Statistics and Probability Commons^™

Explainability In Deep Learning For Density Regression, Dalton James Oxford

Graduate Theses and Dissertations

Classical statistical methods focus on explainability and inferential power. Machine learning and deep learning can handle non-linear, high-dimensional data better than traditional methods. In modeling, a clear understanding and interpretation are essential to decision-making. Recent work in quantile regression and extreme modeling has begun to use deep learning due to its performance on high-dimensional, non-linear data. Semi-Parametric Quantile Regression (SPQR) is a nonparametric spline-based approach to quantile regression that estimates the conditional PDF and CDF of the response. Semi-Parametric Quantile Regression for Extremes (SPQRx) is a recent extension of SPQR that provides two features: out-of-sample estimation and accurate extreme-tailed estimation. …

Two Topics In Survival Analysis: Restricted Distance Covariance Test For Non-Proportional Hazard And A New Estimation For Dropout Rate, Ruizhe Yin

Graduate Theses and Dissertations

When treatment effects change over time, standard statistical methods, such as the log-rank test and the Cox proportional hazards model, may give misleading results. This dissertation presents the restricted distance covariance (rdcov) test, a nonparametric method that compares survival curves between groups within a chosen study period [0, τ] using right censored data. The statistic measures the dependence between pre-specified group labels and survival times using pairwise distances from Kaplan-Meier estimates. Our method does not rely on the proportional hazards assumption, and it equals zero only when survival functions are identical across groups. Thus, this test can be applied to …

Tree-Based Differential Item Functioning Detection Methods: Exploring Their Performance In Diverse Measurement Scenarios, Nana Amma Berko Asamoah

Graduate Theses and Dissertations

Despite the availability of numerous methods for detecting differential item functioning (DIF), the continued development and evaluation of innovative, data-driven approaches remains essential. Tree-based methods, in particular, represent a significant advancement in DIF detection. Unlike some traditional techniques, they can simultaneously screen multiple variables for DIF without discretizing continuous variables, and do not require the pre-specification of focal and reference groups; capabilities that are especially valuable in today’s diverse and multifaceted assessment contexts. However, research systematically examining the performance of these methods under realistic measurement conditions is limited. This dissertation, in three simulation studies, critically examines the robustness and practical …

Exploring Latent Mediation Through Bayesian Regularization Methods Of Lasso, Ridge, Horseshoe, Spike-And-Slab, Ethan Harris

Graduate Theses and Dissertations

Regularization is a powerful tool to combat overfitting and drive sparsity in complex models. Regularization was initially applied in regression modeling but has been increasingly utilized in structural equation modeling where its utility in identifying the essential components has helped improve modeling. As structural equation models have increased in complexity both in the number of indicators but also the number of latent factors, researchers have begun to investigate how applying Bayesian regularization to these systems can further push the limits on modeling complex models with limited sample sizes. One area where research is limited is the application of Bayesian regularizations …

Application Of Ordinal Regression Models To Acquired Stress Resistance In Wild Strains Of Saccharomyces Cerevisiae, Carson Stacy

Graduate Theses and Dissertations

This thesis explores the application of ordinal regression to the analysis of semi-quantitative growth assays often used when comparing fitness for different strains of the model yeast Saccharomyces cerevisiae. For stress survival assays, yeast stress resistance is measured using an ordered survival score that ranges from 0 (no growth) to 4 (confluent growth). Traditional approaches to analyze this type of data either treats data as a nominal categorical variable or as a continuous numerical variable. These approaches risk loss of information or violation of testing assumptions. In contrast, cumulative logit ordinal regression uses the information contained in the order …

Nonparametric Methods For Bayesian Community Detection In Complex Networks, Kedran Young

Graduate Theses and Dissertations

Network analysis is becoming an increasingly popular interdisciplinary area of study, with emerging interest in fields like sociology, biology, economics, and ecology. Within the niche of network analysis, capturing the community structure of a network is one important achievement that many statisticians have been working toward over recent decades. The most popular modeling technique for latent community detection is the Stochastic Block Model (SBM), which falls into the category of latent variable models and will serve as the baseline model throughout this thesis. SBM is widely regarded as the most effective community detection method as it detects latent community membership …

