Statistics and Probability Commons^™

When The Best-Fit Model Is Not Best: The Glass Slipper Fallacy And Latent Growth Mixture Modelling, Jonathan L. Chia, Markus Wettstein, Andree Hartanto

Research Collection School of Social Sciences

Despite the use of latent growth mixture modelling (LGMM) to study longitudinal changes, existing practices may inadvertently impede this very investigation. Although subgroup trajectories may theoretically differ in their structure (e.g., some subgroups being linear, some curvilinear), the current convention advocates overreliance on the baseline model to derive subsequent profile trajectories, which may obscure these structural differences. In this article, we provide a brief description of extant LGMM practices, after which we explicate the pitfalls of the current approach. Finally, we provide a principled approach for LGMM research moving forward. Specifically, we recommend specifying a set of theoretically plausible models …

Modeling Mean And Variability Of Anxiety In Ecological Momentary Assessment Data Using Mixed-Effects Location–Scale Models, Trenzy Odero

Electronic Theses and Dissertations

Ecological Momentary Assessment is a method of collecting repeated measures of people in real time within natural environments. This results in hierarchical data that has a significant amount of variation at the person level. The traditional linear mixedeffects models assume that the residual variance is constant, which might not be true when the residual variance varies among individuals as well as in time. This thesis uses mixed-effects location-scale (MELS) models to model the mean and variance of an EMA outcome together. By introducing the possibility of variability in residual variance within and across individuals and with covariates, the MELS framework …

Machine Learning For Predictive Energy And Emissions Modeling Of Vehicles And Power Grids In The United States, S M Tanvir Faysal Alam Chowdhoury

Dissertations

The environmental benefits of electric vehicle (EV) adoption depend on more than replacing internal combustion engine vehicles with electric powertrains. EV adoption reshapes electricity demand, interacts with regional generation mixes, and influences travel behavior and congestion, creating a coupled transportation-energy system in which vehicle and power-plant emissions must be evaluated together. This dissertation develops machine-learning frameworks for predicting energy consumption and emissions from vehicles and power grids under rising EV adoption. The first component forecasts grid emissions from EV charging. Using simulation data from NREL's Cambium database, a Prophet-based time-series framework predicts carbon dioxide, nitrous oxide, and methane emission rates …

Laplace Factor Models In High-Dimensional Data, Siqi Liu, Xuerong Meggie Wen, Akim Adekpedjou, Guangbao Guo

Mathematics and Statistics Faculty Research & Creative Works

Laplace factor models (LFMs) provide a heavy-tailed alternative to Gaussian factor models by representing high-dimensional observations through a low-rank common component and Laplace-distributed idiosyncratic errors. This paper develops an assumption-consistent finite-sample analysis of matrix concentration, covariance estimation, and Monte Carlo integration under this model. We first formulate the model with explicit dimensional, independence, covariance, and identifiability conditions. Standard matrix Laplace-transform and matrix Bernstein inequalities are then recalled with their precise applicability conditions. Because untruncated Laplace variables are neither almost surely bounded nor strongly log-concave, these standard results cannot be applied directly in the forms commonly used for bounded or Gaussian-like …

Learning Latent Structure In High-Dimensional Data Via Geometry And Graphs, Haozhe Chen

All Graduate Theses and Dissertations, Fall 2023 to Present

Modern datasets often contain many measured variables for each observation, such as gene-expression levels, brain activity signals, or features in tabular data. These data are also often noisy, meaning that useful patterns are mixed with measurement error or irrelevant variation. Although such datasets can appear complex, they are frequently represented by simpler hidden structures, such as trajectories, clusters, or relationships between observations. This dissertation develops methods for uncovering these hidden structures by learning geometric and graph-based representations directly from data. The first part introduces Functional Information Geometry, which represents local patterns in high-dimensional data using functional features and constructs a …

Unifying And Expanding Global And Local Variable Importance Methods For Explainable Machine Learning, Kelvyn K. Bladen

All Graduate Theses and Dissertations, Fall 2023 to Present

Machine learning methods are powerful analytical tools used across all scientific disciplines and many other fields of investigation for prediction and inference from diverse data sources. Despite their broad applicability, machine learning methods are often highly complex and difficult to interpret. Developing a greater understanding of which variables most influence a response is essential for increasing the interpretability of these models and supporting informed decision-making. This research focuses on improving how we evaluate the importance of these variables.

