribution. If the High Priority customers need feedback, they lose their priority and join the Low Priority queue. At any instant, if the server is broken down, the server provide service with slow mode for that current customer and then the server will go into a repair process. When there are no customers present in both the queues, the server close-down …

Qwixx Strategies Using Simulation And Mcmc Methods, Joshua W. Blank

Master's Theses

This study explores optimal strategies for maximizing scores and winning in the popular dice game Qwixx, analyzing both single and multiplayer gameplay scenarios. Through extensive simulations, various strategies were tested and compared, including a scorebased approach that uses a formula tuned by MCMC random walks, and race-to-lock approaches which use absorbing Markov chain qualities of individual score sheet rows to find ways to lock rows as quickly as possible. Results indicate that employing a scorebased strategy, considering gap, count, position, skip, and likelihood scores, significantly improves performance in single player games, while move restrictions based on specific dice roll sums …

Spatial Durbin Model On The Utilization Of Delivery At Health Facilities: A 2017 Indonesian Demographic And Health Survey Analysis, Indah Sri Wahyuni, Ira Gustina, Martya Rahmaniati Makful, Tris Eryando

Kesmas

The utilization of delivery at health facilities is a major intervention in reducing 16 to 33% of deaths. This study aimed to determine the model of utilization of delivery at health facilities in Indonesia in 2017 and its influential factors. This study used secondary data from the 2017 Indonesian Demographic and Health Survey using a Spatial Durbin Model (SDM) approach. The population was mothers aged 15 – 49 years, spread across 34 provinces of Indonesia, and had 15,321 samples. The results showed that the Moran’s I value was positive (0.146) and significant at p-value = 0.007, indicating clustered regions with …

Mapping For Tracking Sexually Transmitted Infections By Subdistricts In Surabaya, Indonesia, Destri Susilaningrum, Brodjol Sutijo Suprih Ulama, Fausania Hibatullah, Diandra Soja Anjani

Kesmas

The 2014 shutdown localization of prostitution in Surabaya City, East Java Province, Indonesia, has given rise to an illegal prostitution industry, resulting in the spread of uncontrolled sexually transmitted infections (STIs). Mapping needs to be done to track the spread of the disease. This study used secondary data on STIs in 2020 from the Surabaya City Health Office. By using biplot analysis, this study sought to offer a detailed understanding of the distribution and dynamics of STI cases in different parts of Surabaya. The early-stage syphilis was found in Tegalsari and Krembangan Subdistricts; then, gonorrheal urethritis was found in Tandes, …

Morphometric Analysis And Taxonomic Re-Evaluation Of Pepsis Cerberus Lucas And P. Elegans Lepeletier (Hymenoptera: Pompilidae: Pepsinae: Pepsini), Frank E. Kurczewski, Akira Shimizu, Diane H. Kiernan

Insecta Mundi

Hurd (1952) separated Pepsis cerberus Lucas from P. elegans Lepeletier (Hymenoptera: Pompilidae: Pepsinae: Pepsini) based on external morphology and biogeography. Vardy (2005) synonymized the familiar and historically well-documented P. cerberus and P. elegans, combining these Nearctic taxa with several Neotropical variants in an extremely broad definition of P. menechma Lepeletier. In doing so, Vardy (2005) breached the principle of nomenclatural stability. He ignored the prevailing usage and clearly violated articles 23.2, 23.3 and 23.9.1.2 of the ICZN (1999). Morphological differences, ecological divergence, and narrow sympatric geographic distribution of P. cerberus and P. elegans …

A Symbolic Approach To Nonlinear Time Series Analysis, Ranjan Karki, Nibhrat Lohia, Michael B. Schulte

SMU Data Science Review

Current nonlinear time series methods such as neural networks forecast well. However, they act as a black box and are difficult to interpret, leaving the researchers and the audience with little insight into why the forecasts are the way they are. There is a need for a method that forecasts accurately while also being easy to interpret. This paper aims to develop a method to build an interpretable model for univariate and multivariate nonlinear time series data using wavelets and symbolic regression. The final method relies on multilayer perceptron (MLP) neural networks as a form of dimensionality reduction and the …

Reevaluating Texas Energy Market Forecasts In The Wake Of Recent Extreme Weather Events, Robert A. Derner, Richard W. Butler Ii, Alexandria Neff, Adam R. Ruthford

