Statistics and Probability Commons^™

Entropic Dynamics Approach To The Classical Limit Of Quantum Mechanics: Decoupling Of The Center Of Mass Motion For A Mesoscopic Particle, Fatimah Judayba

Electronic Theses & Dissertations (2024 - present)

In the Entropic Dynamics (ED) approach, quantum mechanics is derived from the principles of entropic inference and information geometry. The ED approach differs from other interpretations by making a clear commitment to distinguishing which variables are ontic (real) and which are epistemic. The classical limit for the center of mass (CM) coordinate is achieved for a large number of particles, M →∞, while Planck’s constant ℏ remains finite. Typically, the emergence of the classical limit requires decoherence through interactions with the external environment. In this work, we investigate whether the classical behavior of the CM coordinate in a mesoscopic system …

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 …

On Sharpest Tail Bounds For Functions Of Tail Bounded Random Variables, Stephen Harrison

Mathematics & Statistics ETDs

Consider n real/complex, independent/dependent random variables with respective tail bounds and g a measurable function of the r.v.’s. Consider f the “sharpest” tail bound of g (sharpest in the sense, if f were any less, then for some X1, ..., Xn satisfying the conditions, g(X1, ..., Xn) would not satisfy the tail f). Significant research has been done to approximate f often with high accuracy. These results are often of the form, for g in this family, and tail bounds of Xk in this family, f is bounded by some f′ with high accuracy. However, the question “what would it …

Wacsaw: An Adaptive, Statistical Method To Classify Movement Into Sleep And Wakefulness States, Austin Vandegriffe, V. A. Samaranayake, Matthew S. Thimgan

Mathematics and Statistics Faculty Research & Creative Works

Wearable actimeters can improve our understanding of sleep in the natural environments. Current algorithms may produce inaccuracies in specific individuals and circumstances, such as quiet wakefulness. New hardware allows data collection at higher frequencies enabling sophisticated analytical methods. We have developed a novel statistical algorithm, the Wasserstein Algorithm for Classifying Sleep and Wakefulness (WACSAW), to identify behavioral states from recordings of everyday movement. WACSAW employs optimal transport techniques to identify segments with differing activity variability. Functions characterizing the segments' movement distributions were clustered into two groups using a k-nearest neighbors and labeled as sleep or wake based on their proximity …

Content And Consequences: Impact Of Representation In Stem Higher Education Instructional Content On Marginalized Students, Nichole Ventura

Doctorate in Education

This qualitative study examined representation of historically marginalized students in STEM instructional content at the higher education level and its impact on their learning experiences. Despite growing diversity initiatives in STEM enrollment, curricular materials often fail to reflect the identities of underrepresented students. Using critical theory and interpretivist approaches, this research investigated how representation—or its absence—shapes students' sense of belonging, academic identity formation, and persistence. Through semi-structured interviews with undergraduate students from historically marginalized backgrounds, and purposeful sampling, this study captured the lived experiences of students engaging with STEM instructional materials. Interview protocols explored how students perceive their representation in …

A Leslie System For A Demographic Simulation: From An Actuarial Point Of View, David Kings

Electronic Theses and Dissertations

This thesis develops a discrete stochastic linear systems interpretation of age–stage demographic evolution grounded in Leslie operators and realized in a discrete-event simulation implemented with salabim. The central claim is that one annual cycle of the simulation constitutes a cone-preserving, stochastic affine transformation on a high- dimensional population state vector indexed by age, sex, marital status, household type, employment, and education, and that the composition of yearly operators yields a random matrix product whose top Lyapunov exponent is the stochastic counterpart of the Perron–Frobenius growth rate (Caswell, 2001; Tuljapurkar, 1997)[1, 2]. The actuarial bridge is constructed by mapping simulated survival …

A Persistent Homology Framework For Scrna-Seq: Assessing Clustering Robustness And Quantifying Preprocessing And Integration Effects On Topological Features., Jonah Daneshmand

