Statistics and Probability Commons^™

Developing A Humpback Whale Vocalization Detector Using Machine Learning Models, Lucas Kantorowski

Master's Theses

Humpback whale songs are notoriously complex. Identification of humpback whale song units requires bioacousticians to tediously listen, analyze, and annotate collected sound data. Even sparse data requires listening to the entirety of the collected acoustic data. In this study, three hours of audio containing over one-thousand humpback whale song units was collected in Monterey Bay, California.

Prior studies have seen success using convolutional neural networks by performing image classification on hundreds of hours worth of spectrograms. Our study uses traditional machine learning models, as they are less computationally demanding, and require less data.

We use time splitting and Mel-frequency cepstrum …

Muon Lifetime: Theory, Experiment, And Simulation, Soren Agustin Munoz

Physics

This senior project investigates the muon lifetime through three complementary approaches: theoretical calculation, laboratory measurement, and computational simulation. The theoretical component develops the necessary background from relativistic field theory to the effective weak interaction, culminating in the leading-order Fermi-theory prediction of τ ≈ 2.2 μs, which explains why the muon lifetime lies on the microsecond scale.

The experimental component measures the lifetime of stopped cosmic-ray muons using a plastic scintillator, photomultiplier tube, and analog timing electronics. A binned Poisson likelihood fit to the primary 15-day acquisition run τ = 2.17^+0.03_-0.09 μs, consistent with the accepted value within the …

Crab: A Novel Clustering Score Using Clustering With Rivals And Buddies For Unsupervised Learning, Allen Choi

Master's Theses

Unsupervised clustering algorithms today are used across a wide variety of fields such as biology, engineering, and industry in order to classify observations into groups where labels are not provided. This can provide important latent information regarding the observations within groups, as well as insight regarding the groups themselves. In order to judge the optimal number of clusters for an unsupervised clustering algorithm, many methods exist such as the Elbow Method and Silhouette Score; however, these methods come with drawbacks and are not necessarily flexible across many unsupervised methods. We present a novel clustering score framework relying on a resampling-based …

On M-Estimation: From Theory To Examples, Alexander Yuan

Master's Theses

M-estimation provides a unified framework for statistical procedures defined as optimizers of data-dependent criterion functions. This thesis gives an expository account of M-estimation in classical and high-dimensional settings. The classical part develops weak convergence, empirical process tools, and the argmax framework for studying consistency, rates of convergence, and weak limits. Examples including least squares, maximum likelihood, robust location estimation, change-point estimation, and empirical risk minimization illustrate regular and non-regular asymptotic behavior.

The high-dimensional part studies regularized M-estimators, where the focus shifts to finite-sample error bounds and model selection guarantees. Topics include decomposable regularizers, restricted strong convexity, non-convex penalties, and sparsistency. …

Hot Hands Or Chance Happenings? A Simulation-Based Approach For Wnba Teams, Ruben Jimenez

Master's Theses

The hot hand is a polarizing topic in basketball analytics: fans, stakeholders, and even players themselves assert confidently their belief or disbelief in the idea that players who perform well will continue to do so over an extended period of time. Statistical research has been conducted since as early as 1985 to attempt to disprove or prove the existence of this phenomenon. More recent works have refuted the earliest objections to the hot hand’s existence, with conclusions aided by robust simulation techniques. In this work, we compare hypothesis tests using multiple simulation techniques to explore the hot hand at the …

Is The Hot Hand Real? Evidence From A Permutation And Hierarchical-Based Analysis, Cameron Z. An

Master's Theses

The hot-hand phenomenon, often described as the tendency for individuals to experience prolonged streaks of success that exceed what would be expected under random performance, has been widely studied across many disciplines, particularly basketball. Early studies attempted to evaluate this effect through various techniques, often concluding that the hot-hand phenomenon was largely a myth. However, recent studies have begun to revisit previous analyses using improved statistical techniques, with some claiming evidence of a discernible hot-hand effect. This study examines the presence of the hot-hand effect in the modern NBA by testing whether observed shooting patterns deviate from those simulated under …

Structured Dynamic Factor Analysis Of Environmental Time Series With Application To Morro Bay Estuary, Jose Garcia

