Statistics and Probability Commons^™

Forecasting Equity Betas Using Option-Implied Moments, Ivan Kolesnikov

CMC Senior Theses

Traditional beta estimates are constructed from historical stock‑and‑market returns and therefore adjust only as fast as realized data accrue. This thesis investigates whether the forward‑looking information embedded in equity‑option prices can enhance beta forecasts. Using near‑end‑of‑day quotes for 236 S&P 500 firms between 2007 and 2024, I extract risk‑neutral variance and skewness, construct five alternative beta estimators (historical, option‑implied, and three hybrids), and evaluate them against realized betas over six‑, twelve‑, and twenty‑four‑month windows. Rolling‑OLS beta remains the most accurate benchmark at short horizons, yet option‑implied moments add economically and statistically significant value when systematic exposure is expected to change …

Analyzing Political Sentiment On Micro-Blogging Data: A Lexicon And Machine Learning Approach To The 2024 U.S. Presidential Election, Ava Grey

CMC Senior Theses

This paper explores the trends in sentiment towards U.S. presidential candidates Kamala Harris and Donald Trump through micro-blogging social media text during the five months leading up to the election. Two datasets of varying sizes and origins were used to contextualize and validate analysis findings. The analyses include both a lexicon-based approach and a machine learning predictive method. Common sentiment analysis techniques like term frequency, term frequency inverse, various lexicons, and n-grams were utilized during the lexicon approach. During the modeling, a random forest was utilized in addition to the methods used during the lexicon approach. Results showed that overall …

The Matryoshka Doll Prior – Principled Multiplicity Correction In Bayesian Model Comparison, Andrew Womack, Daniel Taylor-Rodríguez, Claudio Fuentes

Mathematics and Statistics Faculty Publications and Presentations

This paper introduces a general and principled construction of model space priors with a focus on regression problems. The proposed formulation regards each model as a “local” null hypothesis whose alternatives are the set of models that nest it. Assuming constant ratio of prior probabilities for any “local” null and its alternatives provides a natural isomorphism of model spaces (like a matryoshka doll), constituting an intuitive way to correct for multiplicity in Bayesian model selection and averaging problems. This isomorphism yields the Poisson distribution as the unique limiting distribution over model dimension under mild assumptions. We compare this model space …

Adverse Childhood Experiences, Depression And Subjective Cognitive Decline By Gender: A Moderated Mediation Analysis, Monique J. Brown, Darlingtina K. Esiaka, Jaya Viswanathan

Behavioral Science Faculty Publications

Studies assessing depression as a mediating factor between adverse childhood experiences (ACEs) and subjective cognitive decline (SCD) are lacking. Therefore, the aims of this study were to: (1) determine the mediating role of depression in the association between ACEs and SCD; and (2) assess the moderating role of gender. Data were obtained from the 2023 Behavioral Risk Factor Surveillance Study (BRFSS) survey (N = 38,600). Crude and adjusted path analyses were used to determine the mediating role of depression between ACEs and SCD. Adjusted analyses controlled for sociodemographic confounders. ACEs were positively associated with depression (B = 0.129, p …

Model-Free Organization Of Patient Reported Outcomes Data: Geometrical Rep-Resentation Of The Modified Compartmen-Talization Method, Manasi Sheth, N. Rao Chaganty

Mathematics & Statistics Faculty Publications

There is a recent advancement in the field of mathematics and statistics to understand the geometry or connectedness of the data due to the massive amounts of data being generated. The data provided for analyses are usually very large and need to be organized and minimized in order to make it more useful and meaningful. In biostatistics or medical field, it is important for patients to have access to high-quality, safe and effective and/ or efficacious medical products. It is quite necessary to ascertain that the patients and their care-partners stay at the center of the regulatory decision-making process. In …

Understanding The Impact Of The Medicaid Expansion On Hospital Length Of Stay And Emergency Department Use In Kentucky, Cameron Bushling

Theses and Dissertations--Epidemiology and Biostatistics

Three related analyses were performed to try to understand the immediate effects of Medicaid expansion on hospital systems in Kentucky. Medicaid expansion led to a large, sudden increase in the number of individuals eligible for various health care needs. This sudden increase in demand for health services lead to initial hypotheses regarding hospitals’ ability to handle this demand. The first analysis examined hospital average length of stay (LOS) using a linear mixed-effects model. Length of stay was modeled longitudinally between 2013 and 2015 to determine if significant changes in the slope of LOS could be detected after expansion (2014). Separate …

Changes In Cancer Diagnosis And Survival In The United States During The Covid-19 Pandemic, Justin T. Burus

Theses and Dissertations--Epidemiology and Biostatistics

The COVID-19 Pandemic led to global societal disruptions as political leaders and public health authorities attempted to control the spread of the newly discovered SARS- CoV-2 virus. While these measures were designed to lessen morbidity and mortality from a novel pathogen, their impact was also felt in many other, often unintended ways. The purpose of this dissertation is to use cancer surveillance research methods to examine the association between COVID-19 Pandemic-related disruptions and changes in the normal diagnosis and care of cancer in the United States.

