Statistics and Probability Commons^™

Classification In Supervised Statistical Learning With The New Weighted Newton-Raphson Method, Toma Debnath

College of Graduate Studies: Theses & Dissertations

In this thesis, the Weighted Newton-Raphson Method (WNRM), an innovative optimization technique, is introduced in statistical supervised learning for categorization and applied to a diabetes predictive model, to find maximum likelihood estimates. The iterative optimization method solves nonlinear systems of equations with singular Jacobian matrices and is a modification of the ordinary Newton-Raphson algorithm. The quadratic convergence of the WNRM, and high efficiency for optimizing nonlinear likelihood functions, whenever singularity in the Jacobians occur allow for an easy inclusion to classical categorization and generalized linear models such as the Logistic Regression model in supervised learning. The WNRM is thoroughly investigated …

Utility In Time Description In Priority Best-Worst Discrete Choice Models: An Empirical Evaluation Using Flynn's Data, Sasanka Adikari, Norou Diawara

Mathematics & Statistics Faculty Publications

Discrete choice models (DCMs) are applied in many fields and in the statistical modelling of consumer behavior. This paper focuses on a form of choice experiment, best-worst scaling in discrete choice experiments (DCEs), and the transition probability of a choice of a consumer over time. The analysis was conducted by using simulated data (choice pairs) based on data from Flynn's (2007) 'Quality of Life Experiment'. Most of the traditional approaches assume the choice alternatives are mutually exclusive over time, which is a questionable assumption. We introduced a new copula-based model (CO-CUB) for the transition probability, which can handle the dependent …

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.

Scalar-On-Function Regression: Estimation And Inference Under Complex Survey Designs, Ekaterina Smirnova, Erjia Cui, Lucia Tabacu, Andrew Leroux

Mathematics & Statistics Faculty Publications

Increasingly, large, nationally representative health and behavioral surveys conducted under a multistage stratified sampling scheme collect high dimensional data with correlation structured along some domain (eg, wearable sensor data measured continuously and correlated over time, imaging data with spatiotemporal correlation) with the goal of associating these data with health outcomes. Analysis of this sort requires novel methodologic work at the intersection of survey statistics and functional data analysis. Here, we address this crucial gap in the literature by proposing an estimation and inferential framework for generalizable scalar-on-function regression models for data collected under a complex survey design. We propose to: …

Assessing The Utility Of Breast Cancer Polygenic Risk Scores And Association With Clinical Factors In A Population Of Breast Cancer Patients, John L. Slunecka

Dissertations and Theses

INTRODUCTION: Breast cancer (BC) is the most common cancer among women and is classified as a complex disease. Advances in population genomics have led to the development of polygenic risk scores (PRSs) with the potential to enhance current risk models, but replication is often limited. OBJECTIVE: We sought to assess the predictive capabilities of two high-powered BC PRSs in a sample population selected for breast cancer. In addition, the capacity of the PRSs to predict clinical variables that could improve BC screening and treatments was explored. METHODS: Two published PRS algorithms (313 vs 3820) were used to score female subjects …

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 …

The Effects Of Bureaucratic Corruption On The Financial Constraints Of Nigerian Small Businesses, Obinna Franklin Ezeibekwe

Graduate Research Theses & Dissertations

In this paper, I conduct the first empirical analysis to examine the impact of bureaucratic corruption on small business financial constraints in Nigeria. This study is also the first to compare the average treatment effect (ATE) with the local average treatment effect (LATE) framework to account for potential variations in treatment effects for small Nigerian firms with less than 100 employees. Using the bivariate probit method and two binary instruments, I find that corruption significantly increases the likelihood of financial constraints for a typical micro, small, and medium enterprise (MSME) by approximately 64 to 68 percentage points. When I use …

Optimizing Sports Outcome Prediction Through Feature Engineering And Machine Learning, Vitor S. Freitas

Graduate Theses/Dissertations

The challenge of predicting the outcome of a team game lies in the high complexity and dynamics of the sports data. This thesis focuses on the aspect of using feature engineering and the genetic algorithm to predict the winner and the score of various sports events. Generally, it deals with how machine learning algorithms are combined with state-of-the-art feature engineering techniques in sports datasets derived from various sports disciplines. In this thesis, five different machine learning models have been applied, classification and regression trees (CART), random forest (RF), stochastic gradient boosting (SGB), eXtreme gradient boosting (XGBoost), and extreme learning machine …

A Bayesian Inversion For Emissions And Export Productivity Across The End-Cretaceous Boundary, Alexander A. Cox

Dartmouth College Master’s Theses

The end-Cretaceous mass extinction was marked by both the Chicxulub impact and the ongoing emplacement of the Deccan Traps flood basalt province. Both of these events perturbed the environment by the emission of climate-active volatiles, primarily CO2 and SO2. To understand the mechanism of extinction, we must disentangle the timing, duration, and intensity of volcanic and meteoritic environmental forcings. In this thesis, we used a parallel Markov chain Monte Carlo approach to invert for the aforementioned volatile emissions, export productivity, and remineralization from 67 to 65 million years ago using the LOSCAR (Long-term Ocean-atmosphere-Sediment CArbon cycle Reservoir) model. The parallel …

Title: I: L1-Norm Matrix Completion For Recommender Systems Ii: Conjecturing-Based Classification, Fatemeh Valizadeh Gamchi