Electronic Theses and Dissertations

As single-cell RNA sequencing (scRNA-seq) data expands, robust methods for integrating diverse datasets are critical. This dissertation applies Persistent Homology (PH), a technique from Topological Data Analysis (TDA), to a collection of scRNA-seq datasets spanning eight tissue types to quantify how data integration affects topological features and biological interpretability. We assessed global topological structure using Betti curves, Euler characteristics, and persistence landscapes across raw, normalized, and integrated data representations. Our analysis revealed a performance inversion: while conventional methods excelled on unintegrated data, high-granularity topological methods, particularly those sensitive to global data structure, became superior after integration. This suggests a synergy …

Error Reduction Methodology And Data Simulation For Interval Data, Ranik Christopher Jelinek

Undergraduate Honors Capstone Projects

Chronic kidney disease (CKD) is a progressive condition affecting hundreds of millions of individuals worldwide. However, clinical datasets often record continuous laboratory measurements as categorical intervals rather than precise numerical values. This interval-censored structure presents methodological challenges for standard regression-based classifiers. This study compares three strategies for handling interval-valued predictors prior to fitting a logistic LASSO model: (1) midpoint imputation, which replaces each interval with its arithmetic center; (2) ordinal encoding, which maps intervals to integer ranks; and (3) a Monte Carlo simulation approach, which repeatedly samples uniformly from each observed interval and averages predictions across replications. Using a 10-fold …

The Impact Of Transmission Thresholds Across Multiple Scales On The Spread Of Chronic Wasting Disease In Wisconsin, Jen Mcclure

All Graduate Theses and Dissertations, Fall 2023 to Present

Wildlife diseases can be difficult to control once they are established. This is especially true when they spread through contact with infectious material left in the environment. One such disease is chronic wasting disease (CWD), a fatal illness affecting deer and related species in North America and other regions. CWD is caused by prions, misfolded proteins that can remain infectious for years after shedding by infected hosts.

Recent research shows that CWD infection does not always follow from the gradual accumulation of prions through small contact events. Rather, an individual may need to encounter a certain prion dose all at …

Implications Of The Attenuated Allee Effect On Population Dynamics, Dana Strong

All Graduate Theses and Dissertations, Fall 2023 to Present

The Allee effect is an ecological phenomenon characterized by a per capita growth rate that increases as the population size increases in the context of low population density. The Allee effect can lead to rapid extinction events. Consequently, ecologists can attempt to control the strength of the Allee effect to help increase the population (in the case of endangered species) or decrease the population (in the case of parasites or pests).

This research aimed to study not the strength of the Allee effect, but the intensity of the Allee effect, or how rapidly cooperation between individuals causes the per capita …

Machine Learning Applications: Cell Tracking And Nonparametric Estimation Of Non-Smooth Divergences, Mina Mahbub Hossain

All Graduate Theses and Dissertations, Fall 2023 to Present

This thesis brings together two important research directions: how to compare different sets of data more accurately, and how to better understand how brain cancer cells move and change shape.

In the first part, we look at a problem in statistics: measuring how different two data sources are from each other. Traditional methods often make strong assumptions, which may not always hold in real situations. Our approach avoids those assumptions by using an ensemble method, a way of combining many weak estimators into one stronger result. This makes the method more flexible and reliable, especially when dealing with complex or …

(Si15-140) Designing Bayesian Double Sampling Plans Based On Zero Inflated Poisson Distribution, Priyadharshini R., Shalini K., Hemalatha R., Sangeetha S.

Applications and Applied Mathematics: An International Journal (AAM)

The implementation of attribute-based sampling inspection serves as a quality control technique used across numerous industries to evaluate items or workflow processes. When the data exhibits a substantial number of zero counts, the zero-inflated Poisson (ZIP) distribution serves as an effective model for accommodating this zero-inflation. Double sampling plan (DSP) is a quality check method where the decision to approve or decline a batch comes after examining two samples, providing more conclusive information compared to a single sample plan (SSP). In practice, effective decision-making regarding submitted lots considers both within-lot and between-lot variations, which can be addressed through the use …

(Si15-142) Selection Of Single Sampling Plans Based On Zero Inflated Binomial Distribution Using Cost Optimization, Sangeetha S., Shalini K., Hemalatha R., Priyadharshini R.

