A Copula Discretization Of Time Series-Type Model For Examining Climate Data, Dimuthu Fernando, Olivia Atutey, Norou Diawara

Mathematics & Statistics Faculty Publications

The study presents a comparative analysis of climate data under two scenarios: a Gaussian copula marginal regression model for count time series data and a copula-based bivariate count time series model. These models, built after comprehensive simulations, offer adaptable autocorrelation structures considering the daily average temperature and humidity data observed at a regional airport in Mobile, AL.

Bayesian Analyses For Time-Varying Data And Opinion Dynamics, Torin Quinlivan

Graduate Research Theses & Dissertations

We consider Bayesian analyses for time-varying data from the opinion dynamics in social networks and the processes of sensorimotor learning. Firstly, understanding the underlying opinions of social media users is a difficult process, as they must be understood filtered through the messages sent. To understand how to best estimate the latent opinions, we use a Bayesian approach to estimate various characteristics of the users and the network. We present a model for using Bayesian methods for this problem, along with a simulation study to demonstrate effectiveness. Secondly, incentivization with punishments or rewards may affect human skill learning. To investigate the …

Univariate Extreme Value Analysis Of Quantitative Investment Management, George Agbenyega Zumanu

Graduate Research Theses & Dissertations

The evolution of product development within the variable annuity (VA) business have sparked interest in quantitative investment management, particularly as most VA issuers have integrated volatility-controlled funds into their annuity portfolios. Despite the existence of empirical research on statistical analysis of extreme values in conventional investments, there has been a notable gap in research focus towards risk modeling in volatility-controlled funds.

This study contributes by analyzing and modeling the extreme values of investments in volatility-controlled funds, comparing them to conventional equity funds. The financial returns of S&P Dow Jones Indices (SPDJI) indices - SPXTR, risk control SPXT18UT, and managed risk …

Refining The Inverse Lipschitz Constant For Injective Relu Networks, Cole Rausch

Electronic Theses and Dissertations

In this thesis, we study the Inverse Lipschitz Constant (ILC) of injective ReLU layers. We study the tightness of the ILC lower bound established in Puthawala et al. Our approach has three components. First, we find that the conditions for injectivity on lines yield a weaker condition than the general condition given in Puthawala et al. Second, we perform numerical experiments to judge the tightness of the existing ILC lower bound and find that bound is overly conservative. Third, we identify the source of the potential slack in the proof of the existing ILC bound, and perform further numerical experiments …

Advanced Techniques In Time Series Forecasting: From Deterministic Models To Deep Learning, Xue Bai

Graduate Theses, Dissertations, and Problem Reports (ETD)

This dissertation discusses three instances of temporal prediction, applied to population dynamics and deep learning.

In population modeling, dynamic processes are frequently represented by systems of differential equations, allowing for the analysis of various phenomena. The first application explores modeling cloned hematopoiesis in chronic myeloid leukemia (CML) via a nonlinear system of differential equations. By tracking the evolution of different cell compartments, including cycling and quiescent stem cells, progenitor cells, differentiated cells, and terminally differentiated cells, the model captures the transition from normal hematopoiesis to the chronic and accelerated-acute phases of CML. Three distinct non-zero steady states are identified, representing …

Gwid: An R Package And Shiny Application For Genome-Wide Analysis Of Ibd Data, Soroush Mahmoudiandehkordi, Mehdi Maadooliat, Steven J. Schrodi

Mathematical and Statistical Science Faculty Research and Publications

Summary

Genome-wide identity by descent (gwid) is an R package developed for the analysis of identity-by-descent (IBD) data pertaining to dichotomous traits. This package offers a set of tools to assess differential IBD levels for the two states of a binary trait, yielding informative and meaningful results. Furthermore, it provides convenient functions to visualize the outcomes of these analyses, enhancing the interpretability and accessibility of the results. To assess the performance of the package, we conducted an evaluation using real genotype data derived from the SNPs to investigate rheumatoid arthritis susceptibility from the Marshfield Clinic Personalized Medicine Research Project.

