Statistical Models Commons^™

Advancing Real-World Implementation Of The Well Optimized Linear Finder (Wolf) High-Speed Atmospheric Turbulence Compensation Method, Timothy Evan Coon

Theses and Dissertations

This dissertation advances the real-world implementation of the Well Optimized Linear Finder (WOLF) method for high-speed Atmospheric Turbulence Compensation (ATC). Atmospheric turbulence introduces phase aberrations into optical wavefronts and degrades image quality in terrestrial imaging systems. Traditional phase diversity methods are computationally intensive and poorly suited to real-time operation. The WOLF method addresses these limitations through a novel, point-wise formulation of the optical transfer function (OTF) as a structured autocorrelation of the generalized pupil function (GPF). This formulation enables the estimation of phase aberrations at individual spatial coordinates with distributed computational complexity.

The research begins by developing a MATLAB-based simulation …

Experimental Design And Analysis For Decision Making: Methodology And Applications, Yezhuo Li

All Dissertations

This dissertation develops and applies advanced statistical and optimization frameworks to enhance decision-making under uncertainty, particularly in engineering and manufacturing contexts. First, we introduce an approach for the optimal design of controlled experiments that accounts for observational covariates, enabling more precise and personalized decisions. Second, we explore the application of constrained Bayesian optimization, using Gaussian process surrogate models, to optimize composite cure processes, significantly reducing computational effort while maintaining high predictive accuracy. Building on this foundation, we extend Bayesian optimization to bivariate Gaussian process models that capture correlations between objective and constraint functions, offering new insights into multidimensional decision landscapes. …

Unified Hybrid Censoring Samples From Power Pratibha Distribution And Its Applications, Mahmoud Mansour, Hebatalla H. Mohammad Dr, Khalaf S. Sultan Prof.

Basic Science Engineering

This paper suggests an extensive inferential method for the Power Pratibha Distribution (PPD) under Unified Hybrid Censoring Schemes (UHCSs), since there is a growing interest in flexible models in both reliability and service operations. This work studies the PPD model using standard Maximum Likelihood Estimation methods and modern Bayesian approaches too. Using a complex architecture, UHCS simulates tests more closely to what is done in practice than by using more basic censoring schemes. Using analysis, the probability and statistical ranges are carefully calculated for the parameters. Tests demonstrate that Bayesian estimation gives better results than many other methods for estimation, …

Variable Importance, Knockoff Filters, And Improving False Discovery And False Negative Rates, Nicholas Ehlman

Dissertations

Tree ensemble methods such as Random Forests and Boosted Trees have introduced a range of variable importance statistics, offering powerful tools for feature selection. The advent of knockoff filters marked a significant advancement by combining the use of these variable importance statistics with the ability to control the False Discovery Rate (FDR). However, achieving a low FDR frequently comes at the cost of a high False Negative Rate (FNR), limiting the power of such approaches. In this work, we propose a novel method for leveraging knockoff variables to keep both FDR and FNR low. While this method does not have …

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 …

Forecasting Influenza Rates Using Machine Learning: A Study Of Chatgpt's Predictive Accuracy, Sara Saleh

University Honors Theses

This study evaluates ChatGPT's ability to forecast influenza rates, such as the number of flu cases, hospitalizations, and death during peak season periods using CDC data, and comparing forecasts against actual results to calculate statistical accuracy and consistency. Influenza forecasting is essential for public health planning, but traditional methods may not always provide timely or accurate predictions. In this research study, ChatGPT was utilized to predict the influenza rates for the following week based on the previous week's data obtained from the FluView surveillance system. The predicted rates were compared to the actual influenza rates to assess the model's overall …

Bandwagon Behavior In Major League Baseball, Daniel E. Erro

Master's Theses

This study investigates “bandwagon” behavior among Major League Baseball (MLB) fans by analyzing Google search interest data from 2004 to 2019. Drawing on publicly available information from Google Trends, the analysis explores how fluctuations in search activity align with team performance during both the regular season and postseason. Hierarchical linear models are used to estimate expected levels of fan interest based on team performance and market characteristics. Deviations from these expectations during the regular season are interpreted as evidence of bandwagon or anti-bandwagon behavior. A drop-off in interest following playoff elimination is also examined to capture shifts in fan attention …