Applications and Applied Mathematics: An International Journal (AAM)

Economic design of sampling plans involves creating sampling plans that minimize the total cost associated with the inspection process while ensuring quality. It aims to address the quality risk concerns of both producer and consumer, ensuring product quality while minimizing inspection costs. This article’s objective is to design single sampling plans by attributes based on Zero-inflated Binomial (ZIB) distribution, using cost optimization principles by developing an economic model aimed at achieving optimal total cost by considering the Average Total Inspection (ATI). Numerical illustration is provided to illustrate the selection of single sampling plans under ZIB distribution that minimizes producer’s total …

Long-Term Behavior Of Subordinated Branching Processes With Prevailing Emigration, George Yanev

School of Mathematical & Statistical Sciences Faculty Publications

This paper deals into the long-term behavior of subordinated critical branching processes with migration. We focus on scenarios where emi­gration is the dominant factor and introduce additional randomness in timing through a subordination mechanism, involving renewal processes. The key findings highlight how the initial population size and the interar­rival mean time influence both asymptotic behavior of the non-extinction probability and corresponding Yaglom type limit theorems. We also study an alternating regenerative process, when the population cycles between zero and positive states. This research complements previous studies for processes when immigration prevails over emigration.

Generalized Transversality Conditions For Fuzzy Quantum-Symmetric Variational Problems Via Granular Approach, Martin Bohner, Ewa Girejko, Agnieszka B. Malinowska, Linh Nguyen, Baruch Schneider, Tri Truong

Mathematics and Statistics Faculty Research & Creative Works

This paper investigates fuzzy q-symmetric variational problems with natural boundary conditions. Based on the relative distance measure fuzzy arithmetic and horizontal membership functions (HMFs), we propose novel concepts of differentiability and integrability for fuzzy functions on quantum geometric subsets of real numbers. Then, fundamental foundations of q-symmetric calculus of variations based on HMFs are provided. With the help of HMFs and granular q-symmetric differentiability, we derive necessary optimality conditions for fuzzy q-symmetric variational problems that depend on free endpoints. Moreover, sufficient conditions for minimizers of q-symmetric variational problems are obtained. Some numerical examples illustrating the proposed approach are presented.

Novel Statistical And Topological Data Analyses Of 2d Electronic Images, Robert L. Paige, Vic Patrangenaru

Mathematics and Statistics Faculty Research & Creative Works

In this paper, novel statistical and topological data analyses of 2D images are developed. One considers methodologies based on the Region Covariance Descriptor (RCD) and Topological Data Analysis (TDA) rooted in the simplicial as well as cubical persistent homologies. These methods provide statistical methods for data from populations of complex data objects that are elements of non-Euclidean spaces. The 2D image data considered consist of pictures of two leaves—A and B—from the same tree, twenty of each leaf, from different perspectives. The novel statistical procedures developed are used for correctly determining that leaf A images and leaf B images are …

Rethinking Iterative Proportional Fitting: Scalable And Hybrid Approaches To Joint Distribution Fitting, William Ofosu Agyapong

Open Access Theses & Dissertations

The Iterative Proportional Fitting (IPF) algorithm is widely used in contingency table estimation, survey weighting, and synthetic population generation due to its simplicity and strong theoretical foundation for matching observed marginal distributions. However, in high-dimensional settings, IPF faces substantial computational and memory demands, as well as statistical instability caused by sparse contingency tables. Moreover, IPF is less useful in modern population synthesis tasks that require both scalability and realism because, despite its superiority in matching known marginal distributions, it cannot produce realistic out-of-sample data points. To address these limitations, we first propose a blockwise IPF framework, in which the feature …

Quantifying The Sensitivity Of Land Use Land Cover Metrics Through Simulation Techniques, Haley Burger