Availability …

Self-Exciting Point Processes In Real Estate, Ian Fraser

Theses and Dissertations (Comprehensive)

This thesis introduces a novel approach to analyzing residential property sales through the lens of stochastic processes by employing point processes. Herein, property sales are treated as point patterns, using self-exciting point process models and a variety of statistical tools to uncover underlying patterns in the data. Key findings include the identification and explanation of clustering in both space and time, and the efficacy of a temporal Hawkes process with a sinusoidal background in predicting home sale occurrences. The temporal analysis starts by employing the state of art techniques for time series data like regression, autoregressive, and autoregressive integrated moving …

Multiscale Modelling Of Brain Networks And The Analysis Of Dynamic Processes In Neurodegenerative Disorders, Hina Shaheen

Theses and Dissertations (Comprehensive)

The complex nature of the human brain, with its intricate organic structure and multiscale spatio-temporal characteristics ranging from synapses to the entire brain, presents a major obstacle in brain modelling. Capturing this complexity poses a significant challenge for researchers. The complex interplay of coupled multiphysics and biochemical activities within this intricate system shapes the brain's capacity, functioning within a structure-function relationship that necessitates a specific mathematical framework. Advanced mathematical modelling approaches that incorporate the coupling of brain networks and the analysis of dynamic processes are essential for advancing therapeutic strategies aimed at treating neurodegenerative diseases (NDDs), which afflict millions of …

Development Of Probabilistic Dynamic Model Building And Bayesian Machine Learning Approaches, Samuel Oladayo Adeyemo

Graduate Theses, Dissertations, and Problem Reports (ETD)

Abstract

Development of Probabilistic Dynamic Model Building and Bayesian Machine Learning Approaches

Samuel Adeyemo

The recent years have seen a tremendous increase in the use of artificial intelligence (AI) and machine learning (ML) for the development of data-driven mathematical models needed for performing real-time optimization, model-based control, performance optimization, dynamic data reconciliation, and process performance monitoring. However, the development of data-driven models is faced with some challenges including lack of model interpretability, sensitivity of algorithm to noise in training data, limited extrapolation capabilities and violation of conservation laws. Drawing motivation from these existing gaps, this work aims to develop robust …

A Journey From Univariate To Multivariate Functional Time Series: A Comprehensive Review, Hossein Haghbin, Mehdi Maadooliat

Mathematical and Statistical Science Faculty Research and Publications

Functional time series (FTS) analysis has emerged as a potent framework for modeling and forecasting time-dependent data with functional attributes. In this comprehensive review, we navigate through the intricate landscape of FTS methodologies, meticulously surveying the core principles of univariate FTS and delving into the nuances of multivariate FTS. The journey commences with an exploration of the foundational aspects of univariate FTS analysis. We delve into representation, estimation, and modeling, spotlighting the effectiveness of various parametric and nonparametric models at our disposal. The stage then transitions to multivariate FTS analysis, where we confront the intricacies posed by high-dimensional data. We …

Maximizing The Number Of H-Colorings Of Graphs With A Fixed Minimum Degree, John Engbers

Mathematical and Statistical Science Faculty Research and Publications

For graphs G and H, an H-coloring of G is an adjacency-preserving map from the vertex set of G to the vertex set of H.

Reducing Food Scarcity: The Benefits Of Urban Farming, S.A. Claudell, Emilio Mejia

Journal of Nonprofit Innovation

Urban farming can enhance the lives of communities and help reduce food scarcity. This paper presents a conceptual prototype of an efficient urban farming community that can be scaled for a single apartment building or an entire community across all global geoeconomics regions, including densely populated cities and rural, developing towns and communities. When deployed in coordination with smart crop choices, local farm support, and efficient transportation then the result isn’t just sustainability, but also increasing fresh produce accessibility, optimizing nutritional value, eliminating the use of ‘forever chemicals’, reducing transportation costs, and fostering global environmental benefits.

Imagine Doris, who is …

Optimal Stopping And Related Topics, Jackson Scott Hebner

Honors Scholar Theses

Suppose we are observing a randomly evolving system and have the ability to freeze it at any time. If we want to maximize some function of the state of the system, how can we determine the best time to freeze the system based on observations only up until the present moment? That is, without seeing the future, how can we form a rule for stopping the system such that we optimize the expected value of the function of interest to us? This is an informal statement of the concept of optimal stopping, a topic with deep theory and numerous applications. …

A Nonparametric Test For Comparing Survival Functions Based On Restricted Distance Correlation, Quinyang Zhang

Mathematical Sciences Faculty Publications and Presentations

In this article, we propose an omnibus test for comparing two survival functions under non-proportional hazards. The test statistic is based on a product-limit estimate of the restricted distance correlation, which is closely related to the L₂ distance between survival curves. The strong consistency is established under mild regularity conditions. Our simulation studies show that the new test has satisfactory power under proportional hazard and various non-proportional hazards settings including delayed treatment effect, diminishing effect, and crossing survival curves; therefore, it can be a competitive alternative to the existing omnibus tests such as Kolmogorov-Smirnov test, Cramer-von Mises test, two-stage …