The first two studies of this dissertation analyzed reductions in cancer diagnoses in the …

Hybrid Mixtures Of Factor Analyzers For High Dimensional Data, Kazeem Abiodun Kareem

Dissertations, Master's Theses and Master's Reports

Factor analysis is a powerful tool for modeling latent structures in high-dimensional data, traditional approaches assume a single global structure, limiting their ability to capture heterogeneity. The Mixture of Factor Analyzers (MFA) extends classical factor analysis by modeling data as a mixture of Gaussian-distributed local subspaces, effectively uncovering cluster-specific latent structures. However, MFA relies on Gaussian mixtures, making it sensitive to outliers and ill-suited for heavy-tailed data. The Mixture of $t$-Factor Analyzers (M$t$FA) addresses these limitations by incorporating multivariate $t$-distributions, improving robustness. Despite their advantages, both MFA and M$t$FA face significant computational challenges in high-dimensional settings, particularly due to costly …

Theory And Applications Surrounding Markov Chains, Joseph J. Quisito Jr., Gallean Brown, Elijah Yoder

Capstone Showcase

This capstone project explores the Markov Chain – a mathematical model used to describe systems that transition between states based on probabilities. It begins by introducing the fundamental concepts, including transition matrices, state classifications, and stationary distributions. The paper then applies Markov Chain theory to real-world scenarios, such as simulating Snakes and Ladders games, predicting soccer match outcomes for Manchester United, and generating texts from movie lines. Finally, it discusses key findings, challenges, and potential areas for future research in the field.

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 …

Time Series Modeling Of Akron Air Quality Index (Aqi) Data, Mason Yurich

Williams Honors College, Honors Research Projects

With the increase in population and industrialization around the world, climate has become a major concern for many researchers. One measure that has drawn much interest is air quality. There are available resources that track the Air Quality Index (AQI) in most large cities, but there is a general lack of information regarding Air Quality forecasts, even for one day in the future. This project aims to find a useful statistical model for representing and predicting the AQI measure in Akron, Ohio over time. By using historical air quality data from the United States Environmental Protection Agency and AQI.in, an …

Risk Factors For Autism Spectrum Disorder: A Statistical And Machine Learning Perspective, Supti Biswas

Open Access Master's Theses

his study explores factors associated with autism spectrum disorder (ASD) through analysis of a rich dataset comprising maternal and child characteristics. The data were carefully cleaned and preprocessed to address missing values and ensure analytical consistency. Statistical analyses and advanced visualization techniques were used to uncover patterns linking ASD status with variables such as maternal age, prenatal smoking, and education level. To further assess predictive capacity and feature importance, multiple supervised machine learning algorithms - logistic regression, decision trees, random forests, and support vector machines (SVM) - were applied. ASD appears to be influenced by a complex interplay of demographic …

Comparison Of Machine Learning Models For Colon Cancer Survival: Predictive Modeling Approach, Reuben Adatorwovor, Motolani E. Ogunsanya, Bin Huang, Richard Charnigo, Olufunmilola Abraham

Biostatistics Faculty Publications

Background: Colon cancer is a leading cause of cancer-related deaths worldwide, with survival influenced by risk factors, treatment type, and patient characteristics. Traditional statistical models, such as Kaplan-Meier curves, have been widely used to estimate survival probabilities. However, these models often have difficulty handling complex interactions, covariates, and nonlinear relationships between risk factors. Recently, machine learning (ML) techniques have emerged as promising tools for improving survival prediction by handling large covariates and capturing complex patterns.

Objective: This study compares several ML models to accurately estimate colon cancer survival by leveraging data from the Kentucky Cancer Registry. By identifying key risk …

Disentangling The Inverse Relationship Between Cancer And Alzheimer’S Or Parkinson’S Disease: A Systematic Review On Mendelian Randomization Studies, Khine Zin Aung, Su Su Zin, Xian Wu, Zin W. Myint, Shama D. Karanth, Steven Estus, Christopher M. Norris, Peter T. Nelson, David W. Fardo, Erin L. Abner, Yuriko Katsumata

Biostatistics Faculty Publications

Introduction

Although studies have reported an inverse relationship between cancer and neurodegenerative diseases such as Alzheimer's disease (AD) and Parkinson's disease (PD), findings remain inconsistent. Observational studies are limited by survival bias and reverse causation. To better understand the relationship, we conducted a systematic review of Mendelian randomization (MR) studies examining both directions—assessing cancer as a risk factor for AD or PD, as well as AD or PD as exposures influencing cancer risk.