How Argentina Won The 2022 Fifa Men's World Cup: A Data Story, Aniruddha Parthasarathy

Dissertations, Theses, and Capstone Projects

This project analyzes Argentina’s 2022 FIFA Men’s World Cup win using open-source football (soccer) data. The project evaluates the team’s performance at a micro-level across three domains: without possessing the ball, possessing the ball and the team’s in-game management tactics. A statistical framework, i.e., multiple linear regression modeling, was used to identify the five key defensive actions influencing the Argentinian team’s intensity of pressure applied, and visualized by heatmaps and time-segmented plots. More specifically, an Expected Threat (xT) analysis quantified the threat or danger from passes and progressive carries (moving the ball at least 10 meters), revealing that Lionel Messi’s …

Opening The Black Box With Regal: A Novel Explainable Ai Approach To Uncover Key Predictors In Search And Rescue Success, Brandon Hyunjun Kim

Master's Theses

The outcome of a search and rescue (SAR) operation is influenced by a complex, non-linear interplay among numerous factors, including geographic context, subject-specific characteristics, and environmental conditions. The high dimensionality and intricate dependencies among these variables pose significant challenges to traditional exploratory modeling approaches, limiting their ability to uncover meaningful patterns and relationships associated with mission success. This study introduces Rules Based Explanations for Generated neighborhoods Around Localized cases (REGAL), a novel adaptation of the Local Interpretable Model-agnostic Explanations (LIME) framework to explain deep multimodal neural networks and what key features it assesses to determine search and rescue success. REGAL …

Welfare Implication Of Alternative Tax Rates Adjustment Policy In Nigeria: A Dsge Analysis, Umar B. Ibrahim, Isah F. Abubakar

CBN Journal of Applied Statistics (JAS)

This study sets out to determine the desirable policy adjustment in the tax rate for Nigeria that ensures the least welfare cost. A calibrated small open-economy New Keynesian Dynamic Stochastic General Equilibrium (NKDSGE) model of the Nigerian economy is applied to achieve this objective. Within this framework, we examined the impact of an increase in value-added tax (VAT) rate from 7.5 to 15 percent on key macroeconomic variables relative to the impact of an increase in company income tax (CIT) rate from 30 to 35 percent on macroeconomic variables. Furthermore, we examined the welfare costs of the increases in the …

Property Testing Ai: An Efficient Frontier, Paul Sopher Lintilhac

Dartmouth College Ph.D Dissertations

In this dissertation, we take a step towards addressing the major problem of a lack of standardized and rigorous approaches to testing and evaluation of AI systems. Taking inspiration from both the fields of Property Testing and Property Based Testing (for programs), we develop a novel taxonomy of partially overlapping classes of properties of AI systems, including simple properties, compound properties, higher order properties, data relation properties, and architecture-utility properties. We argue that this taxonomy categorizes a diverse set of AI traits -- including accuracy, fairness, robustness, monotonicity, point-wise and global privacy properties, sensitivity, and more -- according to the …

Resale Revolution: Trend Implications From Media Presence Transcended To Luxury Retail Markets, Penelope Prochnow

Capstone Projects

This study aims to deepen understanding of fashion trend decline from peak popularity to obsolescence, with implications for sustainability and producer profit margins. It investigates how the attributes and media presence of fashion items influence their journey from high-end editorial coverage to resale platforms. Using survival analysis to model trend lifetimes and cosine similarity metrics to compare resale and magazine keyword frequencies, alongside machine learning for price prediction, the study uncovers critical temporal patterns. Results show that resale trends reflect magazine content with a lag of approximately 18 to 30 months and draw from long-wave revivals spanning 6 to 14 …

Contribution Of Various Factors On The Rate Of Traffic Accidents In The Us, Martin Mnatsakanyan

Undergraduate Research Symposium Lightning Talks

Background:

Until 2020, the number of traffic accidents has been steadily decreasing. After 2020, the number started increasing until 2022, then started s lowly decreasing again. Most drivers aren’t fully aware of the reason behind all of these accidents.

