Statistics and Probability Commons^™

Conditional Product Sampling For Gaussian Process Implicit Surfaces, Song Shi

Dartmouth College Master’s Theses

Gaussian Process Implicit Surfaces (GPISes) provide a powerful and unified stochastic geometry representation for rendering surfaces, volumes, and the rich continuum between them. Recent work has shown that GPISes can model a broad space of visual appearances under a unified light transport framework. However, practical rendering with GPISes remains challenging: existing estimators can become inefficient for particular correlation structures, and highly anisotropic or heightfield-like GPISes require specialized treatment to obtain robust variance reduction.

This thesis extends recent work on GPIS rendering by introducing a new next-event estimation (NEE) technique for anisotropic GPISes.We show that standard NEE provides diminishing benefits as …

Multi-Level Variable Selection Using A Bart-Enhanced Mixed-Effects Framework, Keming Zhang, Yaoyao Li, Jungang Zou, Sijian Wang, Bernadette A. Fausto, Liangyuan Hu

College of Health Professions Faculty Papers

Selecting important individual- and cluster-level predictors has become increasingly critical in healthcare research, where data often exhibit hierarchical structures due to collection from multiple clusters. Mixed-effects models, which account for within-cluster correlation and between-cluster heterogeneity, are a natural approach for multilevel variable selection. However, currently available variable selection methods for multilevel data are predominantly based on mixed-effects models that impose restrictive parametric assumptions, potentially limiting their utility when the underlying relationships are nonlinear or involve interactions. While nonparametric methods have shown promise for variable selection in non-clustered data, they have been much less studied in the multilevel setting. Moreover, nonparametric …

An Analytical Framework For Quantifying Urban And Community Resilience To Natural Hazards From Cell-Phone Gps-Location And Traffic-Flow Data, Georgios Chatzikyriakidis

Civil and Environmental Engineering Theses and Dissertations

Urban areas are increasingly exposed to natural hazards while accommodating a growing share of the global population, yet a consistent science-based framework for quantifying urban and community resilience remains lacking. This dissertation develops a physics-based analytical framework grounded in statistical mechanics and the quantitative theory of Brownian motion. A city is conceptualized as a complex medium in which citizens move analogously to Brownian particles within a viscoelastic environment, influenced by socioeconomic interactions and infrastructure functionality.

A central premise is that urban resilience, interpreted as engineering resilience (an outcome), can be quantified through a single metric: the mean-square displacement MSD=⟨r²(t)⟩, of …

Continuous Polygenic Trait Evolution Under Brownian Motion With Gaussian Mixture Models, Mary S. Hopkins

Mathematics & Statistics ETDs

Gaussian mixed-models (GMMs) show promise as a tool for modeling polygenic trait evolution for multiple taxa with established phylogenetic comparative methods (PCMs). When phenotypic traits are influenced by more than one gene, neither a gene tree nor a species tree may be completely adequate to model specific cross-taxa dependencies. In such cases common solutions include using trees inferred from concatenated DNA sequences [35, 95] and consensus gene trees [35]. The GMM-based model, first proposed by Jiang in 2017 [55] allows traits to evolve on more than one tree with distinct topologies. This approach provides a framework for trait evolutionary modeling …

Bayesian Designs For Two-Arm Clinical Trials With Time-To-Event Endpoints: Incorporating Historical Data Through Power Priors, Sara Hajraf H. Almutiri

Mathematics & Statistics ETDs

Bayesian methods provide a flexible framework for time-to-event analysis by incorporating prior information. The power prior offers a systematic way to borrow information from historical data. This approach is especially valuable in clinical research, where historical data can enhance inference in early-phase trials with limited sample sizes. This dissertation develops Bayesian approaches for two-arm survival studies using both closed-form and simulation-based methods. The closed-form inference is derived under exponential and Weibull survival models. Under the proportional hazards framework, the posterior is derived through a normal approximation to the log hazard ratio, allowing inference on the treatment effect when the variance …

Bayesian Spatiotemporal Model For Counterfactual Estimation In Socioeconomic Studies, Duwani W. Gonzalez