One common approach is to shuffle the values of a variable and see how much the model accuracy gets worse. Another approach …

Spatial Prediction Under Uncertainty: Methodological And Computational Advances In Bayesian Maximum Entropy, Kinspride K. Duah

All Graduate Theses and Dissertations, Fall 2023 to Present

Environmental decisions such as infrastructure design, water management, and snow load estimation depend on spatial data that are often incomplete or uncertain. In many cases, measurements are not exact values but ranges, reflecting limitations in data collection methods. Traditional mapping techniques typically simplify these uncertain measurements, which can lead to less accurate predictions. This dissertation introduces improved statistical tools for making spatial predictions when data are uncertain or partially known. By utilizing a framework called Bayesian Maximum Entropy (BME), this research demonstrates how exact measurements and range-based data can be combined in a mathematically consistent way. The work demonstrates that …

Community Detection In Bipartite Networks Using Bipartite Stochastic Block Models With Node-Level Covariates, Geraldine Elaine Percival

Dissertations

In this age, monumental webs of data demands for perpetual cultivation of ways to untangle these webs of information. One of the many curiosities is how to systematically group entities. When clustering, one avenue to take is ascertaining the interconnectedness between the data points, and gauging their influence to each other. This perspective is programmed to model the relationships between the data presented as a network. Many of the methods being used today are algorithm-based, which may pose limitations in understanding and explaining the uncertainty revolving around the data. Hence, it is proposed to steer towards a model-based approach that …

Evaluating Machine Learning Models On Classification Of Novel Cyber Attacks In The Healthcare Domain, Promise Ehimen

Dissertations, Theses, and Projects

The increasing adoption of the Internet of Medical Things (IoMT) has improved healthcare delivery through connected medical devices while simultaneously expanding the cybersecurity risks facing healthcare organizations. Although machine learning based intrusion detection systems have demonstrated high detection accuracy, their ability to respond reliably to previously unseen cyberattacks remains uncertain. This study investigated how a Neural Network model and a Logistic Regression model classified novel cyberattacks within the IoMT environment. The Neural Network and Logistic Regression models were both trained and tested using a subset of the CICIoMT2024 benchmark dataset. The Neural Network achieved 99.82% test accuracy and a 0.94 …

A Mathematical Decision-Making Framework For Athlete Development In A Collegiate Taekwondo Community: Prioritizing Coaching Interventions Using Statistical Analysis And The Analytic Hierarchy Process, King Harold A. Recto, Hazel Jade L. Antonio, Jhyrald Anthony P. Dalida

Electronics, Computer, and Communications Engineering Faculty Publications

Athlete development within collegiate sports communities requires informed decisions regarding the prioritization of coaching interventions and allocation of developmental resources. However, such decisions are frequently guided by experience and intuition, limiting opportunities for systematic and evidence-based decision-making. This study develops a mathematical decision-making framework for athlete development by integrating statistical analysis and the Analytic Hierarchy Process (AHP) within a collegiate taekwondo community. Data were collected from 25 collegiate taekwondo athletes who satisfied established eligibility criteria, including participation in University Athletic Association of the Philippines (UAAP) competitions during the previous three seasons. Athletes evaluated coaching practices across five dimensions: Training and …

Interpretable Case-Control Inference Through Log-Linear General Location Models, Zacharia Stuart

Mathematics & Statistics ETDs

This dissertation analyzes one of the few publicly available NFL injury datasets to study field type and non-contact lower-limb injuries. Field type is studied jointly with other risk factors to understand how these factors interact to affect injury risk. The data were gathered through a case-control sampling scheme, which limits direct inference on absolute injury probabilities. While not the most common approach for case-control data, this dissertation models the retrospective distribution directly through Log-Linear General Location Models (Log-Linear GLOMs). Through a log-linear structure placed on a log-odds-ratio reparameterization, the model provides directly interpretable marginal and interaction contributions to injury log-odds …

The Uncertainty Principles, Lee Michael Felicetti

Mathematics & Statistics ETDs

The Heisenberg uncertainty principle is a central aspect of quantum mechanics, but also illustrates an essential quality of the Fourier transform. After Heisenberg, a variety of uncertainty inequalities emerged in the fields of physics and mathematics. In this thesis we will analyze the Heisenberg uncertainty principle in both the setting of quantum mechanics and Fourier analysis. We will then look at how the work of Heisenberg has been expanded upon in both physics and mathematics. Particularity, we will see how uncertainty principles can be applied to signal recovery and explore current research in this field.