Aleci: An R Package For Non-Parametric Confidence Intervals On Accumulated Local Effects Plots, Matthew R. Lister

All Graduate Reports and Creative Projects, Fall 2023 to Present

Machine learning models can take a collection of inputs and craft an output. The mathematical formulas these models use to calculate their outputs easily become too complex or time consuming for a human to analyze. Collectively, we refer to these as black box models. Accumulated local effects plots (ALE) are a method for adding interpretability and visibility into the effects that individual variables contribute to the predictions made by black box models. The method designed by D.W. Apley calculates equally spaced point estimates of the response value to construct a graph across the range of the variable of interest. AleCI …

Computer Vision In Soccer: Yolov11 Analytics Engine For Quantifying Game Strategy, Connor S. Maurer

Data Science Undergraduate Honors Theses

Single-shot object detection capabilities significantly reduce computational overhead for real-time computer vision in sports analytics at 60 FPS. YOLO11’s lightweight CNN gives promising accuracy while meeting the low-latency demand of dynamic soccer matches. As data-driven approaches take over the sport of soccer, efficient player tracking systems become critical for informing coach’s strategies. I prototype the ETL (Extract, Transform, Load) process of data collected from a single- shot detection program and evaluate its viability for estimating player fatigue. YOLO11 detects players, the ball, and other characteristics, with the output transformed by homography to estimate the positions in the real world. These …

Nonparametric Methods For Bayesian Community Detection In Complex Networks, Kedran Young

Graduate Theses and Dissertations

Network analysis is becoming an increasingly popular interdisciplinary area of study, with emerging interest in fields like sociology, biology, economics, and ecology. Within the niche of network analysis, capturing the community structure of a network is one important achievement that many statisticians have been working toward over recent decades. The most popular modeling technique for latent community detection is the Stochastic Block Model (SBM), which falls into the category of latent variable models and will serve as the baseline model throughout this thesis. SBM is widely regarded as the most effective community detection method as it detects latent community membership …

Innovative Methods For The Design And Analysis Of Phase Ii Clinical Trials, Feng Tian

Dissertations and Theses (Open Access)

Drug development has become increasingly time-consuming, costly, and risky in recent years. There is significant potential for improving clinical trial designs, particularly for phase II trials, which play a critical role in the drug development process. Innovative methods are especially necessary for addressing key challenges in phase II trials in terms of dose-ranging study, patient population selection, and decentralized clinical trials (DCTs). This dissertation presents a comprehensive set of methodologies that address these critical issues with three projects. The first project introduces a Bayesian adaptive dose-ranging design that integrates both efficacy and toxicity data to evaluate each dose comprehensively. The …

Application Of Ordinal Regression Models To Acquired Stress Resistance In Wild Strains Of Saccharomyces Cerevisiae, Carson Stacy

Graduate Theses and Dissertations

This thesis explores the application of ordinal regression to the analysis of semi-quantitative growth assays often used when comparing fitness for different strains of the model yeast Saccharomyces cerevisiae. For stress survival assays, yeast stress resistance is measured using an ordered survival score that ranges from 0 (no growth) to 4 (confluent growth). Traditional approaches to analyze this type of data either treats data as a nominal categorical variable or as a continuous numerical variable. These approaches risk loss of information or violation of testing assumptions. In contrast, cumulative logit ordinal regression uses the information contained in the order …

Expressive And Interpretable User Engagement Prediction Using Multivariate Survival Processes, Akshay Aravamudan

Theses and Dissertations

The ability to characterize how information diffuses online is of paramount importance to stakeholders that are interested in tasks such as proposing solutions for mitigating and countering dis/misinformation, predicting user engagement of content in social media, planning marketing campaigns to roll-out products and planning dissemination of political campaign messaging among others. One such facet of learning the dynamics of information diffusion is the ability to predict user engagement or the popularity of a single piece of information as it spreads through an online medium. Existing works in this regard mainly either obfuscate user level information or utilize frameworks that are …

Nonlinear Power Function Model Changepoint Detection., Jacob Steven Townson

Electronic Theses and Dissertations

Most work surrounding changepoint analysis focuses on linear models. This dissertation explores changepoint detection in nonlinear power function models, specifically focusing on models where the constant multiplier and power are the parameters to be estimated in addition to the changepoint parameter. The study assumes an asymptotic framework as the number of observations approaches infinity. The study explores various model fitting algorithms, and decides to employ the Newton-Raphson method for parameter estimation, with a custom implementation developed to optimize the process. The research first establishes the strong consistency of estimators for the model without a changepoint. Building on this result, consistency …