Statistical Science Theses and Dissertations

Impact evaluations of regional development programs often require estimating counterfactual outcomes for a small number of treated regions using survey-based areal data. In practice, evaluators typically rely on two-group quasi-experimental methods such as propensity score matching (PSM) and Difference-in-Differences (DiD). These approaches perform poorly when only a few regions receive treatment, and when the set of observed covariates is limited or only partially relevant. Moreover, they typically do not explicitly exploit the spatial and temporal dependence present in survey-based areal data such as in ACS (American Community Survey). This dissertation develops a family of Bayesian spatial predictive models for directly …

A Modified Maximum Likelihood Estimation Algorithm For Modeling Threshold Exceedances With The Generalized Pareto Distribution, Jeffrey Harkness

UNLV Theses, Dissertations, Professional Papers, and Capstones

A modified maximum likelihood estimation (MLE) algorithm is proposed for modeling threshold exceedances with the generalized Pareto distribution (GPD). The algorithm addresses multiple issues with an approach originally published in the Journal Computational Statistics and Data Analysis (Castillo and Serra, 2015). The modified algorithm is intended to be comparatively simple to understand and implement, accurate in the handling of boundary conditions, relatively fast and reliable for most data sets, and relatively easy to transfer between computer languages by leveraging existing optimization routines.

A reproducibility study of work in recent literature published in the journal Extremes (Belzile, et al., 2023) is …

Digital Literacy And Language Proficiency As Factors Of Accessible Digital Training In The Hospitality Industry: Employee Perspectives Of Training And Working In A Diverse Industry, Gillian Bowden

UNLV Theses, Dissertations, Professional Papers, and Capstones

This explanatory sequential mixed methods study explored how digital literacy and language proficiency impact employees’ access to and engagement with digital training, as well as how these experiences influence their perceptions of training and the organization. In the quantitative phase, survey data were collected from hourly employees at a large foodservice corporation (n=67). Four constructs were assessed: digital literacy, language proficiency, accessibility, and engagement. Results indicated strong, statistically significant relationships with higher levels of digital literacy and language proficiency associated with greater accessibility and increased engagement with digital training materials. The large effect sizes suggest these competencies play a meaningful …

Effect Of The Sava Syndemic On Hiv Viral Suppression Among People Living With Hiv In The United States: A Scoping Review And Meta-Analysis, Jacquelyn Rodriguez

UNLV Theses, Dissertations, Professional Papers, and Capstones

The SAVA syndemic highlights the interconnected and mutually reinforcing nature of substance use, violence victimization, and HIV/AIDS. The synergistic interaction of these conditions creates structural and behavioral barriers that disrupt the HIV care continuum and contribute to significant health inequities. Achieving a suppressed viral load is a critical clinical outcome for people living with HIV, while viral non-suppression can be an indicator of poor health, elevated transmission risk, and disease progression. Still, the association between SAVA factors and viral suppression/non-suppression outcomes within U.S. populations remains inconsistently characterized due to heterogeneous methodologies and variable inclusion of high-risk groups. This mixed-methods study …

Delineating Differences In Firing Rate Estimates Of Healthy And Parkinsonian Single-Unit Basal Ganglia Recordings, Richard R. Foster, Cheng Ly

Biology and Medicine Through Mathematics Conference

No abstract provided.

Mitigating Parameter Identifiability Issues Through Model Calibration On The Data-Informed Active Subspace: An Example In Tumor Growth, Allison L. Lewis, Rebecca A. Everett

Biology and Medicine Through Mathematics Conference

No abstract provided.