Wavelet Compression As An Observational Operator In Data Assimilation Systems For Sea Surface Temperature, Bradley J. Sciacca

LSU New Orleans Theses and Dissertations

The ocean remains severely under-observed, in part due to its sheer size. Containing nearly billion of water with most of the subsurface being invisible because water is extremely difficult to penetrate using electromagnetic radiation, as is typically used by satellite measuring instruments. For this reason, most observations of the ocean have very low spatial-temporal coverage to get a broad capture of the ocean’s features. However, recent “dense but patchy” data have increased the availability of high-resolution – low spatial coverage observations. These novel data sets have motivated research into multi-scale data assimilation methods. Here, we demonstrate a new assimilation approach …

Integrating Machine Learning Methods For Medical Diagnosis, Jazmin Quezada

Open Access Theses & Dissertations

Abstract:The rapid advancement of machine learning techniques has revolutionized the field of medical diagnosis by offering powerful tools to analyze complex data sets and make accurate predictions. In this proposed method, we present a novel approach that integrates machine learning and optimization models to enhance the accuracy of medical diagnoses. Our method focuses on fine-tuning and optimizing the parameters of machine learning algorithms commonly used in medical diagnosis, such as logistic regression, support vector machines, and neural networks. By employing optimization techniques, we systematically explore the parameter space of these algorithms to discover the most optimal configurations. Moreover, by representing …

Stochastic Optimal Control Of Conditional Mckean-Vlasov Equations With Jump And Markovian Switching, Charles Samuel Conly Sharp

Theses and Dissertations

This thesis obtains a number of results in stochastic optimal control for conditional McKean-Vlasov equations with jump and Markovian switching. First, we prove the uniqueness of the solutions and derive a relevant version of Itô's formula. We provide the dynamic programming principle and prove the associated verification theorem. A stochastic maximum principle is established. Further, we derive the relationship between dynamic programming and the stochastic maximum principle. Additionally, we utilize our stochastic maximum principle result for a mean-variance portfolio selection problem.

Aspects Of Stochastic Geometric Mechanics In Molecular Biophysics, David Frost

All Dissertations

In confocal single-molecule FRET experiments, the joint distribution of FRET efficiency and donor lifetime distribution can reveal underlying molecular conformational dynamics via deviation from their theoretical Forster relationship. This shift is referred to as a dynamic shift. In this study, we investigate the influence of the free energy landscape in protein conformational dynamics on the dynamic shift by simulation of the associated continuum reaction coordinate Langevin dynamics, yielding a deeper understanding of the dynamic and structural information in the joint FRET efficiency and donor lifetime distribution. We develop novel Langevin models for the dye linker dynamics, including rotational dynamics, based …

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 …

Using Gamification To Foster Student Resilience And Motivation To Learn, And Using Games To Teach Significance Testing Concepts In The Statistics Classroom, Todd Partridge

All Graduate Theses and Dissertations, Fall 2023 to Present

Two studies are outlined in this dissertation.

In the first study, elements of Super Mario Bros. videos games were used to change the way college students in a beginners’ statistics course were graded on their work. This was part of an effort to help students remain optimistic in the face of challenging coursework and even failure on assignments and tests. The study shows that the changes made to the grading structure did help students to keep trying and to use the materials given to them by their professor until they achieved their desired grade in the course, and suggests ways …

Langevin Dynamic Models For Smfret Dynamic Shift, David Frost, Keisha Cook Dr, Hugo Sanabria Dr

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Divisibility Probabilities For Products Of Randomly Chosen Integers, Noah Y. Fine

Rose-Hulman Undergraduate Mathematics Journal

We find a formula for the probability that the product of n positive integers, chosen at random, is divisible by some integer d. We do this via an inductive application of the Chinese Remainder Theorem, generating functions, and several other combinatorial arguments. Additionally, we apply this formula to find a unique, but slow, probabilistic primality test.