Latent Variable Dyadic Regression Models For Predicting Over/Under Bets In Sports Betting, Alexcia Trejo

Graduate Theses and Dissertations

This thesis explores the use of latent factor models to uncover hidden structures in pair wise outcomes derived from Over/Under betting markets in sports betting. Specifically, we implement and evaluate the Eigen model, a latent space model that represents dyadic data using node-specific vectors whose inner product govern edge probabilities. By modeling relationships between teams as adjacency matrices of binary outcomes, we investigate the extent to which the Eigen model captures both homophily, the tendency of similar teams to yield consistent betting results, and stochastic equivalence, where different teams exhibit indistinguishable patterns of Over/Under outcomes. A Bayesian formulation of the …

Comparison Of Statistical And Machine Learning Genomic Prediction Methods In Plant Breeding: Case Studies In Maize And Soybean, Igor Kuivjogi Fernandes

Graduate Theses and Dissertations

Plant breeding is essential to increase genetic gain and food production worldwide. This study was conducted to evaluate new ways to use machine learning (ML) to tackle plant breeding challenges, where two ideas were tested — the first chapter focuses on how to combine genetic and environmental data using ML to improve the prediction of maize grain yield in multi-environment trials, while the second chapter centers on how to couple feature selection of molecular markers with ML to enhance prediction of yield in soybean, and, in both cases, ML approaches were compared to well-established statistical methods greatly adopted by the …

Gan With Skip Patch Discriminator For Biological Electron Microscopy Image Generation, Nishith Ranjon Roy

Graduate Theses and Dissertations

GAN models have been successfully used for image generation in various sections such as real-life objects like human faces, cars, animal faces, landscapes, etc. This work focuses on biological electron microscopy (EM) image generation. Unlike other real-life objects, biological EM images are obtained through electron microscopy techniques to study biological specimens. Electron microscopy offers high resolution and magnification capabilities, making it a powerful tool for visualizing biological structures at the nanoscale. However, using GAN models for biological EM image generation poses challenges due to the complex and unique arrangements of biological structures and the sparse and asymmetrical patterns in EM …

Sparse Neural Network To Enhance Performance Under Limited Parameter Constraints., Nailah Rawnaq

Graduate Theses and Dissertations

Over the past decade, the widespread adoption of deep neural networks has been a breakthrough driven by significant computational advancements. Additionally, the number of parameters of those models is exponentially increasing for performing complex tasks and achieving better performance. However, in most practical cases, often there are constraints in the number of parameters due to limited resources in storage size and computational cost. Network pruning can lead to an optimal solution to this problem. In this thesis, I present supporting evidence to the hypothesis that higher sparsity leads to better performance for a convolution-based neural network. I perform performance studies …

Effects Of Measurement Error In Student Pre-Post Test Score On The Recovery Of The Estimates Of Teachers Value-Added Scores, Merlin J. Kamgue

Graduate Theses and Dissertations

Abstract Background: Value-added models (VAMs) are statistical tools used to gauge a teacher’s impact on student performance by analyzing standardized test scores. These models project students’ future performance based on past scores and compare the projection to actual outcomes, accounting for differences in student backgrounds. However, the standard error of measurement (SEM) inherent in all measurement tools is often overlooked in VAMs. Aims and Objectives: This study aims to investigate the impact of test reliability on teacher and school score estimates within a Bayesian framework. We will precisely manipulate the reliability of standardized tests by adjusting the standard error of …

Hierarchical Spatial Abundance Models For Migratory Shorebirds, Md Shahbaz Alam

Graduate Theses and Dissertations

Predicting the distribution and abundance of migratory shorebirds is crucial for effective conservation planning. This research applies hierarchical spatial models to predict counts and spatial variations of three shorebird species: Semipalmated sandpiper (sesa), Ruddy turnstone (rutu), and Whimbrel (whim). Different versions of the Poisson, Negative Binomial, and Hurdle regression models are employed to tackle specific data characteristics, such as overdispersion and excess zeros. Model comparisons are performed in terms of likelihood measures and cross-validation. The Hurdle model for sesa and rutu and the Negative Binomial model for whim effectively captured spatial patterns, highlighting potential hotspots. Mean predictive count further emphasized …