All Graduate Theses and Dissertations, Fall 2023 to Present

As human activities and climate change continue to reshape our landscape, understanding how land use changes over time is becoming increasingly important. Accurate ways to track and analyze these changes are essential for governments, businesses, and communities to make informed decisions. Monitoring agricultural land is particularly critical, as shifts in land use can impact food production and environmental pollutants. One of the primary tools used in the United States to monitor agricultural land is the Cropland Data Layer (CDL), an annual map created by the United States Department of Agriculture (USDA) from satellite images. While the CDL is highly accurate, …

Bayes In The Brain: A Review Of Everything Is Predictable: How Bayesian Statistics Explain Our World, (2024) By Tom Chivers., Michael T. Catalano

Numeracy

Tom Chivers’ Everything is Predictable: How Bayesian Statistics Explain Our World, is an interesting and wide-ranging narrative on Bayesian thinking, its history, and its applicability to both our everyday lives and the pursuit of scientific truth. Although appropriate for the non-expert, afficionados and teachers of quantitative literacy should find the plethora of examples, links to psychology as it applies to how people reason about probabilities, and even Chivers’ philosophical musings informative and thought-provoking.

Minimal Error Functions On Irregular Subsets Of The Real Line, Robert Michael Dukes

Mathematics & Statistics ETDs

Chebyshev Polynomials, those that minimize the maximal error on a compact set, are one of the most practical tools for approximating smooth functions. The classical results are on the set [-1, 1]; in this paper, we extend to more complicated subsets of the real line. We demonstrate some classical results and then take the result from [2] on regular Parreau-Widom Sets and extend it to semi-regular sets, defined as sets whose regular part is closed. We introduce the Regularity Coefficient as a series formed by evaluating the Green’s Function at irregular points. This new machinery is applied to the lower …

A Data-Driven Approach To Time Series Forecasting And Clustering Of U.S. Regional Drug Overdose Mortality, Koshali Hamy Muthunama Gonnage

Mathematics & Statistics ETDs

The increasing rate of drug overdose deaths in the United States poses a critical public health challenge, particularly due to the surge in synthetic opioids and other high-risk substances. This study presents a data-driven framework that integrates time series forecasting and clustering techniques. Monthly mortality data for five key drug types: cocaine, fentanyl, heroin, methamphetamine, and oxycodone were analyzed using four time series forecasting models: ARIMA, ETS, TBATS, and NNAR. These models were evaluated using standard accuracy metrics RMSE, MAPE, and MAE to assess predictive performance. Signal decomposition approach based on Singular Value Decomposition and subspace modeling was employed to …

Exact Sampling Of The Six-Vertex Model Using Coupling From The Past, Malaeka Amir

DePaul Discoveries

This paper aims to explore the six-vertex model through simulations designed to investigate the behavior of configurations under specific domain wall boundary conditions. To generate random configurations, we employ the Markov Chain Monte Carlo method while addressing the challenge of mixing times by utilizing the Coupling from the Past (CFTP) algorithm. Implemented in Python, our approach leverages CFTP to ensure exact sampling, avoiding the uncertainty of convergence in traditional Monte Carlo methods. We explore the monotonicity property within this framework and prove that it is only maintained by the steps of this algorithm for very particular values of the parameters.

Dice Math And Probability, Warren Campbell

SEAS Faculty Publications

The manufacture of dice for tabletop games is a billion-dollar industry. In gaming circles and online forums, the concept of “cursed dice” is a popular topic. Dice are inherently unfair due to the difficulty of manufacturing them with perfect geometric tolerances and uniform material densities. A common method for testing dice fairness is the chi-square statistic, which is typically assumed to follow the chi-square distribution. However, this assumption is only asymptotically valid.

