Other Statistics and Probability Commons^™

(R2161) Robust Optimization Of Industrial Hazardous Waste Location-Routing Problem Considering Response Actions To Environmental Risk, Sharareh Teimoori, Farhad Hosseinzadeh Lotfi, Seyyed Esmaeil Najafi, Navid Rafiei

Applications and Applied Mathematics: An International Journal (AAM)

The management of hazardous industrial waste has emerged as a significant global challenge due to rapid technological advancements. Industrial hazardous waste management systems must be designed not only to be cost-effective but also to minimize environmental risks. This study proposes a mixed-integer programming model for the location-routing of industrial hazardous waste that incorporates both primary and secondary environmental risks, along with suitable response actions. Furthermore, a scenario-based robust optimization model is developed to address uncertainties in the quantities of industrial hazardous waste. A case study is conducted to demonstrate the applicability and comparative performance of the nominal and robust models. …

A Copula-Based Framework For Multivariate Count Time Series With Mixed Marginal Distributions, Dimuthu Fernando, Yuxin Wen, Wimarsha Jayanetti

Engineering Faculty Articles and Research

We developed a class of multivariate integer-valued time series models using copula theory. Each count time series is modeled as a Markov chain, with serial dependence characterized through copula-based transition probabilities for Poisson and negative binomial marginals. Cross-sectional dependence is modeled via a trivariate Gaussian or a “t-copula”, allowing for both positive and negative correlations and providing a flexible dependence structure. Model parameters are estimated using likelihood-based inference, where the trivariate Gaussian or t-copula integrals are evaluated through standard randomized Monte Carlo methods. Simulation results, along with an analysis of annual counts of major hurricanes (Category 3+) across the North …

A New Approach To Generate Combinatorial Patterns In Logical Analysis Of Data And Its Application To Predict College Retention, Salihah Ahmed E. Jaafari

Theses and Dissertations

Student retention and degree completion remain central challenges for higher-education institutions, with significant implications for student success, institutional effectiveness, and public accountability. While advances in predictive analytics have enabled earlier identification of students at risk of withdrawal, many commonly used machine learning approaches suffer from limited interpretability, constraining their practical usefulness for advising, intervention, and policy decision making. This dissertation addresses the problem of predicting student persistence by developing and evaluating optimization based, interpretable classification models within the Logical Analysis of Data (LAD) framework. Building on existing LAD formulations, this research introduces two novel pattern generation models, the Best Term …

Bayesball : A Comprehensive Framework For Predicting Ucl Injury, Brady M. Pinter, Will Best Ph.D.

SPARK Symposium Presentations

Ulnar Collateral Ligament (UCL) reconstruction, commonly referred to as Tommy John Surgery, has seen a significant rise among Major League Baseball (MLB) pitchers, prompting growing interest in identifying the mechanical and performance-based factors that contribute to injury risk. While previous studies have examined these relationships using traditional frequentist approaches separately, this study combines multiple different model techniques to present a broad framework for finding significant predictors of UCL Surgery. These models include Lasso and Ridge Regression,  Principal Component Regression (PCR) , Partial Least Squares Regression (PLS) , Random Forest, Multiple Linear Regression, and a Bayesian Statistical Model. Using these models, …

Information Theory Analysis Of The Solar Wind Magnetic Structures For Space Weather Prediction, Katherine Holland

Doctoral Dissertations and Master's Theses

Forecasting space weather at Earth is highly complicated, because of the limited measurements of the dynamic processes in the Sun that span multiple temporal, spatial, and energy-scales. The solar wind is a highly structured, multi-scale, evolving plasma and consists of coronal mass ejections (CMEs), stream interaction regions (SIRs), expanding flux tubes (Borovsky, 2008), and interplanetary magnetic field (IMF) discontinuities and fluctuations. The aim of this research is to improve our understanding of the evolution and dissipation of different scale-size solar wind magnetic structures as they move from the Sun-Earth Lagrange point 1 (L1) to Earth's bow shock and, ultimately, to …

Estimation Of Net Premium For Flight Delay Insurance Using The Aggregate Loss Model: A Case Study Of Indonesia Otas, Azka Nurul Husna, Yulial Hikmah, Ira Rosianal Hikmah

Jurnal Vokasi Indonesia

Air transportation, as one of the most chosen transportation modes, is frequently susceptible to delays. Flight Delay Insurance offers a vital solution to mitigate the financial losses associated with this risk. Premium pricing is a key factor influencing the decision to purchase this insurance, particularly on Online Travel Agent (OTA) platforms where product offerings are often highly comparable. The aggregate loss method is employed herein to ascertain the net premium (or pure premium) price. The loss severity component (X) is modeled using an empirical distribution, while the loss frequency component (N) is modeled using a Negative Binomial distribution with parameters …