A Two-Part Validation Study Of The Sexual Minority Identity Emotion Scale, Henrietta Kadi Tettey-Tawiah

Graduate Theses and Dissertations

A number of existing studies indicate that there is some correlation between pride and shame and various behavioral health outcomes like anxiety, depression, and self-harm in the general population. Research also confirms that this relationship is true among sexual minorities as well. This study sets itself up to interrogate this assertion vis-à-vis sexual minority adolescents (SMAs). Consequently, confirmatory factor analysis (CFA) and differential item functioning (DIF) detection analysis were performed on the 35-item Sexual Minority Identity Emotion Scale (SMIES) for SMAs. A tree-based modeling technique, specifically conditional inference trees (CIT), was then employed to explore and make predictions about the …

Automatic Appraisals Of Houses, Sloan Scroggin

Graduate Theses and Dissertations

Multiple hedonic models and an automatic appraiser model were used to create a residential house’s estimated sales price. The goal is to use the limited data available to a REALTOR® to estimate the future sales price of a residential home without the aid of pictures of the property or viewing the physical property. The first model automates some of the actions of an appraiser by finding comparable sales based on proximity, based both on distance between houses and characteristics of the houses, and then calculating a weighted average price for an estimated sales price of future sales. If the model …

Bayesian Learning Of Spatiotemporal Source Distribution For Beached Microplastic In The Gulf Of Mexico, David Pojunas

Graduate Theses and Dissertations

Over the last several decades, plastic waste has gradually accumulated while slowly degrading in terrestrial and oceanic environments. Recently, there has been an increased effort to identify the possible sources of plastic to understand how they affect vulnerable beaches. This issue is of particular concern in the Gulf of Mexico due to the presence of oil, natural gas, and plastic production. In this thesis, we expand upon existing Bayesian plastic attribution models and develop a rigorous statistical framework to map observed beached microplastics to their sources. Within this framework, we combine Lagrangian backtracking simulations of floating particles using nurdle beaching …

Comparative Analysis Of Teacher Effects Parameters In Models Used For Assessing School Effectiveness: Value-Added Models & Persistence, Merlin J. Kamgue

Graduate Theses and Dissertations

Longitudinal measures for students have become increasingly popular to estimate the effects of individual teachers and schools. Value-added models are one of the approaches using longitudinal data to evaluate teachers and schools. In the value-added model (VAM) literature, many statistical approaches have been developed and used to estimate teacher or school effects on student learning. This study opted to use a Bayesian multivariate model for evaluating teacher effects. The generalized persistence models can handle longitudinal data, not vertically scaled, allowing for a below-par teacher’s effects correlation across test administrations. This study first generated longitudinal students’ test score data and used …

Analyses Of Effect Indices Across Single-Case Research Designs In Counseling, Cian L. Brown

Graduate Theses and Dissertations

Single case research design (SCRD) is a common methodology used across clinical disciplines to determine treatments effectiveness by comparing treatment conditions to baseline conditions in individual cases, usually among researchers working with smaller samples. Although popular within behavioral disciplines such as special education and behavioral analysis, studies have begun to emerge in counseling. However, guidance and current understanding of the use of SCRD in counseling is limited. A content analysis of counseling journals from 2003 to 2014 yielded only 7 studies using SCRD. In 2015, the flagship counseling journal, Journal of Counseling and Development, published a special issue on the …

Comparing Predictive Performance Of Garch And Stochastic Volatility Models, Swapnaneel Nath

Graduate Theses and Dissertations

This paper compares the predictive performance of two commonly used financial models, the Generalized Auto-Regressive Conditional Heteroskedasticity (GARCH) model, and the Stochastic Volatility model. Both techniques are used in the finance literature to model returns on an asset; the main difference between the two is that the former holds volatility as deterministic, whereas the latter treats it as a stochastic component. Three 10-year periods (2006-15, 2008-17, and 2010-19) of returns of the S&P-500 Index are used to train the two models. The parameter estimation is done using Hamiltonian Monte Carlo. Then, using Sequential Monte Carlo updates, returns for 2016, 2018, …

A Comparative Study Of Techniques For Non-Monotonic Dependence With Emphasis On Sensitivity To Sample Size, Noise Level And Computational Attributes, Fariha Tasnim