SMU Data Science Review

This paper provides updated forecasts of energy demand in Texas and recognizes the impact of sustainable energy. It is important that the forecasts of the adoption of sustainable energy are reexamined after Winter Storm Uri crippled the Texas power grid and left many without power. This storm highlighted the issues the Texas power grid had and has continued to struggle with in supplying the state with energy. This paper will offer an overview of the relevant literature on the adoption of sustainable energy and relevant events that have occurred in the state of Texas that will give the reader the …

Leveraging Transformer Models For Genre Classification, Andreea C. Craus, Ben Berger, Yves Hughes, Hayley Horn

SMU Data Science Review

As the digital music landscape continues to expand, the need for effective methods to understand and contextualize the diverse genres of lyrical content becomes increasingly critical. This research focuses on the application of transformer models in the domain of music analysis, specifically in the task of lyric genre classification. By leveraging the advanced capabilities of transformer architectures, this project aims to capture intricate linguistic nuances within song lyrics, thereby enhancing the accuracy and efficiency of genre classification. The relevance of this project lies in its potential to contribute to the development of automated systems for music recommendation and genre-based playlist …

Reports Of Autosomal Recessive Disease And Consanguineous Mating Within The Human Population, Johnathon L. Schluter

Master's Theses

It is anecdotally evident when investigating published reports of autosomal recessive disease that a substantial number of cases are the result of related (consanguineous) mating. This research seeks to quantify the percent of manuscripts describing autosomal recessive diseases published between 2000 and 2020 in which consanguineous mating is indicated. We analyzed 602 peer-reviewed manuscripts to identify the percentage of cases presented in which consanguineous mating was indicated, the underlying genes (novel gene or new mutation) and geographical region. These papers were accessed through a specific set of parameters on the free access PubMed Central (PMC) database. A total of 552 …

Context Aware Music Recommendation And Playlist Generation, Elias Mann

SMU Journal of Undergraduate Research

There are many reasons people listen to music, and the type of music is largely determined by what the listener may be doing while they listen. For example, one may listen to one type of music while commuting, another while exercising, and yet another while relaxing. Without access to the physiological state of the user, current music recommendation methods rely on collaborative filtering - recommending music based on what other similar users listen to - and content based filtering - recommending songs based on their similarities to songs the user already prefers. With the rise in popularity of smart devices …

Towards A New Role Of Mitochondrial Hydrogen Peroxide In Synaptic Function, Cliyahnelle Z. Alexander

Student Theses and Dissertations

Aerobic metabolism is known to generate damaging ROS, particularly hydrogen peroxide. Reactive oxygen species (ROS) are highly reactive molecules containing oxygen that have the potential to cause damage to cells and tissues in the body. ROS are highly reactive atoms or molecules that rapidly interact with other molecules within a cell. Intracellular accumulation can result in oxidative damage, dysfunction, and cell death. Due to the limitations of H₂O₂ (hydrogen peroxide) detectors, other impacts of ROS exposure may have been missed. HyPer7, a genetically encoded sensor, measures hydrogen peroxide emissions precisely and sensitively, even at sublethal levels, during …

Time Scale Separation In Life-Long Ovarian Follicles Population Dynamics Model, Romain Yvinec, Frédérique Clément, Guillaume Ballif

Biology and Medicine Through Mathematics Conference

No abstract provided.

Multi-Type Branching Processes In Time-Varying Environments, Arash Jamshidpey

Biology and Medicine Through Mathematics Conference

No abstract provided.

Modeling Human Temporal Eeg Responses To Vr Visual Stimuli, Richard R. Foster, Connor Delaney, Dean J. Krusienski, Cheng Ly

Biology and Medicine Through Mathematics Conference

No abstract provided.

Statistical Approaches For The Early Detection Of Colorectal Cancer Using Longitudinal Biomarkers, Emily Berry

Statistical Science Theses and Dissertations

Colorectal cancer (CRC) is the third leading cause of cancer-related death in the United States [45]. CRC is believed to advance from adenomatous polyps creating a unique opportunity for both early detection and cancer prevention [4, 23]. Like other diseases, CRC screening reduces mortality by detecting cancer at earlier, more treatable stages; however, it can also reduce incidence through the removal of precancerous lesions [4]. As a result, screening is recommended for average-risk adults ≥ 45 years of age and includes a variety of tests [4, 12]. Despite alternate screening options, colonoscopy capacity is often cited as a barrier to …

The Performance Of Arima And Arfima In Modelling The Exchange Rate Of Nigeria Currency To Other Currencies, Adewole Ayoade I.