Master's Theses

This thesis develops a structured dynamic factor analysis (sDFA) framework for decomposing multivariate environmental time series into latent biological and physical components. The methodology is applied to five years of high-resolution passive monitoring data collected from two sites in Morro Bay, California from 2020 through 2024. Relative contribution indices are developed based on the structured DFA that measure how much each latent process contributes to each observed variable at any given time. Structured DFA models fit to the application data suggest site-specific patterns in how biological and physical processes affect water quality variables. At the bay mouth location, physical processes …

A2s Uplink Latency Minimization For Wildfire Monitoring Systems Using Mbse And Stochastic Modeling, Luis Giovanni Wang

Master's Theses

Wildfire response depends on how quickly a detection reaches the people who act on it, and the slowest remaining step is often the link that carries an alert from a remote sensing platform to a satellite. This thesis models the latency of that link, the Air-to-Space uplink, for a wildfire-monitoring UAV that carries a Starlink terminal and sends an ALERT packet to a serving Low Earth Orbit satellite. The uplink is difficult to predict because both the UAV and the satellite move, and because the wildfire environment degrades the channel at the moment the data matters most.

The thesis uses …

Multimodal Machine Learning For Soil Burn Severity Mapping Across California Wildfires, Sanjana Checker

Master's Theses

Accurate mapping of soil burn severity (SBS) is critical for post-fire watershed management, erosion risk assessment, and ecological recovery planning, yet traditional field-based approaches remain costly, time-intensive, and spatially limited. This thesis presents a machine learning pipeline for wall-to-wall SBS classification across California wildfires using multi-sensor satellite imagery, terrain derivatives, and bioclimatic covariates. Field-collected SBS observations (n = 2,180) from 52 wildfires occur- ring between 2013 and 2025, sourced from the U.S. Forest Service and CAL FIRE, were used to train and evaluate multiple classification architectures within a Google Earth Engine and Google Cloud-based prediction framework. After upsampling the unburned …

Using Ensemble Disagreement To Stabilize Conformal Prediction Under Distribution Shift, Patrick D. Murphy

Master's Theses

Semantic segmentation of eelgrass from drone imagery is crucial for coastal habitat monitoring, restoration, and management, as these habitats continue to see rapid changes due to climate change and human influence. However, the reliability of generalizing a deployed classification model relies on both high-accuracy segmentation as well as robust uncertainty quantification that holds up when conditions change over years or locations. Conformal prediction (CP) is a method that converts a classifier's output into prediction sets with a guaranteed average coverage level for in-distribution data. However, the “vanilla” conformal score can often under-cover in hard or out-of-distribution (OOD) regions under drift. …

Empirical Comparisons Of Partial Dimension Reduction Algorithms In High-Dimensional Regression, Nathan Greenfield

Master's Theses

In high-dimensional regression problems, dimension reduction methods are often used to address the challenges of multicollinearity and estimation instability. Partial dimension reduction extends these ideas by applying dimension reduction to a subset of the predictors, while the remaining predictors are modeled without compression. This approach is particularly useful when it is important to retain variability and interpretability in certain predictors.

This thesis investigates the empirical performance of partial dimension reduction algorithms and introduces a novel algorithm, Iterative Partial Residual (IPR). Two algorithms are considered: a baseline algorithm, Marginal Residual (MR), and the proposed IPR method. Their predictive performance is evaluated …

Deep Learning Framework For Option Pricing, Kyle Rytand Bistrain

Master's Theses

Accurately pricing American options with market data presents a significant challenge, as foundational models like the Black-Scholes-Merton (BSM) model rely on assumptions that deviate from real-world financial data -- such as log-normal returns, constant volatility, and no dividends -- and fail to account for the key early exercise feature of American options. While parametric models can adjust for these features, the complexity of the resulting models renders them prohibitively difficult to apply in practice for nonspecialists. In response, modern machine learning (ML) techniques provide a set of flexible and powerful alternatives, and recent research has explored the application of ML …

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 …

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 …

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 …

Topodino: Self-Supervised Topological Representation Learning For Neuronal Morphologies, Yasser Binbisher