Graduate Theses and Dissertations

Evaluating association between variables is often of interest by many researchers. To serve this purpose, different association measures have been developed. However, type of relation between variables affects the degree of relationship. Hence, detection of the rela- tionship between variables is germane to measuring the correlation coefficient. With that mindset, here we explored six non-monotonic measure of association techniques and com- pared them with three classical approaches. Due to inconsistency in definition and range of different techniques, it is not feasible to compare the correlation estimates as their nature of variability differ. Therefore, we used permutation test based on Monte …

Characterization Of Public Opinion On Severity Of Mental Illness And Hiv Based On Individual Traits Using Hierarchical Multi-Category Probit Models, Md Moinul Ahsan

Graduate Theses and Dissertations

In this thesis, we focus on modeling categorical response variables from public opinion datasets. A hierarchical probit model was used to analyze these different variables. Particularly for multinomial data, we tried different covariate settings to see the model’s performance. For that purpose, we tried two different estimation techniques. The first algorithm uses identified parameters by fixing the first diagonal element of the covariance matrix at 1. The second algorithm uses one unidentifiable parameter and subsequently identifies the parameters by fixing the trace of the covariance matrix. The results from the simulation study confirm that the trace-restricted algorithm performs better with …

Effects Of Land Use On Soil Microbial Communities In Tropical Montane Forests Of Malaysian Borneo, Yang Kai Tang

Graduate Theses and Dissertations

Land use, such as logging and forest conversion to agriculture, can modify soil physicochemical and biological properties, and affect soil health. To understand how land use change can impact soil properties and canopy structure, we used a land use gradient in Malaysian Borneo consisting of six sites, including old growth forests, mixed forests, and agriculture fields. Specifically, we aimed to answer the following questions: (1) How do soil physicochemical properties vary across land use types? (2) Does bacterial diversity and composition vary across different land use types? (3) Does fungal diversity and composition vary across different land use types? We …

Efficient Hierarchical Space-Time Models For Large Areal Datasets With Application To Forest Inventory Mapping Using Remote Sensing Imagery, Md Kamrul Hasan Khan

Graduate Theses and Dissertations

The focus of this dissertation is development of a novel hierarchical framework, that can be used for predictive modeling of Forest Inventory and Analysis (FIA) data over large regions. This dissertation has two significant contributions. Based on a study region in north-central Wisconsin, we analyze satellite imagery, along with a sample of national forest inventory field plots, to monitor and predict changes in forest conditions over time. The auxiliary data from the satellite imagery of this region are relatively dense in space and time, and can be used to learn how forest conditions changed over that decade. However, these records …

Mle And Eap Methods For Estimating Ability Scores For Data Of Varying Sample Size And Item Length, Sahar Taji

Graduate Theses and Dissertations

In this research, the performance of two popular estimators, Maximum Likelihood Estimator(MLE) and Bayesian Expected a Posteriori (EAP) is studied and compared in estimating the latent ability score in an Item Response Theory (IRT) model. The 2-Parameter Logistic (2PL) IRT model which is characterized by difficulty and discrimination item parameters is used to estimate the latent ability scores. Several datasets are generated for variety of sample size and item length values. The Monte-Carlo simulation is used to analyze the performance of the estimators. Results show that MLE produces reliable results with low root mean square error (RMSE) across all datasets. …

Hypothesis Testing And Parameter Estimation In Mixture Cure Models For Cancer Survival Data, Mohammod Mahmudur Rahman

Graduate Theses and Dissertations

In oncology clinical trials, when a treatment is administered to the patient population, a certain subset of patients may respond to the treatment while the other does not. The positive responders with long-term survival are considered “statistically cured” and can be referred to as cured patients or long-term survivors. When a proportion of patients achieve long-term survival, the hazard functions of two arms (control vs. treatment) are no longer proportional. As a result, the traditional log-rank test, which is the most popular test to evaluate the effectiveness of a treatment in clinical trials, tends to lose its power. In this …