Latent Transition Analysis: A Statistical Method For Identifying Underlying Subgroups Over Time, Holmes Finch

Perspectives on Early Childhood Psychology and Education

Researchers working in early childhood research are often interested in assessing change over time in multiple variables. In addition, they may wish to ascertain whether there exist subgroups in the data with respect to these variables, and whether/how membership in these groups is related. Latent transition analysis (LTA) provides such researchers with a useful tool for investigating questions around such groups, including their composition, frequency, and the likelihood of moving from one to another at different points in time. The purpose of this manuscript is to provide a full demonstrate of LTA and show how it can be used to …

A Tutorial For Identifying And Comparing Change Points In Developmental Trajectories, Holmes Finch

Perspectives on Early Childhood Psychology and Education

Researchers in a variety of social science fields work with sequential data, such as measurements made over time. In some instances, one or more of the moments (e.g., mean, variance) of the series may change abruptly at some point in the sequence, yielding what is known as a change point. There is a broad literature describing methods for changepoint detection. Researchers working with multiple sequential series containing change points may be interested in comparing the locations of these changes. The purpose of this manuscript is to demonstrate how a researcher can detect changepoints and compare changepoints between two or more …

Using Multilevel Modeling To Understand Nested Data, Holmes Finch

Perspectives on Early Childhood Psychology and Education

Researchers in the social sciences often work with nested data, in which individuals are collected in higher level clusters. For example, educational research often involves working with samples in which students are nested within schools. Standard data analyses, such as regression and analysis of variance (ANOVA), yield statistically biased results when this nested structure is ignored. One widely used and effective approach for handling such nested data is multilevel modeling. The purpose of this manuscript is to review the basics of multilevel modeling and to provide the reader with a fully worked example in which the analytic approach and results …

Using Effect Sizes, Confidence Intervals, And The Bayes Factor To Better Understand The T-Test, Analysis Of Variance, And Regression Results, Holmes Finch

Perspectives on Early Childhood Psychology and Education

Null hypothesis testing is a widely used paradigm for assessing research hypotheses across the social sciences. Despite their ubiquity, researchers have discussed a number of problems and limitations to hypothesis testing and have suggested alternatives that might provide greater depth and explanation of research results. The purpose of this paper is to describe the use of several such alternatives and to show how they can be integrated with one another and with null hypothesis testing in order to provide a more holistic view of research hypotheses.

A Statistical Analysis Of Current And Future Hurricane Activity In The North Indian Ocean, Basil Lund

2026 Symposium

A hurricane is defined as a tropical storm with winds sustained at 74 mph or greater. I examined major (category 3 and above) hurricane activity over the North Indian Ocean from the years 1972-2019 as reported by Colorado State University Hurricane Forecast Archive. Using RStudio, I conducted a binomial analysis of the CSU dataset to calculate probabilities of zero to ten years with one or more major North Indian Ocean hurricanes in the next decade. I conducted a geometric analysis to determine probabilities associated with waiting periods for the next year with a major hurricane, as well as a Poisson …

The Legacy Of Lead: Lead Exposure's Harmful Effects And Its Concentration In Poc Communities, Layla Sophronia Barber

Student Theses 2015-Present

This thesis examines the disproportionate burden of lead exposure carried by low income, POC communities. The systemic nature of this problem is a symptom of a longstanding legacy of environmental injustice in the United States. Decades of federal neglect are reflected in the higher statistics of lead exposure and poisoning in predominantly black communities. While it is understood that lead exposure poses a serious threat to physical health and early cognitive development, there is a discouraging lack of urgency to remove the toxin from non-wealthy communities. The material covered by this thesis aims to identify and correct the discriminatory social …

Assessing Trends In Medical Students’ Perceptions Regarding Statistical Analysis, Ethan Noble, Valeriy Kozmenko, Paul Thompson

Scholarship Pathways Program

Assessing Trends in Medical Students’ Perceptions Regarding Data Analysis and Statistics Knowledge and Skills

Ethan Noble, MD | Mentors: Valeriy Kozmenko, MD, Paul Thompson, PhD

Introduction: The use of evidence-based medicine requires that physicians are able to properly analyze and interpret the results of new research. The development of new research and medical knowledge is swift, and a strong foundation in statistics and research is needed for physicians and medical students to keep up with new research. Curriculum in medical education often lacks in-depth coverage of the subject, and additional curriculum has been shown to enhance student confidence and ability …

Developing A Comprehensive Resource Guide For Caregivers Within The Area Agency On Aging, Aiden R. Murphy