Methods

We systematically reviewed MR studies investigating the causal relation between cancer and either AD or PD. Cancer could be specified as either an exposure or an …

Incident Atherosclerotic Cardiovascular Disease Among Veterans By Gender Identity: A Cohort Study, Carl G. Streed Jr., Meredith S. Duncan, Kory R. Heier, T. Elizabeth Workman, Lauren B. Beach, Guneet K. Jasuja, Hill L. Wolfe, Landon D. Hughes, John R. O’Leary, Melissa Skanderson, Joseph L. Goulet

Biostatistics Faculty Publications

Background: Transgender and gender diverse (trans) populations are at elevated risk for atherosclerotic cardiovascular disease (ASCVD).

Objective: Measure the association of gender identity and gender-affirming hormone therapy (GAHT) with ASCVD outcomes.

Design: Cohort study.

Participants: Over 1 million veterans receiving care in the Veterans Health Administration.

Main Measures: Gender identity was identified via a validated natural language processing (NLP) algorithm. Incident ASCVD (acute myocardial infarction, ischemic stroke, or revascularization after the baseline date) was identified via International Classification of Diseases diagnosis codes among veterans without prevalent ASCVD. We calculated sample statistics stratified by gender identity and used Cox proportional hazard …

Implementation Of Project-Based Instruction In Statistics Higher Education Courses, Jennifer A. Daddysman

Theses and Dissertations--Education Sciences

Project-based instruction is an instructional methodology based in constructivism that aligns with recommendations from the American Statistical Association for teaching statistics, including incorporating real-world data and examples, collaboration, and scaffolding (GAISE College Report ASA Revision Committee, 2016; GAISE Steering Committee, 2024; Krajcik & Blumenfeld, 2005; Tishkovskaya & Lancaster, 2012). This study examined current use of project-based instruction in United States higher education courses in statistics and the supports for and challenges to implementing this type of instruction.

This study used qualitative research methodology in the integrative pedagogy and diffusion of innovation frameworks. Voluntary response surveys were distributed via two sections …

Effects Of Chain Length, Saturation, And Bases On Saponification, Sarah Fenik

Williams Honors College, Honors Research Projects

This project will analyze the effects of chain length and saturation of fatty acids on saponification processes, as well as the effects of the base used in the reaction. Stearic acid, lauric acid, and oleic acid will be used for the fatty acid comparisons, and sodium hydroxide and potassium hydroxide will be used for the base comparisons. Stearic acid is considered a long chain fatty acid, while lauric acid is considered a short chain fatty acid. Oleic acid is a monounsaturated fatty acid. Five soap products are be made: sodium stearate, sodium laurate, sodium oleate, potassium stearate, and potassium oleate. …

An Insight Into Mediation Analysis, Nicholas Mccracken

Williams Honors College, Honors Research Projects

Mediation is an ideology often present in the social sciences. A mediator is meant to serve as the middle point between one party and another, taking the communications from one party and ensuring that the other party can comprehend that of the original party. Though this is very popular in social sciences, we can apply a statistical concept to it as well. We can explain the relationship between two parties and a mediator through a series of statistical equations, known as Baron and Kenny’s Equations. With these equations, we can determine how one variable is meant to impact another variable …

Extremal Trees For Random Walks, Ben Bridenbaugh

Mathematics, Statistics, and Computer Science Honors Projects

A random walk is a sequence of adjacent vertices that are chosen uniformly at random from the neighbors of the previous vertex. An access time is the average length of time that a random walk takes to reach a target probability distribution from a starting probability distribution, given an optimal stopping rule. This paper deals with characterizing the trees of diameter d and on n vertices that extremize three different types of access times.

Methods In Statistics, Machine Learning, And Deep Learning For Combining Multi-Omics Dataset, Md Mutasim Billah

Dissertations, Master's Theses and Master's Reports

Transcriptome-wide association studies (TWAS) have emerged as a powerful strategy to bridge genome-wide association studies (GWAS) with gene regulatory mechanisms by integrating genotypic data with gene expression data. While early TWAS methods typically rely on linear models and single-tissue expression references, recent advances underscore the need for flexible, multi-tissue approaches that can capture heterogeneous regulatory architectures and tissue-specific expression patterns. This dissertation introduces a three‑part research project that advances multi‑tissue transcriptome‑wide association studies (TWAS) along complementary axes of methodology, statistical power, and modelling flexibility.

In chapter One, TWAS‑CTL introduces a two‑stage cross‑tissue learner that trains any user‑chosen single‑tissue imputers (STLs) …