Ensemble Tree-Based Machine Learning For Imaging Data, Reza Iranzad

Graduate Theses and Dissertations

In particular medical imaging data, such as positron emission tomography (PET), computed tomography (CT), and fluorescence intravital microscopy (IVM), have become prevalent for use in a wide variety of applications, from diagnostic purposes, tracking diseases' progress, and monitoring the effectiveness of treatments to decision-making processes. The detailed information generated by medical imaging has enabled physicians to provide more comprehensive care. Although numerous machine learning algorithms, especially those used for imaging data, have been developed, dealing with unique structures in imaging data remained a big challenge. In this dissertation, we are proposing novel statistical tree-based methods with more efficient and more …

Hiding In Plain Sight: Accounting For Rate Heterogeneity In Trait Evolution Models, James Boyko

Graduate Theses and Dissertations

Within the last four decades, phylogenetic comparative methods have become the defacto method of analysis for comparative biologists. The availability of high-quality comparative datasets has been matched by an explosion of possible phylogenetic models. In large part, the efforts to increase the realism of phylogenetic comparative methods has been successful as evidenced by their widespread use. To this extensive literature, my contributions are modest. I have focused my dissertation work on two main themes. First, most phenotypic evolution is not independent of other phenotypes. Changes in a particular character may influence changes in another and modeling these characters in isolation …

Improving Computation For Hierarchical Bayesian Spatial Gaussian Mixture Models With Application To The Analysis Of Thz Image Of Breast Tumor, Jean Remy Habimana

Graduate Theses and Dissertations

In the first chapter of this dissertation we give a brief introduction to Markov chain Monte Carlo methods (MCMC) and their application in Bayesian inference. In particular, we discuss the Metropolis-Hastings and conjugate Gibbs algorithms and explore the computational underpinnings of these methods. The second chapter discusses how to incorporate spatial autocorrelation in linear a regression model with an emphasis on the computational framework for estimating the spatial correlation patterns.

The third chapter starts with an overview of Gaussian mixture models (GMMs). However, because in the GMM framework the observations are assumed to be independent, GMMs are less effective when …

The Effects Of Metronomic And Maximum-Tolerated Dose Chemotherapy In Colorectal Cancer Angiogenesis: A Combined Approach Using Endoscopic Diffuse Reflectance Spectroscopy And Mrna Expression, Ariel Isaac Mundo Ortiz

Graduate Theses and Dissertations

Colorectal cancer (CRC) continues to be one of the most incident and deadliest types of cancer worldwide. Chemotherapy has proven effective to reduce tumor burden for CRC patients, but there are several disadvantages associated with the use of mainstay maximtolerated dose (MTD) chemotherapeutic strategies. Metronomic chemotherapy (MET) has been developed as an alternative that addresses the shortcomings of maximum-tolerated dose chemotherapy but so far its effectiveness as a neoadjuvant strategy for CRC has not been explored.

This dissertation uses a combined optics and molecular biology approach (using diffuse reflectance spectroscopy and mRNA expression) to study the changes in angiogenesis and …

Multi-Trophic Biodiversity Increases With Increasing Structural Complexity Of Forest Canopy, Ayanna St. Rose

Graduate Theses and Dissertations

Understanding the effects of forest canopy structural complexity on multi-trophic diversity is critical for conserving biodiversity and managing land sustainably. But multi-trophic diversity is often ignored when making decisions about land management due to lack of cost- and time-effective methods to evaluate it. Here, we explored a new method based on widely available remote sensing data to quantify canopy structural complexity and its relationships with multi-trophic biodiversity at landscape scale using 32 forested sites of the National Ecological Observatory Network. We investigated the influence of vertical and horizontal structural complexity of forest canopy on multi-trophic (primary producers, herbivores (beetles), omnivores …

Posterior Predictive Model Checking Of The Hierarchical Rater Model, Nnamdi Chika Ezike

Graduate Theses and Dissertations

Fitting wrongly specified models to observed data may lead to invalid inferences about the model parameters of interest. The current study investigated the performance of the posterior predictive model checking (PPMC) approach in detecting model-data misfit of the hierarchical rater model (HRM). The HRM is a rater-mediated model that incorporates components of the polytomous item response theory (IRT) model, such as the partial credit model (PCM) and generalized partial credit model (GPCM), at the second level of the hierarchy, to model examinees’ responses to performance assessments. To date, the HRM has not been rigorously evaluated using PPMC techniques. Monte Carlo …