Public Health Capstone Projects

This project developed a new universal caregiver resource guide for caregivers within the Area Agency on Aging, in order to improve resource navigation and workflow efficiency. Resources were collected, verified, and organized into a new, streamlined guide via the ARIA chatbot, covering multiple needs. Caregiver resources were collected and verified by the capstone student and mentor, Michael Kroeker, and organized into a centralized knowledge base within the ARIA chatbot. A mixed methods evaluation was conducted utilizing a 5-point Likert scale with three quantitative questions and one open-ended qualitative question. The data was given to the SeniorLine staff, who wanted to …

Does Your Sleep Really Matter?, Kristy Riddle

Student Scholar Symposium Abstracts and Posters

In this project, I am tracking 10 of my daily statistics revolving around my routine. I am using an Oura Ring to help accomplish some of the statistics. These include: readiness score, sleep score, screen time on cell phone, time spent on social media, steps taken, stress levels, restorative time, pages read, homework time spent, and oz of water consumed. I will be utilizing Excel for my data and will have around 3 months worth of statistics. hope to learn more about my levels of efficient sleep and how I can better improve my motivation as a student. This project …

Freshman 15? Freshman 50?? The Reality Of Daily Life Habits Of A First Year College Student, Gregorio R. Salgado

Student Scholar Symposium Abstracts and Posters

This project presents a personal data tracking study in which I collected daily self-reported metrics over the course of the Spring semester using Excel. The variables tracked include sleep duration, caloric intake, screen time, social media usage, phone checks per day, family communication, and personal spending. The goal of this project is to identify meaningful patterns and correlations between daily habits and personal well-being.

Data was collected through a combination of manual logging and smartphone-generated daily reports. This study explores potential relationships between variables such as sleep duration and social media usage, as well as the association between family communication …

Genetic Analysis Of Triplicated Genes Affecting Sex-Specific Skeletal Deficits In Down Syndrome Model Mice, Kourtney Sloan, Kristina M. Piner, Pathum Randunu Nawarathna Kandedura Arachchige, Charles R. Goodlett, Yann Herault, Gayla R. Olbricht, Joseph M. Wallace, Randall J. Roper

Mathematics and Statistics Faculty Research & Creative Works

Down syndrome (DS) is caused by the triplication of human chromosome 21 (Hsa21), resulting in skeletal insufficiency (low bone mineral density) and altered bone development. DS mouse models recapitulate these deficits, including sexual dimorphism in long bone alterations. Historically, Ts65Dn mice provided much of the insight behind DS-related skeletal deficits with ∼100 trisomic orthologous genes, but there are concerns about the genetic fidelity in this model due to the included triplication of genes not homologous to Hsa21. A new DS model, Ts66Yah, subtracted the non-Hsa21 homologous trisomic genes from Ts65Dn but has not been evaluated for long bone deficits. Comparing …

The Impatience Of Winning: An Analysis Of Time Discounting, Predictive Modeling, And The Nba Draft, Alec R. Plante

Business and Economics Honors Papers

This paper examines whether NBA draft decisions can be better explained by incorporating non-geometric time discounting into a model of general manager decision making. Using a dataset of 285 NBA draft prospects over a 12-year period, the impact of college statistics on Value Over Replacement Player (VORP) is determined, and these impact values are then used to create a “predicted” VORP for the first 4 seasons of each player’s career: a projection of what a general manager might think of a prospect’s future value given their college statistics. Following this, geometric and hyperbolic time discounting models are applied to estimate …

Do Dreams Reflect Our Culture? A Statistical Analysis On Dream Narratives, Michal Kuderski

Honors Capstones

Dreams are often viewed as personal experiences, but they may also reflect cultural influences. This project investigates whether dream content varies across cultures by analyzing written dream reports from American, Japanese, and Peruvian college students using data from DreamBank.net. The study applies text analysis techniques to identify common themes and compares language patterns, including the use of ‘I’ and 'We,' to examine differences in self-focus. Statistical methods for count data are used to evaluate these patterns, along with resampling to address differences in sample size. Preliminary findings suggest that both dream themes and language use may vary by cultural …

Fossil-Fuels In A Decarbonized Country? Modeling The Drivers Of Icelandic Oil Sales, Inbal Armony