Mapping And Modeling Threat-Evoked Brain States After Early Life Adversity, Taylor W. Uselman

Biomedical Sciences ETDs

Early life adversity (ELA) increases lifelong neuropsychiatric vulnerability. Yet how ELA reorganizes brain-wide activity and circuit coordination across later experience remains unclear. This dissertation tests the hypothesis that ELA alters adult brain-wide activity and responses to threat through disrupted coordination among neural systems that regulate emotional experience, including prefrontal-limbic and monoaminergic systems. Longitudinal manganese-enhanced MRI of adult mice exposed to standard or fragmented early care, combined with computational processing and statistical modeling, quantified brain states before, during, and long after innate predator threat. These studies established that acute threat evokes large-scale, distributed brain activity that evolves over time. ELA potentiates …

Volatility Spillovers Between Stock Prices And Exchange Rates: Insights For Risk Management And Investment Strategies: Evidence From China, India, And Pakistan Using Bekk-Garch Models, Samreen Fatima, Humera Sultana, Muhammad Najamuddin Dr., Saba Naz

The Indonesian Capital Market Review

This study investigates the dynamics of volatility and its spillover effects between the stock markets of China, India, and Pakistan, and their respective exchange rates (USD/CNY, USD/INR, and USD/ PKR). Volatility is modeled using the Symmetric and Asymmetric BEKK-GARCH (1,1) and DCCGARCH (1,1) models, based on daily return series covering the period from January 1, 2019, to January 31, 2025. The empirical results indicate that both the employed models are adequate for capturing the volatility dynamics. The findings reveal that the highest value of portfolio weights and hedging efficiency of KSE-100 Index–USD/PKR provide optimal portfolio allocation and highest hedging performance …

Quantitative Methods In Education: A Practical Introduction To Statistics, Yukiko Maeda, John Gipson, Sheila Hurt, Katie H. Dufault

Purdue University Press Books

Educational research often involves understanding complex patterns in student achievement, teacher effectiveness, and institutional performance. Quantitative Methods in Education: A Practical Introduction to Statistics is designed to equip current and future educators and researchers with a basic comprehension of the statistical tools necessary to effectively analyze and interpret educational data. In today’s data-driven world, the ability to leverage statistical techniques is essential for making informed decisions that can enhance learning outcomes and maximize learner potential. This book provides a systematic approach to exploring these trends using both descriptive and inferential statistics, providing readers with the knowledge to conduct rigorous analyses …

Feasibility And Acceptability Of Automated Texts To Offer, Screen, And Enroll Patients In A Cancer Clinical Trial Financial Reimbursement Program: Mixed Methods Study, Ashley E Santaniello, Hena Patel, Sarah Milinski, Mohan Balachandran, Vivian Nguyen, E. Paul Wileyto, Robert H. Vonderheide, Dana Dornsife, Robert G. Johnson, Carmen E. Guerra

Student Papers, Posters & Projects

BACKGROUND: Out-of-pocket (OOP) costs pose a significant barrier to participating in cancer clinical trials (CCTs). Financial reimbursement programs (FRPs) that reduce the burden of OOP costs can support participation in CCTs if the information is readily available to participants at the time of enrollment. Prior studies have shown the importance and impact of FRPs, but despite improvements, significant barriers still remain.

OBJECTIVE: This study was designed to explore the feasibility and acceptability of automated texts designed to offer, screen, and enroll CCT participants in an FRP for OOP travel and lodging-related clinical trial costs.

