Statistics and Probability Commons^™

Guidelines For Standard Basic Notations In Applied Statistics, Abhaya Indrayan, Shivani Saini Ms

COBRA Preprint Series

Whereas some statistical notations are standard and uniformly used by different workers, many are not. Varying notations lead to confusion among the readers, particularly those engaged with applied statistics material, such as medical professionals. This communication proposes that all basic notations be standardized so that the same notations are consistently used by different authors, in different books, journals, and articles for the benefit of those who are not rigorously trained statisticians. Guidelines for such standard notations are also provided. The lead must be taken by statisticians.

Predicting Criminal Behavior In Major Us Cities, Madison A. Price

SPARK Symposium Presentations

In recent years, especially post pandemic, there has been a decrease in crime in the United States. Unfortunately, the country’s violent crime rates are still significantly higher compared to similar high-income countries, so what predicts crime in major American cities? There is tons of research to support the idea that demographics can offer some insight into predicting crime. There are countless online resources that seek to identify major crime centrals in the United States (Petrino, 2025). In the late 1990s, researchers noticed that crime rates in cities had a downward slope due to an important contributor: demographic change (Fox & …

Investigating The Role Of Humic Acid In The Adsorption Mechanics Of Acetaminophen On Potassium Persulfate-Aged Polyethylene Terephthalate (Pet), Andrew Littleton, Maria Danielle Garrett, Phd

SPARK Symposium Presentations

Pharmaceutical contaminants such as acetaminophen (APAP) are showing a rising presence in aquatic environments, where their interactions with microplastics (MPs) can potentially modulate natural degradation mechanisms. Concurrent presence of the two substances has been shown to potentiate increase their individual harmful effects. This study investigates whether oxidative aging and humic-acid surface modification of PET microplastics influence APAP adsorption.

In this study, UV-aging was reproduced using an iron (II)-activated potassium persulfate (Fe(II)-KPS) oxidation system. Aqueous dissolved organic matter (DOM) is simulated using multi-hour exposure to humic acid. The MPs are then removed from the solution to examine adsorption mechanisms. While most …

Essays On Accelerated Failure Time Models For Recurrent Event Data, Emmanuel Masavo Djegou

Doctoral Dissertations

Recurrent event data arise in many fields such as medicine, reliability, insurance, and economics, where the same event may occur repeatedly for a subject. Accelerated Failure Time (AFT) models provide an intuitive framework for relating covariates to event times and offer a useful alternative to proportional hazards models, allowing direct prediction of event timing under right censoring. However, existing AFT extensions for recurrent events, such as accelerated gap time (AGT) models, often fail to account for interventions between events and may not capture complex temporal patterns.

In this work, we first propose a class of semiparametric AGT models incorporating an …

Algorithmic Trading In Idiosyncratic-Payoff Markets: A Multi-Agent System For On-Chain Prediction Contracts, Saif Aldeen A.K. Agha

CMC Senior Theses

This thesis documents the design, deployment, and forward-test evaluation of an evolutionary multi-agent algorithmic trading system on Polymarket, the largest decentralized prediction market. The system pairs a locally-hosted 72-billion-parameter language model with a gradient-boosted statistical filter and an evolutionary selection mechanism that maintains a population of approximately 500 autonomous trading agents. Each agent generates a probability estimate for an event, compares it to the prevailing market price, and trades the resulting disagreement.

The central empirical exercise estimates a panel regression of trade-level profit on the absolute disagreement between the agent's probability estimate and the market price, controlling for agent identity, …

Investigating The Connection Between Als Through The Mutation R522s In The Rna Binding Protein, Dennia Estrella-Vargas, Lydia Uptain

Mathematics

Amyotrophic lateral sclerosis (ALS) is a fatal disease that causes the deterioration of motor neurons , death is usually due to respiratory paralysis. The variant R522S was chosen because it is near a hot spot of pathogenic variants. It is an arginine-to-serine swap, this swap is present in pathogenic variants near the 522 position, such as R514S, R521S, R524S. Recent evidence suggests that arginine-deficiency can influence disease progression.