Exact distributions of the statistic can be computed for dice with few sides and a limited number of rolls—such as 2-sided (D2) and 4-sided (D4) dice—but the computational …

Graph Convolutional Networks Enable Fast Hemorrhagic Stroke Monitoring With Electrical Impedance Tomography, J. Toivanen, V. Kolehmainen, A. Paldanius, A. Hänninen, A. Hauptmann, Sarah J. Hamilton

Mathematical and Statistical Science Faculty Research and Publications

Objective: To develop a fast image reconstruction method for stroke monitoring with electrical impedance tomography with image quality comparable to computationally expensive nonlinear model-based methods. Methods: A post-processing approach with graph convolutional networks is employed. Utilizing the flexibility of the graph setting, a graph U-net is trained on linear difference reconstructions from 2D simulated stroke data and applied to fully 3D images from realistic simulated and experimental data. An additional network, trained on 3D vs. 2D images, is also considered for comparison. Results: Post-processing the linear difference reconstructions through the graph U-net significantly improved the image quality, resulting in images …

Some Results In Thermodynamic Formalism, C. Evans Hedges

Electronic Theses and Dissertations

This dissertation investigates several key questions at the intersection of dynamical systems, computability theory, and thermodynamic formalism. In the symbolic setting, we establish novel results regarding the statistical properties of equilibrium states, deriving bounds on probabilities of configurations and relating these bounds to the Gibbs property through the homoclinic relation. Additionally, we examine the computability of thermodynamic quantities such as pressure, ground state energy, and residual entropy. We show that topological pressure is computable from above for general subshifts and computable for strongly irreducible shifts, with similar results extending to ground state energy and residual entropy.

Extending beyond subshifts, we …

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 …

Ceno: Non-Uniform, Segment And Parallel Zero-Knowledge Virtual Machine, Tianyi Liu, Zhenfei Zhang, Yuncong Zhang, Wenqing Hu, Ye Zhang

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we explore a novel Zero-knowledge Virtual Machine (zkVM) framework leveraging succinct, non-interactive zero-knowledge proofs for verifiable computation over any code. Our approach divides the proof of program execution into two stages. In the first stage, the process breaks down program execution into segments, identifying and grouping identical sections. These segments are then proved through data-parallel circuits that allow for varying amounts of duplication. In the subsequent stage, the verifier examines these segment proofs, reconstructing the program's control and data flow based on the segments' duplication number and the original program. The second stage can be further attested …

Radiation-Induced Cardiotoxicity In Hypertensive Salt-Sensitive Rats: A Feasibility Study, Dayeong An, Alison Kriegel, Suresh N. Kumar, Heather A. Himburg, Brian Fish, S. Klawikowski, Daniel B. Rowe, Marek Lenarczyk, John Baker, El Sayed H. Ibrahim

Mathematical and Statistical Science Faculty Research and Publications

Radiation therapy (RT) plays a vital role in managing thoracic cancers, though it can lead to adverse effects, including significant cardiotoxicity. Understanding the risk factors like hypertension in RT is important for patient prognosis and management. A Dahl salt-sensitive (SS) female rat model was used to study hypertension effect on RT-induced cardiotoxicity. Rats were fed a high-salt diet to induce hypertension and then divided into RT and sham groups. The RT group received 24 Gy of whole-heart irradiation. Cardiac function was evaluated using MRI and blood pressure measurements at baseline, 8 weeks and 12 weeks post-RT. Histological examination was performed …

A Bayesian Approach To Grappa Parallel Fmri Image Reconstruction Increases Snr And Power Of Task Detection, Chase J. Sakitis, Daniel B. Rowe

Mathematical and Statistical Science Faculty Research and Publications

In fMRI, capturing brain activation during a task is dependent on how quickly k-space arrays are obtained. Acquiring full k-space arrays, which are reconstructed into images using the inverse Fourier transform (IFT), that make up volume images can take a considerable amount of scan time. Undersampling k-space reduces the acquisition time but results in aliased, or “folded,” images. GeneRalized Autocalibrating Partial Parallel Acquisition (GRAPPA) is a parallel imaging technique that yields full images from subsampled arrays of k-space. GRAPPA uses localized interpolation weights, which are estimated prescan and fixed over time, to fill in the missing …