Statistics and Probability Commons^™

Computation Of Separate Ratio And Regression Estimator Under Neutrosophic Stratified Sampling: An Application To Climate Data, Abhishek Singh, Hemant Kulkarni, Florentin Smarandache, Gajendra K. Vishwakarma

Branch Mathematics and Statistics Faculty and Staff Publications

In this article, we introduce a novel approach by presenting separate ratio and regression estimators in the context of neutrosophic stratified sampling for the very first time, incorporating auxiliary variables. We have conducted a thorough analysis to estimate these newly proposed estimators' bias and mean square error (MSE) up to the first-order approximation. Theoretically using efficiency comparison criteria, our findings demonstrate the superior performance of these estimators compared to traditional unbiased estimators. Also, numerically based on real-life and artificial data, we have shown the supremacy of the neutrosophic stratified sampling over neutrosophic simple random sampling along with the supremacy of …

Numerical Investigation And Statistical Analysis Of The Flow Patterns Behind Square Cylinders Arranged In A Staggered Configuration Utilizing The Lattice Boltzmann Method, M. Abid, N. Yasin, M. Saqlain, S. Ul-Islam, S. Ahmad

Mathematics & Statistics Faculty Publications

Flow past bluff bodies like square cylinders is important in engineering applications, but flow patterns behind staggered cylinder arrangements remain poorly understood. Existing studies have focused on tandem or side-by-side configurations, while offset orientations have received less attention. The aim of this paper is to numerically investigate flow dynamics and force characteristics behind two offset square cylinders using the single relaxation time lattice Boltzmann method. The effects of changing both the Reynolds number (Re = 1-150) and gap spacing ratio (g* = 0.5-5) between the cylinders are analyzed. Instantaneous vorticity contours, time histories of drag and lift coefficients, power spectra …

Pitching The Use Of Squared And Interaction Terms In Regression Via Baseball Heat Maps, Lucas Chepelsky

Williams Honors College, Honors Research Projects

This project will examine the impact of using second-order terms in regression. For illustration, we use an example of regression where a baseball player's three by three heat map, including the height and distance from inside to outside of the pitch, are variables used to predict batting average. We find that second-order terms are crucial in discovering nonlinear relationships and interaction effects in regression models, and maintain that the common practice of using first-order additive models is insufficient.

To Mean Or Not To Mean: An Investigation Of Regression To The Mean, Hunter Ellis

Williams Honors College, Honors Research Projects

Regression to the mean is a statistical phenomenon that can hide important characteristics of what is truly happening in a research study. Caused by statistical randomness, regression to the mean occurs when extreme values, high or low, are followed by less extreme values. To correctly deal with it, one must understand what it is and how to distinguish its effect on conclusions made from the data. This paper provides examples of regression to the mean in both a medical and academic performance study and explains simple identifiers one can observe. Those are then followed up by the introduction of the …

Ensemble Classification: An Analysis Of The Random Forest Model, Jarod Korn

Williams Honors College, Honors Research Projects

The random forest model proposed by Dr. Leo Breiman in 2001 is an ensemble machine learning method for classification prediction and regression. In the following paper, we will conduct an analysis on the random forest model with a focus on how the model works, how it is applied in software, and how it performs on a set of data. To fully understand the model, we will introduce the concept of decision trees, give a summary of the CART model, explain in detail how the random forest model operates, discuss how the model is implemented in software, demonstrate the model by …

Climate Change's Effect On Flow Regime, Alexander Ialenti

Williams Honors College, Honors Research Projects

This project will test to see if there is a percent increase in non-perennial streams sampled from 2003-2021. Using data provided by The Cleveland Metroparks, sampling events will be separated by date, flow regime classification, and rain data. Current literature supports the claim that many perennial streams, streams that flow year-round, will become non-perennial streams over time. This shift is predicted to be caused by a change in rain patterns. Both the interval between rain events and the intensity of rainfall per event are predicted to increase. My hypothesis is that there will be an increase in the percentage of …

Multiple Imputation For Robust Cluster Analysis To Address Missingness In Medical Data, Arnold Harder, Gayla R. Olbricht, Godwin Ekuma, Daniel B. Hier, Tayo Obafemi-Ajayi

Mathematics and Statistics Faculty Research & Creative Works

Cluster Analysis Has Been Applied To A Wide Range Of Problems As An Exploratory Tool To Enhance Knowledge Discovery. Clustering Aids Disease Subtyping, I.e. Identifying Homogeneous Patient Subgroups, In Medical Data. Missing Data Is A Common Problem In Medical Research And Could Bias Clustering Results If Not Properly Handled. Yet, Multiple Imputation Has Been Under-Utilized To Address Missingness, When Clustering Medical Data. Its Limited Integration In Clustering Of Medical Data, Despite The Known Advantages And Benefits Of Multiple Imputation, Could Be Attributed To Many Factors. This Includes Methodological Complexity, Difficulties In Pooling Results To Obtain A Consensus Clustering, Uncertainty Regarding …

Statistical Modeling Of Bankruptcy Data, Andrew Elsfelder

Williams Honors College, Honors Research Projects

My project uses a dataset of bankrupt and non-bankrupt companies in Taiwan from 1999 to 2009. This data was collected from the Taiwan Economic Journal. The statistical methods I used to model the data are CHAID, CART, and logistic regression. The models created are tools that can predict if a company is bankrupt, or not-bankrupt based on other data about the company. I created multiple models for each of the methods to find the best model for each method. I then analyzed the output from each method. Lastly, I determined which model was the best for this data based on …

Tropical Fish Study In Tahiti, French Polynesia, Miranda Brainard, Caitlyn Swango, Paityn Houglan, Richard Londraville

Williams Honors College, Honors Research Projects

In May of 2023, I embarked on an exciting research journey to Moorea, French Polynesia, alongside fellow students and faculty members from the University of Akron and Syracuse University. This expedition was part of the university-sponsored Tropical Vertebrate Biology course, where we delved into the exploration of various tropical species inhabiting the island, including sea urchins, geckos, and my primary focus, the blackspotted rockskipper.