Theses and Dissertations

Recommendation systems are essential for providing personalized user experiences, but their performance can be affected by outliers especially in traditional collaborative filtering methods that use the L2-norm. To address this challenge, we developed two new algorithms, SharpEl1rs and SharpEl1rs-Impute, based on the L1-norm to improve resistance against extreme values and effectively handle missing data. Our experimental setting was designed to compare these proposed methods with existing techniques. Then our algorithms are applied to real datasets to assess their performance, with findings indicating that our proposed models offer improved accuracy in some cases and solid performance in others for industrial-scale recommendation …

Redesign, Evaluation, And Validation Of A Commercially Viable High-Resolution Melt Based Mixture Screening Tool, Chastyn Smith

Theses and Dissertations

Analysis of evidentiary samples containing DNA from multiple contributors (“mixtures”) is a time intensive process for a forensic analyst and one where the contributor nature of a sample is not revealed until the end of the traditional forensic workflow. Often, at this stage, retesting or additional testing of mixture samples may not be possible, particularly if the DNA collection device did not preserve the DNA well enough; consequently leaving only trace amounts of a contributor’s DNA present. Thus, a new collection device that would allow for the increased preservation/integrity of evidentiary samples as well as a method that would allow …

The Genetic Architecture Of Cervical Change During Pregnancy: From Modeling To Mechanism — Does The Cervix Mediate Maternal Risk For Spontaneous Preterm Birth?, Hope M. Wolf

Theses and Dissertations

This project leverages clinical data and biospecimens from a prospective longitudinal cohort of pregnant women to study the genetic and phenotypic relationships between cervical shortening and the duration of pregnancy. Sonographic cervical length (CL) was measured throughout pregnancy in a cohort of 5,160 Black/African American women in Detroit, Michigan. Maternal DNA samples were sequenced with a next-generation low-pass whole genome platform. The heritability of cervical change during pregnancy and its genetic correlation with gestational age at delivery (GAD) were estimated using Genome-Wide Complex Trait Analysis. These estimates suggest that cervical change is heritable (h²CL = 51%) and highly polygenic trait. …

Applications Of Shape Analysis, Yang Zhang

Graduate Research Theses & Dissertations

Shape analysis is a field of Statistics focused on analyzing and understanding the shape or the geometric properties of objects. We utilize the Bayesian circular cubic smoothing splines to estimate the shapes and introduce a rotation-based alignment method. A simulation study investigates the effect of shape alignment. As an application, we estimate the shapes of hourly crime rates in urban centers across the United States and compare the aligned shapes for different types and locations of crimes. In addition, we apply the proposed shape estimation with alignment to the survival analysis for the length of hospitalization of COVID-19 patients in …

Forecasting The One Month Ahead Joint Distribution Of The Carhart Four Factor Model Using A Copula Method, Michael Nebor

Graduate Research Theses & Dissertations

The Fama and French created factors of Market minus Risk Free (Mkt-RF), Small minusBig (SMB), High minus Low (HML), and the Carhart developed factor of Momentum (MOM) are frequently used together as a four factor model to explain the variation in returns of financial equities. This paper analyzes the joint distribution of these factors by forecasting the one month ahead joint distribution using various copula based methods. The VaR quantiles are calculated throughout the forecasted distribution at the .01, .05, .25, .50, .75, .95, and .99 quantiles. The forecasted distributions are compared against each other by analyzing the exceedances of …

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 …

Gmm And Asset Pricing Model, Yuzhou Liu

Graduate Research Theses & Dissertations

The traditional two-pass regression to estimate risk premium has shortcomings. To get the correct asymptotic standard errors, we need to estimate both time-series regressions and cross-sectional regressions simultaneously. The Generalized Method of Moments (GMM) effectively addresses this issue by its nature fit of asset pricing model. In this paper, I re-examine the risk premium of Carhart’s four-factor model by integrating time-series and cross-sectional regressions within the GMM framework, which enhances the accuracy and reliability of the risk premium estimates.

Influence Of Attack Performance On The Ovc Volleyball Regular Seasons 2022 & 2023, Ignacio Valdemoros

Masters Theses

Understanding the outcome of volleyball games is necessary for coaches before, after, and during a season. There are several ways to gain this understanding, but statistical analysis is fundamental to see the minimum patterns of behavior that influence wins and losses in Volleyball. Furthermore, this analysis helps identify the optimal approach to achieving a goal and determining the most effective alternative to success. Scoring points in Volleyball involves three key skills: serving, blocking, and attacking. Among these skills, attacking plays the most relevant role in determining the outcome of a match. The position on the court (e.g. Outside Hitter, Middle …

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 …

The Geometry Of Dynamic Time-Dependent Best-Worst Choice Pairs, Sasanka Adikari, Norou Diawara, Haim Bar

Mathematics & Statistics Faculty Publications

There has been increasing interest in best–worst discrete choice experiments (BWDCEs) in health economics, transportation research, and other fields over the last few years. BWDCEs have distinct advantages compared to other measurement approaches in discrete choice experiments (DCEs). A systematic study of best–worst (BW) choice pairs can be traced back to the 1990s. Recently, new ideas have been introduced to the subject. Calculating utility helps measure the attractiveness of BW choices. The goal of this paper is twofold. First, we extend the idea of the BW choice pair to include dynamic, time-dependent transition probability and capture utility at each time …

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 …