METHODS: This study used a mixed …

Urban Carbon Emission Early Warning Research Based On The Dpsir Framework And Deep Learning, Xiaochun Zhao, Lingyang Xu, Ying Zhou

Journal of Scientific Information Research

[Purpose/significance] In line with the national requirements for building a carbon emission early warning mechanism, conducting the urban carbon emission early warning research is of great significance for achieving the “dual-carbon” goals. [Method/process] This paper selected 16 prefecture-level cities in Anhui Province as research samples. A carbon emission early warning indicator system was constructed based on the DPSIR framework. By using data from urban statistical yearbooks, the LSTM model was employed with parameter optimization via genetic algorithms to forecast various early warning indicators for 2024-2025.On this basis, a combined subjective-objective weighting method was then applied to calculate the urban carbon …

A Multi-Dimensional Analysis Of China's Future Industry Development Policy Documents, Tianxiang Yao, Wang Xu

Journal of Scientific Information Research

[Purpose/significance] Future industries are important carriers of new quality productive forces which can play a leading role in the economic and social development. Quantitative analysis and evaluation of China's future industry policies can provide support and reference for the formulation, optimization and adjustment of subsequent policies. [Method/process] Taking a total of 84 policy texts at the central, provincial, municipal and county levels in China as the research objects, a three-dimensional analysis framework of "theme-tool-effectiveness" was constructed. By comprehensively applying LDA thematic analysis, content analysis and PMC index model, theme distribution, content characteristics and comprehensive effectiveness of policy texts were deeply …

P-Value Visualizer, Manish Rami

Software

An interactive tool demonstrating what a user set p-value indicates with regards to probability.

Effect Size & Distributional Overlap Visualizer, Manish Rami

Software

An interactive tool comparing a control group and a treatment group, both with standard scores (M = 100, SD = 15). Cohen's d is expressed in standard deviation units. The three shaded regions show what each group's distribution looks like and how much they overlap. You can either use the preset buttons for effect sizes (SLP benchmarks) or the slider to change the values of Cohen's d to examine the distributions.

Exact X2 Statistic Critical Values For Dice Fairness Testing, Warren Campbell

SEAS Faculty Publications

Two questions were addressed: 1) What are the exact values of the c² statistic critical values? 2. Does a dice tower offer improved fairness of dice rolls?  Critical values of the statistic asymptotically approach those given by the continuous chi-square distribution, but the exact distribution is discrete.  The exact distributions only asymptotically approach the chi-square distribution, and the convergence is slow (1/number of rolls).  Th exact distributions are a function of the number of rolls, the chi-square distribution is not a function of the number of rolls.  Exact values of c² at the 90, 95, and 99 percent …

Correlation Visualizer, Manish Rami

Software

An interactive tool to understand correlations. The tool uses an example relationship between phonological awareness (CTOPP-2) and reading fluency. Both measures use standard scores (M = 100, SD = 15). Viewers can adjust r to explore how the strength and direction of correlation affects the scatter pattern and shared variance. Use the slider for r to see corresponding changes in the plot and the values of r and effect size.

What We Know About Accounting Ratios: Methodological Considerations, Wojciech Kuryłek, Oskar Kowalewski

Studia i Materiały Wydział Zarządzania Uniwersytet Warszawski

Purpose: This paper provides a comprehensive literature review of the methodological aspects of financial ratio analysis, consolidating dispersed knowledge on the computation, statistical properties, and appropriate usage of accounting ratios.

Design/Methodology/Approach: The study adopts a narrative literature review methodology, systematically surveying published research on financial ratio distributions, normality testing, data transformations, outlier handling, the proportionality assumption, dimensionality reduction techniques, compositional data analysis, and recommended ratio sets for corporate financial research.

Findings: Financial ratios predominantly deviate from normal distributions, exhibiting skewness, excess kurtosis, and sensitivity to outliers. Transformation techniques such as logarithmic, square root, and Box‑Cox methods yield mixed results in …

Statistical Evaluation Of A New Orleans Historic Rainfall Dataset (1840–1893), Arielle C. Filostrat

LSU Master's Theses

This study evaluates the climatic credibility of a newly identified historical rainfall dataset for New Orleans, Louisiana, spanning 1840–1893. The New Orleans Historical Dataset (NOHD) is compared to a modern observational record from the Audubon rain gauge (1893–2024) to determine whether nineteenth-century rainfall observations are consistent with known precipitation behavior in the region. Establishing the reliability of early records is critical for extending climatological baselines and improving understanding of long-term rainfall variability.