Master's Theses

Neuronal cell types are categorized by transcriptomic identity, yet their morphological heterogeneity defies this classification. In response, researchers have adopted unsupervised graph representation learning as a tool to reveal morphological variation within single-class transcriptomic types. However, the complex geometry of neuronal morphology—especially long axons and dense dendrites—challenges graph neural networks, which struggle with message propagation across extended structures. To mitigate this, current approaches enforce sub-sampling on neuronal graphs and omit axons entirely, sacrificing critical biological features for computational efficiency. To overcome this trade-off, this thesis introduces TopoDINO, a self-supervised, topology-aware representation learning model designed to preserve the full hierarchical organization …

Data Driven Analysis Of Samara Seed Kinematics And Dynamics, Shashwat Sparsh

Master's Theses

Samara Seeds are a class of fruit most famously belonging to the Acer species and are characterized by their single-bladed geometry and their auto-rotation response during descent. This steady-state auto-rotation response is the subject of aerodynamic analysis which aim to quantify the performance. The period prior to the beginning of steady-state auto-rotation is classified as the transition regime and has not been the subject of intense scrutiny.

This thesis employs a data-driven approach to analyzing the kinematic and dynamic response of these seeds during both the transition and auto-rotation stages of flight to quantify the performance with respect to the …

Investigating Social Presence In Collaborative Keys For Asynchronous Courses, Lily P. Cook

Master's Theses

Asynchronous virtual courses have become increasingly popular in the years following the global Covid-19 pandemic. These courses, with no set meeting schedule, offer flexibility to both students and instructors, but pose challenges for developing a collaborative learning environment. The Community of Inquiry framework (Rourke et al., 1999) identifies three essential components in an online course necessary to foster a collaborative environment- teaching presence, cognitive presence, and social presence. Social presence is especially impacted in asynchronous learning settings, which presents challenges for the students to display their personalities and connect with the community. This study investigates Collaborative Keys (CKs), structured collaborative …

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 …

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 …

Policies And Price Controls On The Research And Development Of Orphan Drugs In The United States And The European Union, Bena Pearl Filipczak Smith

Master's Theses

There is substantive literature surrounding the impact of price controls on the research and development (R&D) of new pharmaceutical products. The European Union (EU) and United States (US) are often studied in contrast to examine the influence of price controls as the US has fewer pharmaceutical price controls than the EU.

We find moderate evidence that the US spent more on annual domestic pharmaceutical R&D than the EU between 2004 and 2021, on average, before and after adjusting for GDP growth per capita and year. We find strong evidence that the US increased annual domestic R&D spending at a faster …

Accessible Real-Time Eye-Gaze Tracking For Neurocognitive Health Assessments, A Multimodal Web-Based Approach, Daniel C. Tisdale

Master's Theses

We introduce a novel integration of real-time, predictive eye-gaze tracking models into a multimodal dialogue system tailored for remote health assessments. This system is designed to be highly accessible requiring only a conventional webcam for video input along with minimal cursor interaction and utilizes engaging gaze-based tasks that can be performed directly in a web browser. We have crafted dynamic subsystems that capture high-quality data efficiently and maintain quality through instances of user attrition and incomplete calls. Additionally, these subsystems are designed with the foresight to allow for future re-analysis using improved predictive models, as well as enable the creation …

Causal Inference Using Bayesian Network For Search And Rescue, Amanda Belden

Master's Theses

People who are considered missing have much higher probabilities of being found dead compared to those who are not considered missing in terms of Search and Rescue (SAR) missions. Dementia patients are incredibly likely to be declared missing, and in fact after removing those with dementia the probability of the mission being regarded as missing person case is only about 10%. Additionally, those who go missing are much more likely to be on private land than on protected areas such as forests and parks. These and similar associations can be represented and investigated using a Bayesian network that has been …

Qwixx Strategies Using Simulation And Mcmc Methods, Joshua W. Blank

Master's Theses

This study explores optimal strategies for maximizing scores and winning in the popular dice game Qwixx, analyzing both single and multiplayer gameplay scenarios. Through extensive simulations, various strategies were tested and compared, including a scorebased approach that uses a formula tuned by MCMC random walks, and race-to-lock approaches which use absorbing Markov chain qualities of individual score sheet rows to find ways to lock rows as quickly as possible. Results indicate that employing a scorebased strategy, considering gap, count, position, skip, and likelihood scores, significantly improves performance in single player games, while move restrictions based on specific dice roll sums …