My research team, composed of my co-authors and me, was particularly intrigued by the unique refuge-seeking behavior displayed by blackspotted rockskippers. These amphibious fish are renowned for their remarkable ability to inhabit tide pools and rocky …

Regional Price Index 2023, Department Of Primary Industries And Regional Development, Western Australia

Statistics

The 2023 Regional Price Index (RPI) is the eleventh State Government Index contrasting the cost of a common basket of goods and services at a number of regional locations to the Perth metropolitan region. The RPI is used as the basis for the construction of the public sector district allowance, and by the private sector when considering remuneration packages for remotely located staff.

The RPI provides an insight into differences in regional consumer costs. The 2023 RPI basket of 185 goods and services was priced in 39 regional centres around Western Australia.

The 2023 RPI results show that, overall, prices …

Towards A More Engaged Democracy: Using Statistical Methods To Detect Election Fraud In The 2022 Philippine National Elections, Juan Miguel Cardaño, Bryan Patrick Mande, Seth William Tionko, Aldrich Ellis C. Asuncion, Jeric C. Briones

Mathematics Faculty Publications

This paper aims to show how citizens can further participate in the elections, aside from just voting. Given the accusations of fraud, this study demonstrates how existing election fraud detection methods can be used in the 2022 Philippine National Elections (PNE) context. Specifically, histograms known as 2D vote turnout distributions were first utilized to model the frequency of the winner's percentage of votes based on the voter turnout in each electoral unit, with key parameters introduced to detect fraud. Vote turnout distributions were then simulated using parametric models involving the aforementioned fraud parameters, with the goal of replicating the actual …

Bayesian Estimation Of Hierarchical Linear Models From Incomplete Data: Cluster-Level Non-Linear Effects And Small Sample Sizes, Dongho Shin

Theses and Dissertations

We consider Bayesian estimation of a hierarchical linear model (HLM) from small sample sizes. The continuous response Y and covariates C are partially observed and assumed missing at random. With C having linear effects, the HLM may be efficiently estimated by available methods. When C includes cluster-level covariates having interactive or other nonlinear effects given small sample sizes, however, maximum likelihood estimation is suboptimal, and existing Gibbs samplers are based on a Bayesian joint distribution compatible with the HLM, but impute missing values of C by a Metropolis algorithm via a proposal density having a constant variance while the target …

Multi-Omics Integrative Analysis For Incomplete Data Using Weighted P-Value Adjustment Approaches, Wenda Zhang, Zichen Ma, Yen Yi Ho, Shuyi Yang, Joshua Habiger, Hsin Hsiung Huang, Yufei Huang

Faculty Publications

The advancements in high-throughput technologies provide exciting opportunities to obtain multi-omics data from the same individuals in a biomedical study, and joint analyses of data from multiple sources offer many benefits. However, the occurrence of missing values is an inevitable issue in multi-omics data because measurements such as mRNA gene expression levels often require invasive tissue sampling from patients. Common approaches for addressing missing measurements include analyses based on observations with complete data or multiple imputation methods. In this paper, we propose a novel integrative multi-omics analytical framework based on p-value weight adjustment in order to incorporate observations with incomplete …

A Comparative Analysis Of A Family Of Advanced Iterative Optimization Methods In Nonlinear Regression, Tanmoy Kumar Debnath

College of Graduate Studies: Theses & Dissertations

Classical statistical supervised learning optimization techniques like the Gauss-Newton Iterative Method (GNIM), Weighted Gauss-Newton Iterative Method (WGNIM), Reweighted Gauss-Newton Iterative Method (RGNIM), and Levenberg-Marquart (LM) algorithm extend the nonlinear least squares method. The WGNIM improves model fitting by controlling heteroscedasticity in the linear and nonlinear models. A comparative analysis of the GNIM, WGNIM, RGNIM, and LM methods for fitting nonlinear models is presented. A step-wise diagnosis for structural multicollinearity in the reweighted linearized model is investigated via the Variance Inflation Factor (VIF) to determine variance inflation in the sequence of estimators for the model parameters. Under restricted multicollinearity levels in …

Accounting For Variability Due To Resampling Using Bootstrapping, Dipendra Phuyal

College of Graduate Studies: Theses & Dissertations

Bradley Efron (1979) introduced bootrapping. Typically a researcher is interested in studying a process which generates individuals. The collection of individuals the process has(actual) or could have (conceptual) generated is the population. The collection of conceptual members of the population is an uncountable collection. Hence, the population is anuncountable collection of individuals. The collection of individuals the process has generated (actual individuals) is representative of what the process can generate and will bereferred to as the representative sample. The size of this sample is a nonnegative integervalued random variable N which may be a constant random variable such as in …

Investigating Flash Flood Occurrence Using Negative Binomial Models In Maryland, United States Of America, Zainab O. Akinsemoyin

College of Graduate Studies: Theses & Dissertations

Globally, as extreme weather patterns intensify, flash floods have emerged as one of the most destructive and immediate environmental threats. In Maryland, flash floods are particularly concerning due to its diverse topography and increasing urban development, which exacerbates runoff and overwhelms drainage systems. The state has experienced significant flash flood events, highlighting the need for effective models to manage risks and inform mitigation strategies. While regression models such as the Negative Binomial (NB) and Zero-Inflated Negative Binomial (ZINB) are commonly used for count data analysis, their application to flash flood modeling in the USA, including regions like Maryland, remains limited …

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 …