Historical rainfall observations were first evaluated through archival review using the New Orleans Medical and Surgical Journal and other nineteenth-century meteorological records to verify notable rainfall events. Daily …

Mengukur Capaian Dan Identifikasi Konvergensi Pembangunan Infrastruktur Antarprovinsi Di Indonesia, Ressa Isnaini Arumnisaa', Aisyah Fitri Yuniasih

Jurnal Ekonomi dan Pembangunan Indonesia

Indonesia’s economic challenges are characterized by stagnant economic growth and regional development disparities. This study analyzes the achievement and convergence of infrastructure development across provinces in Indonesia during 2011–2021 through the construction of an Infrastructure Development Index (IPI). The study employs panel data from 33 provinces, using factor analysis to construct the IPI and the First Difference Generalized Method of Moments (FD-GMM) to examine convergence and its determinants. The results show that many provinces still have IDI scores below the national average. Furthermore, the FD-GMM model shows that σ-convergence and β-convergence occur in Indonesia. In addition, GRDP per capita, inflation, …

It's All In The (Exponential) Family: An Equivalence Between Maximum Likelihood Estimation And Control Variates For Sketching Algorithms, Keegan Kang, Kerong Wang, Ding Zhang, Rameshwar Pratap, Bhisham Dev Verma, Benedict Wong

Faculty Conference Papers and Presentations

Maximum likelihood estimators (MLE) and control variate estimators (CVE) have been used in conjunction with known information across sketching algorithms and applications in machine learning. We prove that under certain conditions in an exponential family, an optimal CVE will achieve the same asymptotic variance as the MLE, giving a fixed point algorithm for the MLE. Experiments show the fixed point algorithm is faster and numerically stable compared to other root finding algorithms for the MLE for the bivariate Normal distribution, and we expect this to hold across distributions satisfying these conditions. We show how this algorithm leads to reproducibility for …

Interactive Distribution Visualizer, Manish Rami

Software

An interactive tool visualizing types of distribution. Viewers can morph between a bell curve, box plot, and cumulative frequency curve.

Reliability Vs. Validity Visualizer, Manish Rami

Software

A visualization tool to demonstrate the concepts of reliability and validity.

Each target represents repeated measurements of the same person or construct. The crosshair (✛) marks the true score. Reliability = how tightly shots cluster together. Validity = whether shots center on the true score. Click any panel for a clinical SLP example. Also see notes below the plots.

Estimasi Underground Economy Triwulanan Di Indonesia Pada Tahun 2010–2023, Ghina Anandhia, Hardius Usman

Jurnal Ekonomi dan Pembangunan Indonesia

Underground economics have a significant impact on economy. Underground economy leads to low potential state revenues from the tax sector. This study estimates the quarterly value of the underground economy in Indonesia from 2010 to 2023 using the Error Correction Model (ECM) method. The results show that the average value of the underground economy in Indonesia is IDR138,392.32 billion, equivalent to 5.36 percent of Gross Domestic Product (GDP) and 35.72 percent of tax revenue from 2010 to 2023. GDP and tax burden variables have a positive influence on currency demand.

Existence And Uniqueness Of Positive Solutions For Hilfer–Hadamard-Type Fractional Differential Equations With Γ-Concave And Sub-Homogeneous Operators, Hasan Rasouli, Hojjat Afshari, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

In this research, we present necessary and sufficient conditions for the existence and uniqueness of positive solutions for a class of Hilfer–Hadamard-type fractional differential equations with boundary value problems, including those with integral boundary conditions. The obtained results are conditional on a specific set of strong assumptions, which substantially narrow the class of admissible nonlinearities, coefficients, and boundary data. Thus, the present work extends the Hadamard-type framework to the Hilfer–Hadamard setting only within this restrictive regime, rather than providing a full extension to all Hilfer–Hadamard systems. We utilize the properties of (Formula presented.) -concave and sub-homogeneous operators along with two …