Data-Driven Partitioning In Distributed Optimization For Networked Systems, Prosper Azameti

Theses and Dissertations

The convergence behavior of distributed optimal power flow (OPF) depends strongly on how the power network is partitioned into regions. Classical graph-based methods such as METIS are widely used, but they rely mainly on static topological criteria and do not explicitly incorporate operating-point-dependent information that may affect distributed optimization performance. This thesis develops a data-driven partitioning framework for distributed OPF using graph neural networks (GNNs). Each OPF scenario is represented as a graph in which buses are nodes and transmission lines are edges. Node and edge features capture both structural and operational characteristics of the network. Partition prediction is formulated …

Using Camera-Based Unmarked Spatial Capture-Recapture Modeling To Estimate Reintroduced Elk (Cervus Canadensis) Population Parameters And Distribution In Southeastern Kentucky, Claire Marie Muia

Theses and Dissertations--Forestry and Natural Resources

Estimation of population parameters is important for wildlife management decisions. Elk reintroduced to southeastern Kentucky experienced early irruptive population growth and are currently monitored using a statewide harvest-based statistical population reconstruction model (SPR) across the Kentucky Elk Restoration Zone (KERZ). Because the SPR model is spatially coarse and difficult to scale to the smaller management units comprising the KERZ, we conducted a spatially explicit capture-recapture study using a clustered camera-trapping array deployed for 10 weeks from June–August 2024 to estimate elk population parameters within Management Unit 4. Due to a lack of resights of GPS-marked elk, population parameters were estimated …

Teaching Effectiveness On Secondary Mathematics: Evidence From Pisa—Shanghai-China, Ting Shen

Psychological Science Faculty Research & Creative Works

Educational researchers and policymakers around the world have a strong interest in understanding the underlying reasons for the remarkable academic achievement of Chinese students in the Programme for International Student Assessment (PISA). Although teachers have a significant impact on student achievement, empirical evidence on teaching effectiveness in the Chinese education system has been scarce. This study uses the PISA 2012 Shanghai-China data and employs both multilevel models and quantile regression models to investigate effective teaching factors and their differential effects for students at different mathematics achievement levels. The results reveal the importance of cognitive activation and disciplinary climate as consistent, …

Multivariate Quantile Autoregression-Mixed Data Sampling (Mvqar-Midas) Modeling Of Cost Of Living And Supply Chain Dynamics In Canada., Patrick Gbolonyo

Theses and Dissertations (Comprehensive)

In recent years, the rising cost of living as a result of persistent inflationary pressures, disruptions in the global supply chains, and changes in the macroeconomic landscape has become a critical topic of discussion. To address this, we move beyond a mean-based framework and employ a quantile regression approach. This allows the persistence of each series and the transmis- sion of shocks between the Consumer Price Index (CPI) (the total CPI which is a percentage change over the past 12 months), the Interest Rate (IR)(the target for the overnight rate), the New Housing Price Index (NHPI), and high-frequency supply chain …

Interpretable Sample Uncertainty Measures For Ranked-Choice Election Polls, Jason Liang

CMC Senior Theses

Polling results from traditional single-choice plurality elections are readily interpretable. Simple frequentist population parameters are estimated, including each candidate’s total support and the size of the front runner's lead. If the point estimate for the size of the front runner's lead exceeds the margin of error of the lead, we can conclude that the poll shows a statistically significant front runner. However, the interpretability of these population statistics disappears when applied to ranked-choice voting elections. Because ballots rank multiple candidates and candidates are eliminated in rounds, simple population-wide parameters are not well-defined. In RCV elections, a candidate’s ability to win …

Rank Rebalancing In Commodity And Foreign Exchange Markets, Prateek D. Vyas

CMC Senior Theses

This thesis empirically tests the rank-rebalancing mechanism of Stochastic Portfolio Theory (SPT) across commodity futures, foreign exchange futures, and equity ETFs. The Reverse Price-Weighted strategy (RPW) assigns, to each asset, the market weight of the asset at the opposite price rank, and generates an annualized excess return of 2.90% over the price-weighted (MKT) commodity benchmark, during the period of November 1977 to October 2025 (HAC t = 2.058, p = 0.040). The differential Sharpe ratio (dSharpe) of 0.245 is confirmed by a stationary block bootstrap, with a 𝑝-value of 0.015, and factor regressions controlling for carry, momentum, and value yield …

Assessing The Diversity And Composition Of Crayfish Assemblages In The Ogeechee River Basin, Reginald Turner

College of Graduate Studies: Theses & Dissertations

Crayfish assemblage composition in the southeastern United States is understudied relative to other aquatic taxa, such as aquatic insects and fishes, and the Coastal Plain watersheds of that region are particularly underrepresented in the contemporary literature on this topic. For example, although 38% of the crayfish species in Georgia are considered “species of greatest conservation need,” most of the distributional data used to make these designations are outdated, with some dating back over 50 years. This thesis sought to update our understanding of the contemporary distributions of crayfish species within the Ogeechee River Basin (ORB), a watershed in southeastern Georgia …