Environmental Studies Honors Projects

Although 100% of Iceland’s electricity comes from renewable energy sources, it still relies on fossil fuels for land transportation, marine transportation, aviation, and some industry. Understanding geographic nuances in oil use is critical to achieving Iceland’s goals of carbon neutrality by 2040. As the island has one primary urban center with two thirds of the population, information is lacking about oil use in non-Capital areas and a gap between state and municipal climate plans. Using newly available data of oil sales at the municipality-level in a Small Area Estimation model, we analyze drivers of oil sales across Icelandic municipalities. We …

Progress, Characteristics And Prospects Of Interdisciplinary Research Collaboration At Home And Abroad:Research Based On Literature Published In The Past Five Years, Yueliang Zeng, Ying Yu, Ruirui Gao

Journal of Scientific Information Research

[Purpose/significance] Interdisciplinary research collaboration is an important way to promote knowledge innovation and solve complex social problems in the new era. Reviewing the research progress of interdisciplinary research collaboration at home and abroad in the past five years can help grasp the research frontiers in this field and provide direction for future research. [Method/process] This paper adopts a systematic review method, selecting literature closely related to the theme of interdisciplinary research collaboration from inWeb of Science and CNKI from 2020 to 2024, condensing the research topic, analyzing the main research viewpoints, and summarizing the changing characteristics, then proposing future research …

Research On Academic Journal Evaluation Based On Factor Dimensionality Reduction, Data Weighting, And Journal Characteristics Orientation, Liping Yu, Jing Zhang

Journal of Scientific Information Research

[Purpose/significance] The characteristics of academic journals have important value, and current evaluation systems lack assesment for this dimension. [Method/process] This paper proposes a variable weight method for factor reduction data, firstly uses factor analysis combined with manual classification to determine the characteristics of the journal, and uses Sigmoid function to standardize the public factors to determine the characteristic journals, and then uses the variable weight function to modify the original data for the characteristic indicators of the characteristic journals based on the data of forestry journals in CNKI. Three representative methods including linear weighted aggregation, weighted TOPSIS, and factor analysis, …

A Meta-Analysis Of Corporate Innovation Intention And Its Driving Mechanisms, Yaping Hu, Xuerong Shen, Yi Zheng

Journal of Scientific Information Research

[Purpose/significance] Stimulating corporate innovation intention is a pivotal issue for promoting innovation. However, the academic discourse on its key drivers presents significantly divergent and even contradictory conclusions, leading to theoretical ambiguity and practical guidance challenges. This study aims to systematically and quantitatively integrate empirical research in this field to clarify the true effects of core driving factors and their operational boundaries. [Method/process] Adopting a meta-analysis approach, this study systematically retrieves and screens literature, ultimately analyzes 29 empirical studies and examine four potential moderating variables which include location, data type, industry, and culture. [Result/conclusion] The study finds that government support, internal …

Pyspqr: A Python Package For Density Estimation Using Deep Learning, Cameron Eddy, Reetam Majumder

Electrical Engineering and Computer Science Undergraduate Honors Theses

Splines are used for representing complex functions. In statistics, splines can be used for distributional shapes that are difficult to model by traditional parametric approaches. Ramsay (1) uses M-Spline bases to estimate continuous distributions. Semi-Parametric Quantile Regression (SPQR), developed by Xu and Reich (2), models conditional distributions where a neural network is used to estimate the basis function weights that depend on covariates. (3) implements a package for SPQR in R. We build on this by implementing a version of SPQR in Python with PyTorch. By using PyTorch, we can use more sophisticated deep learning architectures than those available in …

Multi-Population Sufficient Dimension Reduction, Xuerong Meggie Wen, Yuexiao Dong, Li Xing Zhu

Mathematics and Statistics Faculty Research & Creative Works

A novel dimension-reduction method is introduced for multi-population data. The approach conducts a joint analysis that exploits information shared across populations while accommodating population-specific effects. Unlike partial dimension reduction methods, which identify related directions across all populations, or conditional analyses conducted independently within each population, the proposed two-step procedure leverages cross-population information to enhance estimation accuracy. The methodology is demonstrated through simulations and two real-data applications.