A Probabilistic Modeling Analysis Of The Longitudinal Immune Response To Infection And Vaccination Across Demographic Groups And Pulmonary Symptoms, James O'Hanlon, Kaitlyn Sullivan, Lyndsey M. Muehling, Glenda Canderan, Jie Sun, Judith A. Woodfolk, Jeffrey M. Wilson, Rayanne A. Luke

Spora: A Journal of Biomathematics

Antibody and cytokine kinetics describe the dynamic response to immune events such as infection and vaccination. These dynamics are not fully understood, and mathematical characterization may help explain variability across demographic groups and pulmonary symptoms post-acute infection. We fit time-dependent probability models to severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) data to obtain distributions of longitudinal antibody response and cytokine values. To assess differences between groups, an overlap metric is applied to the modeled response curves. Our antibody models suggest significant differences between male and female populations and demonstrate deficient antibody responses of less-healthy groups such as smokers. Our cytokine …

Applications Of Machine Learning For Evaluating Downward-Coupled Stratosphere-Troposphere Interactions And Subseasonal Forecasts Of Opportunity, Elena M. Fernandez

Electronic Theses & Dissertations (2024 - present)

Wintertime stratospheric dynamics provide key information for understanding atmospheric teleconnections and improving subseasonal-to-seasonal (S2S) predictions on timescales of two weeks to two months. Periods of enhanced predictability, often referred to as forecasts of opportunity, arise from large-scale teleconnected variability, within which the stratosphere serves as an important precursor for tropospheric states, such as near-surface temperatures. While traditional diagnostics of downward coupled stratosphere-troposphere interactions typically rely on zonal-mean representations of wind and geopotential height, this dissertation presents an alternative vortex-centric framework through metrics that capture the daily geometric and dynamical evolution of the stratospheric polar vortex. The proposed stratospheric …

Learning Weibull Loss Severity Models From Truncated And Censored Data, Majed Alkhasha

Graduate Studies Theses and Dissertations 2026

In modern actuarial science and risk management, due to various loss control mechanisms, observed severity losses are typically left-truncated at the deductible, right-censored at the policy limit, and scaled by a pre-specified co-insurance factor. This results in two types of actuarial payment random variables: payment-per-payment (PPP) and payment-per-loss (PPL). To learn ground-up Weibull loss severity models from PPP and PPL sample data, we implement two estimation techniques: Maximum Likelihood Estimation (MLE) and the dynamic Method of Trimmed Moments (MTM). MLE is employed to obtain efficient estimates of the Weibull shape and scale parameters. However, MLE may assign unnecessarily large point …

(R2152) New Bivariate Type-2 Gumbel Distribution Based On The Farlie-Gumbel-Morgenstern Copula: Properties And Its Application In Survival Analysis, Muneeb Javed, Said Farooq Shah, Muhammad Osama, Muhammad Atif, Muhammad Farooq

Applications and Applied Mathematics: An International Journal (AAM)

We introduce a new bivariate probability distribution, termed the Bivariate FGM Type-2 Gumbel Distribution, constructed by combining the Farlie–Gumbel–Morgenstern (FGM) copula with the Type-2 Gumbel marginal distributions. This proposed distribution provides a flexible framework for modeling bivariate data and offers a viable alternative to several existing bivariate distributions, especially in scenarios where capturing dependence between variables is crucial. The theoretical properties of the distribution are thoroughly explored. We derive the marginal and conditional distributions, conditional expectations, moment generating function, and product moments. Procedures for random number generation from the distribution are discussed. Reliability-based characteristics, such as the survival function and …

Human Capital, Immigration, And Growth: A State-Level Dynamic Panel Study, William R. Cooper

Graduate Theses and Dissertations (2019 - present)

This study examines whether who immigrates, rather than how many, matters for state economic growth in the United States. It integrates a policy-relevant proxy for skill (H-1B approvals) into an augmented Solow framework that separates immigration's quantity channel from its human capital channel and estimates dynamic effects in a balanced quarterly panel of 50 states (2010 to 2023 ). The empirical strategy estimates a two-step difference GMM Arellano-Bond model that reinforces identification using a double/debiased machine learning (DML) variant that orthogonalizes high-dimensional nuisance components via cross-fitting. This design targets the distinct roles of immigrant headcount versus skill in per capita …