Reducing Uncertainty In Sea-Level Rise Prediction: A Spatial-Variability-Aware Approach, Subhankar Ghosh, Shuai An, Arun Sharma, Jayant Gupta, Shashi Shekhar, Aneesh Subramanian

I-GUIDE Forum

Given multi-model ensemble climate projections, the goal is to accurately and reliably predict future sea-level rise while lowering the uncertainty. This problem is important because sea-level rise affects millions of people in coastal communities and beyond due to climate change's impacts on polar ice sheets and the ocean. This problem is challenging due to spatial variability and unknowns such as possible tipping points (e.g., collapse of Greenland or West Antarctic ice-shelf), climate feedback loops (e.g., clouds, permafrost thawing), future policy decisions, and human actions. Most existing climate modeling approaches use the same set of weights globally, during either regression or …

Using Geographic Information To Explore Player-Specific Movement And Its Effects On Play Success In The Nfl, Hayley Horn, Eric Laigaie, Alexander Lopez, Shravan Reddy

SMU Data Science Review

American Football is a billion-dollar industry in the United States. The analytical aspect of the sport is an ever-growing domain, with open-source competitions like the NFL Big Data Bowl accelerating this growth. With the amount of player movement during each play, tracking data can prove valuable in many areas of football analytics. While concussion detection, catch recognition, and completion percentage prediction are all existing use cases for this data, player-specific movement attributes, such as speed and agility, may be helpful in predicting play success. This research calculates player-specific speed and agility attributes from tracking data and supplements them with descriptive …

The "Benfordness" Of Bach Music, Chadrack Bantange, Darby Burgett, Luke Haws, Sybil Prince Nelson

Journal of Humanistic Mathematics

In this paper we analyze the distribution of musical note frequencies in Hertz to see whether they follow the logarithmic Benford distribution. Our results show that the music of Johann Sebastian Bach and Johann Christian Bach is Benford distributed while the computer-generated music is not. We also find that computer-generated music is statistically less Benford distributed than human- composed music.

Math And Democracy, Kimberly A. Roth, Erika L. Ward

Journal of Humanistic Mathematics

Math and Democracy is a math class containing topics such as voting theory, weighted voting, apportionment, and gerrymandering. It was first designed by Erika Ward for math master’s students, mostly educators, but then adapted separately by both Erika Ward and Kim Roth for a general audience of undergraduates. The course contains materials that can be explored in mathematics classes from those for non-majors through graduate students. As such, it serves students from all majors and allows for discussion of fairness, racial justice, and politics while exploring mathematics that non-major students might not otherwise encounter. This article serves as a guide …

Stochastic Processes And Multi-Resolution Analysis: A Trigonometric Moment Problem Approach And An Analysis Of The Expenditure Trends For Diabetic Patients, Isaac Nwi-Mozu

Computational and Data Sciences (PhD) Dissertations

This dissertation is divided into two distinct parts. The main theme of the first part is to study stochastic processes (and related signal processing questions) using tools in wavelet analysis, functional analysis (we use in particular the trigonometric moment problem), the theory of realization of rational functions, and reproducing kernel Hilbert spaces. A novel form of multiresolution analysis is formulated in the discrete case that is used to study some stochastic processes. Using the trigonometric moment problem, we associate with a vector-valued wide-sense stationary process a multiresolution of a new kind. The notion of realization of rational functions was used …

Probabilistic Modeling Of Social Media Networks, Distinguishing Phylogenetic Networks From Trees, And Fairness In Service Queues, Md Rashidul Hasan

Mathematics & Statistics ETDs

In this dissertation, three primary issues are explored. The first subject exposes who-saw-from-whom pathways in post-specific dissemination networks in social media platforms. We describe a network-based approach for temporal, textual, and post-diffusion network inference. The conditional point process method discovers the most probable diffusion network. The tool is capable of meaningful analysis of hundreds of post shares. Inferred diffusion networks demonstrate disparities in information distribution between user groups (confirmed versus unverified, conservative versus liberal) and local communities (political, entrepreneurial, etc.). A promising approach for quantifying post-impact, we observe discrepancies in inferred networks that indicate the disproportionate amount of automated bots. …

Stressor: An R Package For Benchmarking Machine Learning Models, Samuel A. Haycock

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Many discipline specific researchers need a way to quickly compare the accuracy of their predictive models to other alternatives. However, many of these researchers are not experienced with multiple programming languages. Python has recently been the leader in machine learning functionality, which includes the PyCaret library that allows users to develop high-performing machine learning models with only a few lines of code. The goal of the stressor package is to help users of the R programming language access the advantages of PyCaret without having to learn Python. This allows the user to leverage R’s powerful data analysis workflows, while simultaneously …

An Interval-Valued Random Forests, Paul Gaona Partida

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

There is a growing demand for the development of new statistical models and the refinement of established methods to accommodate different data structures. This need arises from the recognition that traditional statistics often assume the value of each observation to be precise, which may not hold true in many real-world scenarios. Factors such as the collection process and technological advancements can introduce imprecision and uncertainty into the data.

For example, consider data collected over a long period of time, where newer measurement tools may offer greater accuracy and provide more information than previous methods. In such cases, it becomes crucial …