Volatility Modeling With An Application To Risk Parity Portfolios, Kenneth Hou

CMC Senior Theses

This thesis studies volatility modeling in the context of risk parity portfolio construction. I compare three risk parity portfolios that differ only in their underlying volatility model: a historical covariance baseline, a Bayesian stochastic volatility model, and a GRU–GARCH hybrid neural network. Using daily returns on Kenneth French’s five industry portfolios from January 2016 through December 2025, I construct monthly rebalanced portfolios under each model, with the SV and GRU forecasts embedded in hybrid covariance matrices that combine forecasted volatilities with rolling historical correlations. The results document a divergence between forecast accuracy and portfolio performance: the SV model is the …

Inferential Statistics For Industrial Organizational Psychologists: A Practical Guide For Testing Hypotheses Using R, Caitlin Lapine

Open Touro Created

2026

This text aims to provide a practical guide for students in industrial organizational psychology or related fields to complete inferential statistics using R open-source programming language. It provides information about when to use particular statistical analyses and how to perform those with statistical software.

Equilibrium Stability Under Nuclear Confrontation, Martin Bohner, A. A. Martynyuk

Mathematics and Statistics Faculty Research & Creative Works

This article proposes and analyzes mathematical models of confrontation between two and n countries, including countries with nuclear weapons. The proposed models are based on a generalization of Richardson's well-known mathematical model of the arms race. Namely, the factor of hostility is filled with expanded content, including public opinion and the armed forces of the opposing countries. Qualitative analysis of confrontation models is carried out by the method of Lyapunov functions and by applying nonlinear integral inequalities. As a result of the analysis, the conditions for the stability of the equilibrium state of the opposing countries are established, and the …

Threshold Asymmetric Conditional Autoregressive Range (Tacarr) Model, Isuru Ratnayake, V. A. Samaranayake

Mathematics and Statistics Faculty Research & Creative Works

This paper introduces a Threshold Asymmetric Conditional Autoregressive Range (TACARR) model for analyzing the daily price ranges of financial assets. The proposed formulation assumes that the conditional expected range switches between two regimes, representing upward and downward market states, with the disturbance distribution also allowed to vary across regimes. A self-adjusting threshold component, determined by past values of the series, is used to identify the prevailing market regime. In this way, the model is able to capture asymmetric and heteroscedastic volatility behavior in financial markets. The TACARR model is designed to address several limitations of existing price range models, including …

A Variance Decomposition Approach To Inconclusives In Forensic Black Box Studies, Amanda Luby, Joseph B. Kadane

Mathematics and Statistics Faculty Work

In the USA, ‘black box’ studies are increasingly being used to estimate the error rate of forensic disciplines. A sample of forensic examiner participants is asked to evaluate a set of items whose source is known to the researchers but not to the participants. Participants are asked to make a source determination (typically an identification, exclusion, or some kind of inconclusive). We study inconclusives in two black box studies, one on fingerprints and one on bullets. Rather than treating all inconclusive responses as functionally correct (as is the practice in reported error rates in the two studies we address), irrelevant …

Barriers To Immunity: Understanding Covid-19 Vaccine Uptake In Africa, Emilia Blechschmidt

Honors Theses

This thesis examines the factors influencing COVID-19 vaccine uptake across African countries, with a focus on structural, informational, and behavioral barriers to immunization. Drawing on cross-country data, the study analyzes how access to transportation, reliable information, and healthcare resources shape vaccination rates, alongside the effect of demographics and institutional factors in shaping individual perceptions of risk and vaccine safety.

The findings emphasize that the broader strength and preparedness of national health systems strongly influence vaccine uptake. Countries that demonstrated higher coverage of routine childhood immunizations, such as polio and hepatitis B, also tended to perform better in COVID-19 uptake efficiency …

Feasibility, Acceptability, And Preliminary Efficacy Of A Pilot Study To Integrate Buprenorphine Into A Harm-Reduction Drop-In-Center In Kampala, Uganda, Julia Dickson-Gomez, Sergey Tarima, Wamala Twaibu, Dan Katende, Latifah Kyeswa, Laura Glasman, Arthur Kiconco, Sarah Krechel, Bryan Johnston, Moses Ogwal, Brian Byamah Mutamba, Peter Mudiope, Stella Alamo, Rhoda Wanyenze, Geofrey Musinguzi

Biostatistics Faculty Publications

Illicit drug use has been increasing rapidly in Sub-Saharan Africa in the past decade. However, until recently HIV prevention has largely ignored people who inject drugs and medications to treat opioid use disorder (MOUD) were largely absent. This paper reports results of a pilot intervention that integrated buprenorphine into a harm-reduction drop-in-center for people with opioid use disorder (OUD) in Kampala, Uganda. We collected implementation outcomes and changes in self-reported drug use after buprenorphine initiation. We conducted qualitative interviews with a subset of 14 participants who had initiated buprenorphine. Sixty-two participants were screened for OUD, of whom 57 were eligible …