Exploring The Impact Of Statistics Course Modality On Student Learning: A Mixed Methods Approach, Becky Kelleman

Electronic Theses and Dissertations

The importance of statistical literacy has become increasingly evident, as individuals grapple with interpreting statistics to inform critical decisions. Despite the recognized significance of statistical literacy, challenges persist in both educators’ and students’ efforts to navigate the complexities of statistics education. The purpose of this study is to explore the impact of different course modalities on undergraduate students’ academic performance in introductory statistics courses. Using Social Cognitive Theory (SCT) as a theoretical framework, this research aims to shed light on the complex dynamics influencing statistical literacy attainment. By addressing gaps and inconsistencies in the current literature, this study seeks to …

Performance Of The Two Sample Likelihood Ratio Test Under A Nested Dirichlet: A Simulation Study, Edwina Agyeman

Electronic Theses and Dissertations

Compositional data analysis (CoDA) addresses multivariate data constrained to a constant sum, such as proportions or percentages. Originating from early warnings regarding misinterpretation by Pearson (1897), the field was formalized by John Aitchison in 1986, whose foundational work remains highly influential. Over time, new modeling techniques and visualization tools have advanced the field, as noted by Greenacre et al. More recently, Turner et al. proposed an approach based on the Nested Dirichlet Distribution (NDD), which accommodates more flexible dependence structures than the standard Dirichlet model. This thesis builds on the methodology of Turner et al. Chapter 1 introduces the nature …

How’S It Growing? Tools For Observing Snow And Sea Ice In A Changing Arctic Ocean, Ian Alexander Raphael

Dartmouth College Ph.D Dissertations

September Arctic sea ice extent has diminished by roughly 50% in the 45 years since satellite observations began. The Arctic Ocean may experience ice-free summers within the next decade, with implications for habitat, resource extraction, geopolitics, and local and global climate change. To predict how Arctic sea ice will change in the future, we need to understand its behavior in the present. In situ sea ice mass balance measurements (snow accumulation, ice growth, snow and ice surface melt, and bottom melt) are essential for studying the processes driving rapid changes in the ice pack, and for validating remote sensing measurements …

A Study On Fuzzy Time-Series And Its Applications To Stock Price Forecasting, Takeshi Stormer

University Honors Theses

Fuzzy mathematics looks to incorporate the vagueness that exists within the real world, specifically regarding imprecise classes, or non-numerical information expressed as "linguistic" variables. Since most traditional mathematical theories do not have the ability to be applied with the exactness that is otherwise seen in mathematics. As such, there had been many applications of fuzzy mathematics throughout many different fields of mathematics, including that of forecasting. By exploring the fundamentals of fuzzy mathematics, including fuzzy sets, operations of fuzzy sets, the surface level introduction to fuzzy logic, fuzzy relations, operations of fuzzy relations, and fuzzy time-series, this work looks to …

Babies, Babes, And Bayes: Modeling Mother-Infant Feedings With Bayesian Multilevel Hidden Markov Models, Zachary G. Felix

Master's Theses

Understanding the interaction between mother and baby during feeding is critical for the long-term development health of the baby. Overfeeding can lead to later obesity, while underfeeding can lead to malnutrition. In a recent study, the behaviors exhibited by mother-infant dyads across multiple ages of infants have been observed and coded according to the Baby Behaviors when Satiated (BABES) coding scheme. However, creating models using the data obtained from this coding is no simple task since the data coding is continuous, multivariate, and longitudinal in nature. The specific model utilized for these data is a hidden Markov model, since there …

Clusters, Trends, And Choices: Feature Selection In Interactive Statistical Graphics, Dylan Le

Master's Theses

Exploratory data analysis (EDA) is a method for uncovering the structure and key characteristics of data, often through the use of statistical graphics. These visual tools can reveal patterns and trends, and their effectiveness can be enhanced through interactivity. By enabling users to filter data, zoom, and toggle visual features, interactive plots can accelerate and enrich the EDA process. This study extends a previous graphical study by incorporating an interactive framework. Using a statistical lineup protocol with two target patterns (a linear trend and a clustering trend) participants interacted with plots by toggling various aesthetic features, including cluster coloring, ellipses …