The Impact Of Video Assistant Referee (Var) On The English Premier League, Jack Kenyon Brown

Master's Theses

The aim of this study is to examine how the introduction of the Video Assisted Referee (VAR) system influenced the English Premier League (EPL). Since its implementation in the English Premier League in 2019, VAR has been a constant source of debate and controversy. Many studies have been done on the immediate impact of VAR on other elite professional soccer leagues, but the scope of results is very limited and due to be updated. The data for the ensuing analysis consists of 3800 matches played in the English Premier League during the five seasons before (14/15, 15/16, 16/17, 17/18, and …

Recursive Marix Game Analysis: Optimal, Simplified, And Human Strategies In Brave Rats, William A. Medwid

Master's Theses

Brave Rats is a short game with simple rules, yet establishing a comprehensive strategy is very challenging without extensive computation. After explaining the rules, this paper begins by calculating the optimal strategy by recursively solving each turn’s Minimax strategy. It then provides summary statistics about the complex, branching Minimax solution. Next, we examine six other strategy models and evaluate their performance against each other. These models’ flaws highlight the key elements that contribute to the effectiveness of the Minimax strategy and offer insight into simpler strategies that human players could mimic. Finally, we analyze 123 games of human data collected …

Unraveling The History Of Deforestation In The Amazon Rainforest With Statistical Modeling, Ryan Destefano

Master's Theses

The Amazon rainforest, a vital ecosystem of immense biodiversity and global climate significance, faces the ongoing threat of deforestation driven by agricultural expansion. This thesis employs remote sensing techniques, focusing on the Enhanced Vegetation Index (EVI) derived from Landsat satellite imagery, to track land cover dynamics within the Amazon. The study examines historical land cover changes in current plantations in Peru and Brazil, regions where the exact timing of deforestation is uncertain. By analyzing EVI measurements dating back to 1984, inflection points indicative of deforestation events preceding plantation establishment are identified. Statistical modeling techniques, including spline fitting to analyze time …

Using Plankton Edna To Estimate Whale Abundances Off The California Coast: Data Integration And Statistical Modeling, Katherine Chan

Master's Theses

Understanding marine mammal populations and how they are affected by human activity and ocean conditions is vital, especially in tracking population declines and monitoring endangered species. However, tracking marine mammal populations and their distribution is challenging due to difficulties in observation and costs. Using surrounding plankton environmental DNA (eDNA) has the potential to provide an indirect measure of monitoring cetacean abundances based on ecological associations. This project aims to apply statistical methods to assess the relationship of visual abundances of common species of baleen whales with amplicon sequence variants (ASV) of plankton eDNA samples from the NOAA-CalCOFI Ocean Genomics (NCOG) …

Foundations Of Memory Capacity In Models Of Neural Cognition, Chandradeep Chowdhury

Master's Theses

A central problem in neuroscience is to understand how memories are formed as a result of the activities of neurons. Valiant’s neuroidal model attempted to address this question by modeling the brain as a random graph and memories as subgraphs within that graph. However the question of memory capacity within that model has not been explored: how many memories can the brain hold? Valiant introduced the concept of interference between memories as the defining factor for capacity; excessive interference signals the model has reached capacity. Since then, exploration of capacity has been limited, but recent investigations have delved into the …

An Empirical Evaluation Of Neural Process Meta-Learners For Financial Forecasting, Kevin G. Patel

Master's Theses

Challenges of financial forecasting, such as a dearth of independent samples and non- stationary underlying process, limit the relevance of conventional machine learning towards financial forecasting. Meta-learning approaches alleviate some of these is- sues by allowing the model to generalize across unrelated or loosely related tasks with few observations per task. The neural process family achieves this by con- ditioning forecasts based on a supplied context set at test time. Despite promise, meta-learning approaches remain underutilized in finance. To our knowledge, ours is the first application of neural processes to realized volatility (RV) forecasting and financial forecasting in general.

We …