Al-Bahir Journal for Engineering and Pure Sciences

Economic performance of a nation depends majorly on the stability of foreign exchange rate; the economic viability hangs on the exchange rate of local currencies against other currencies across the globe. Box – Jenkins Approach was employed to model the Naira exchange rate to other major currencies using Autoregressive Integrated Moving Average (ARIMA) and The autoregressive fractional integral moving average (ARFIMA) models. This studies aimed on measuring forecast ability of Autoregressive Integrated Moving Average (ARIMA) (p,d,q) and autoregressive fractional integral moving average (ARFIMA) (p, fd, q) models for stationary type series that exhibit features of Long memory properties. Results indicate …

Significant Predictors Of Suicide Rates In The United States: A Multiple Regression Analysis, Alexa L. Darak, Gary Popoli

Undergraduate Research Journal for the Human Sciences

Inspired by Stack's (2021) research, this study investigated the influence of 19 variables on suicide rates across all 50 United States. The variables included political party, gun ownership, registered guns, religion, alcohol consumption, state safety, depression, marriage, divorce, domestic violence, race, mean elevation, and region. Regression analyses revealed that gun ownership significantly impacts suicide rates, with stricter firearm laws correlating with lower suicide rates. Other crucial contributors to suicide risk were alcohol consumption, domestic violence, marital status, divorce, mean elevation, and political party affiliation. The five most statistically significant predictor variables were gun ownership, divorce rates, percentage of White individuals, …

An Improved Bayesian Pick-The-Winner (Ibpw) Design For Randomized Phase Ii Clinical Trials, Wanni Lei, Maosen Peng, Xi K. Zhou

COBRA Preprint Series

Phase II clinical trials play a pivotal role in drug development by screening a large number of drug candidates to identify those with promising preliminary efficacy for phase III testing. Trial designs that enable efficient decision-making with small sample sizes and early futility stopping while controlling for type I and II errors in hypothesis testing, such as Simon’s two-stage design, are preferred. Randomized multi-arm trials are increasingly used in phase II settings to overcome the limitations associated with using historical controls as the reference. However, how to effectively balance efficiency and accurate decision-making continues to be an important research topic. …

Markov Chain Model Of Three-Dimensional Daphnia Magna Movement, Helen L. Kafka

Theses and Dissertations

Daphnia magna make turns through an antennae-whipping action. This action occursevery few seconds, hence, during the intervening time, the animal either remains in place or continues movement roughly along its current course. We view their movement in three dimensions. We divide the movement in the three dimensions into the movement on a two-dimensional lattice and the movement between the different planes. For the movement on the lattice, we construct a second-order Markov chain model to make predictions about which region of the lattice the animal moves to based on where it was at the last two time points. The movement …

Utilizing Arma Models For Non-Independent Replications Of Point Processes, Lucas M. Fellmeth

Theses and Dissertations

The use of a functional principal component analysis (FPCA) approach for estimatingintensity functions from prior work allows us to obtain component scores of replicated point processes under the assumption of independent replications. We show these component scores can be modeled using classical autoregressive moving average (ARMA) models, thus allowing us to also apply the FPCA model to non-independent replications. The Divvy bike-sharing system in the city of Chicago is showcased as an application.

Bayesian Change Point Detection In Segmented Multi-Group Autoregressive Moving-Average Data For The Study Of Covid-19 In Wisconsin, Russell Latterman

Theses and Dissertations

Changepoint detection involves the discovery of abrupt fluctuations in population dynamics over time. We take a Bayesian approach to estimating points in time at which the parameters of an autoregressive moving average (ARMA) change, applying a Markov chain Monte Carlo method. We specifically assume that data may originate from one of two groups. We provide estimates of all multi-group parameters of a model of this form for both simulated and real-world data sets. We include a provision to resolve the problem of confounding ARMA parameter estimates and variance of segment data. We apply our model to identify points in time …

High-Dimensional Mediation Analysis Of Multi-Omics Data, Sunyi Chi

Dissertations & Theses (Open Access)

Environmental exposures such as cigarette smoking influence health outcomes through intermediate molecular phenotypes, such as the methylome, transcriptome, and metabolome. Mediation analysis is a useful tool for investigating the role of potentially high-dimensional intermediate phenotypes in the relationship between environmental exposures and health outcomes. Rapid development of high-throughput technologies have made mediation analysis of multi-omics data critical to gain groundbreaking insights into the biological mechanisms underlying the disease etiology. This dissertation aims to develop mediation analysis methods that utilize the enormous amount of multi-omics data in assessing mechanisms of disease etiology. It contains three projects where I propose advanced mediation …