Statistical Investigations Of Strategies In The Game Ecosystem, Dylan Li

Master's Theses

This work provides a probability-based analysis of strategies in the board game Ecosystem. Ecosystem is a turn-based multiplayer tiling game, where players take turns picking a wildlife card from a limited pool of cards then placing that card on their personal 4x5 grid. The objective of the game is to place the wildlife cards to maximize your score, as each card’s scoring condition depends on the presence or absence of certain cards surrounding it. The goal of this project is to determine optimal strategies for tiling your grid using techniques such as simulation to find optimal grid arrangements and clustering …

A System And Method For Measuring Spatially Varying Surface Appearances With A Study Of Feathers, Jessica Baron-Lis

All Dissertations

Real-world materials, particularly biological structures such as feathers exhibit complex appearances that vary spatially across their surfaces. The field of computer graphics provides a means of understanding such surfaces through material modeling which uses both analytical models and data acquired from light-surface interactions. There are many efforts within the past decade in measuring materials for graphics, but common limitations in these works include not accounting for spatially varying properties and reliance on neural networks and synthetic datasets.

Feathers from modern birds present diverse appearances due to how light interacts with their unique hierarchical microstructures. Variations in those structures lead to …

Mortgage Default Classification Modeling For Variable Analysis, Brendan R. Goggins

Honors College Theses

The financial crisis of the early 2000’s is a prime example of the severe consequences that mortgage default and borrower insolvency can have on economies at large. Mortgage default specifically is a prime case with the popularization of mortgage backed securities and the commonality of this loan structure. Multiple hypotheses and models have been formed to understand the reasons, causes, and consequences of mortgage default. This paper uses both machine learning and statistical classification models to inform an understanding of the variables most significant and impactful to the default outcome of mortgages. Consideration is given to both loan-level microeconomic variables …

An Analytical Prior Selection Procedure For Empirical Bayesian Analysis Using Resampling Techniques: A Simulation-Based Approach Using The Pancreatic Adenocarcinoma Data From The Seer Database, Aditya Chakraborty, Mohan D. Pant

Epidemiology, Biostatistics, & Environmental Health Faculty Publications

Introduction: In the field of medical research, empirical Bayesian analysis has emerged as an increasingly applicable approach. This statistical framework offers greater flexibility, enabling researchers to incorporate prior information and rigorously estimate parameters of interest. However, the selection of suitable prior distributions can be a challenging endeavor, with profound implications for the resulting inferences. To address this challenge, this study proposes a new analytical procedure that leverages resampling techniques to guide the choice of priors in Bayesian analysis. Subject and Methods: The study group consisted of patients who had been diagnosed and had died of pancreatic adenocarcinoma (cause-specific death) who …

Meditation In Qualitative Research For Bracketing And Beyond, Katalin Grajzel

Research Methods and Statistics: Graduate Student Scholarship

In this study, I recounted my experience using mantra meditation during a phenomenological study for the purposes of bracketing. The efficacy and purpose of bracketing have been debated from Husserl (1931), whose aimed was to achieve objectivity, to Heidegger (1962) who advocated for immersion of the researcher, through the French school (Merleau-Ponty, 1964) of middle ground, by whom bracketing was seen as the process to unearth and suspend biases for the better understanding of participants’ experiences (Arsel, 2017; Creswell & Creswell, 2017; Creswell & Poth, 2016; Fischer & Guzel, 2023). In this study, however, I propose another approach to bracketing …

The Economic And Environmental Impact Of Shinkansen And High-Speed Rail Infrastructure: A Comparative Analysis Of Economic Growth And Carbon Emissions Reduction, Dillan R. Victory

SPARK Symposium Presentations

The development of Japan's high-speed rail system, the Shinkansen, has played a pivotal role in the country's post-war economic resurgence. Introduced in 1964 with the Tokaidō Shinkansen, this transformative infrastructure investment significantly reduced travel times, bolstered economic activity around station hubs, and facilitated regional development by enabling urban decentralization. This paper explores the long-term economic benefits of high-speed rail, including its impact on land value, business expansion, and carbon emissions. The case study of the Linear Chuo Shinkansen, Japan's latest maglev project, underscores both the economic promise and the political resistance to expansion, particularly in regions such as Shizuoka.

Using …

Analysis Of Sled Dog Biomechanics, Natalie Bender

Williams Honors College, Honors Research Projects

This paper is an analysis of data collected by Dr Rachel Olson and her team. The data was collected from the same set of sled dogs before and after training for the Iditarod race. The goal of this paper is to draw conclusions on whether the gait of sled dogs’ change with fitness level. The data was cleaned in R to find the average peak for forelimb joint angles per run for each dog. The data was analyzed with 3 different ANOVAs – one including both the shoulder and carpus, one for just the shoulder, and one for just the …

Theoretical Foundations And Applied Performance Of Periodicity-Aware Imputation: Variable Bandpass Block Bootstrap Methods For Incomplete Time Series, Asmaa Ahmad

Electronic Theses & Dissertations (2024 - present)

Time series data are prevalent across a wide range of disciplines, including health surveillance, public policy, and environmental monitoring. In the presence of underlying cyclical patterns, the integrity of time series analysis depends critically on the ability to detect, model, and impute structured missing data without compromising the temporal structure. This dissertation introduces and validates a novel imputation framework that integrates the Variable Bandpass Periodic Block Bootstrap (VBPBB) into multiple imputation procedures, improving the accuracy, robustness, and interpretability of time series models under high rates of missingness and noise. The overarching goal of this dissertation was to develop and evaluate …

Impact Of Urban Development On Uv Exposure: A Clustering And Machine Learning Assessment, Taufik Roni Sahroni Mr., Verdi Yasin, Lulut Alfaris, Reza Ariefka, Ruben Cornelius Siagian, Mohammad Alfin Karim, Nana Rahdiana, Ade Suhara

Journal of Environmental Science and Sustainable Development

The relocation of Indonesia's capital city is anticipated to promote inclusive economic growth while embracing cultural diversity. However, this transition may affect ultraviolet (UV) radiation exposure patterns. The study investigated variations in UV exposure in the IKN region, focusing on urban development factors such as land use and population density that affect public health, sun protection, and skin cancer prevention. The research hypothesized that UV radiation is significantly correlated with these factors. UV Index data from 2010-2023, a hierarchical clustering method, identifies complex data patterns without determining the number of clusters. XGBoost, a machine learning model, was used for handling …

(R2101) Analysis Of Map/Ph/1 Queueing Inventory System With Two Commodity, Working Vacation, (S, S) Replenishment Policy, Essential And Optional Repair, G. Ayyappan, N. Arulmozhi

Applications and Applied Mathematics: An International Journal (AAM)

We examine a queueing inventory model with single server which can offer two types of inventory items: main item (commodity I) and complementary item (commodity II). We assume both commodities have a finite capacity Si, i = 1, 2. Customers reach the system by following the Markovian arrival process (MAP). The service times are considered to be phase-type (PH) distribution. We have considered no customer in the system, even inventory level is positive; the server will start the working vacation, and any customer that arrives during working vacation, the server provides slow service. If an item is not available, the …

Striking A Balance: Market Shock & Responses In Automotive Components Manufacturing, Emma Lane Mcgahey

All Theses

This thesis examines the effects of extreme market shocks on supply chain dynamics within the automotive industry. Through an analysis of demand data from an automotive manufacturer to its component suppliers (January 2018 to May 2024), the study investigates the relationship between market shocks and supply chain responses, providing insights into how auto components inventory management handles downstream responses to market shocks. With supporting public data—from FRED, BLS, and the U.S. Census Bureau resources—we explore two primary relationships: the impact of market shocks on the Average Standard Deviation of Demand (SDO) and the effect of demand variability on expedited pricing …

Decoding Neural Networks: An Information-Theoretic Guide To Interpretability, Error Analysis And Efficiency, Mackenzie J. Meni

Theses and Dissertations

This dissertation addresses critical challenges in neural network design by leveraging entropy-based techniques to improve model efficiency, interpretability, and bias reduction. Focusing on the unique demands of computer vision applications, particularly object detection and classification for real-time systems, this work introduces a series of innovative methods centered on information theory. At the core of these methods is the Probabilistic Explanations of Entropic Knowledge (PEEK) framework, a tool developed to analyze and visualize entropy distributions across feature maps. PEEK offers insights into information flow within neural networks, making it possible to pinpoint layers that contribute meaningfully to decision-making or identify those …

Evaluating Trauma-Informed Design In A Mental Health Setting: A Community-Based Research Case Study, Marie Spence

Electronic Theses and Dissertations

This case study utilized a community-based research framework to explore how the Trauma-Informed Design framework can be implemented in a mental health setting. This study focused on the site of Empower Therapy Practice, a private mental health practice in the Denver Metro Area, to engage clients and staff to participate in advisory boards and inform the interior design of a new office space. To explore the application of Trauma-Informed Design, participants engaged in a variety of research activities, including an evaluative questionnaire, Photovoice, and focus group. Advisory board members identified various aspects of Trauma-Informed Design which meaningfully translate to therapeutic …