Statistical Models Commons^™

A Novel Correction For The Multivariate Ljung-Box Test, Minhao Huang

Computational and Data Sciences (PhD) Dissertations

This research introduces an analytical improvement to the Multivariate Ljung-Box test that addresses significant deviations of the original test from the nominal Type I error rates under almost all scenarios. Prior attempts to mitigate this issue have been directed at modification of the test statistics or correction of the test distribution to achieve precise results in finite samples. In previous studies, focused on designing corrections to the univariate Ljung-Box, a method that specifically adjusts the test rejection region has been the most successful of attaining the best Type I error rates. We adopt the same approach for the more complex, …

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 …

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 …

Exploration And Statistical Modeling Of Profit, Caleb Gibson

Undergraduate Honors Theses

For any company involved in sales, maximization of profit is the driving force that guides all decision-making. Many factors can influence how profitable a company can be, including external factors like changes in inflation or consumer demand or internal factors like pricing and product cost. Understanding specific trends in one's own internal data, a company can readily identify problem areas or potential growth opportunities to help increase profitability.

In this discussion, we use an extensive data set to examine how a company might analyze their own data to identify potential changes the company might investigate to drive better performance. Based …

Nonparametric Derivative Estimation Using Penalized Splines: Theory And Application, Bright Antwi Boasiako

Doctoral Dissertations

This dissertation is in the field of Nonparametric Derivative Estimation using
Penalized Splines. It is conducted in two parts. In the first part, we study the L2
convergence rates of estimating derivatives of mean regression functions using penalized splines. In 1982, Stone provided the optimal rates of convergence for estimating derivatives of mean regression functions using nonparametric methods. Using these rates, Zhou et. al. in their 2000 paper showed that the MSE of derivative estimators based on regression splines approach zero at the optimal rate of convergence. Also, in 2019, Xiao showed that, under some general conditions, penalized spline estimators …

The Use Of Regularization To Detect Racial Inequities In Pay Equity Studies: An Empirical Study And Reflections On Regulation Methods, Christopher M. Peña

Electronic Theses and Dissertations

Since the late 1970s, multiple linear regression has been the preferred method for identifying discrimination in pay. An empirical study on this topic was conducted using quantitative critical methods. A literature review first examined conflicting views on using multiple linear regression in pay equity studies. The review found that multiple linear regression is used so prevalently in pay equity studies because the courts and practitioners have widely accepted it and because of its simplicity and ability to parse multiple sources of variance simultaneously. Commentaries in the literature cautioned about errors in model specification, the use of tainted variables, and the …

Bayesian Statistical Modeling Of Spatially Resolved Transcriptomics Data, Xi Jiang

Statistical Science Theses and Dissertations

Spatially resolved transcriptomics (SRT) quantifies expression levels at different spatial locations, providing a new and powerful tool to investigate novel biological insights. As experimental technologies enhance both in capacity and efficiency, there arises a growing demand for the development of analytical methodologies.

One question in SRT data analysis is to identify genes whose expressions exhibit spatially correlated patterns, called spatially variable (SV) genes. Most current methods to identify SV genes are built upon the geostatistical model with Gaussian process, which could limit the models' ability to identify complex spatial patterns. In order to overcome this challenge and capture more types …

Parameter Estimation For Normally Distributed Grouped Data And Clustering Single-Cell Rna Sequencing Data Via The Expectation-Maximization Algorithm, Zahra Aghahosseinalishirazi

Electronic Thesis and Dissertation Repository

The Expectation-Maximization (EM) algorithm is an iterative algorithm for finding the maximum likelihood estimates in problems involving missing data or latent variables. The EM algorithm can be applied to problems consisting of evidently incomplete data or missingness situations, such as truncated distributions, censored or grouped observations, and also to problems in which the missingness of the data is not natural or evident, such as mixed-effects models, mixture models, log-linear models, and latent variables. In Chapter 2 of this thesis, we apply the EM algorithm to grouped data, a problem in which incomplete data are evident. Nowadays, data confidentiality is of …

Statistical Inference On Lung Cancer Screening Using The National Lung Screening Trial Data., Farhin Rahman

Electronic Theses and Dissertations

This dissertation consists of three research projects on cancer screening probability modeling. In these projects, the three key modeling parameters (sensitivity, sojourn time, transition density) for cancer screening were estimated, along with the long-term outcomes (including overdiagnosis as one outcome), the optimal screening time/age, the lead time distribution, and the probability of overdiagnosis at the future screening time were simulated to provide a statistical perspective on the effectiveness of cancer screening programs. In the first part of this dissertation, a statistical inference was conducted for male and female smokers using the National Lung Screening Trial (NLST) chest X-ray data. A …

A Comparison Of Confidence Intervals In State Space Models, Jinyu Du

Statistical Science Theses and Dissertations

This thesis develops general procedures for constructing confidence intervals (CIs) of the error disturbance parameters (standard deviations) and transformations of the error disturbance parameters in time-invariant state space models (ssm). With only a set of observations, estimating individual error disturbance parameters accurately in the presence of other unknown parameters in ssm is a very challenging problem. We attempted to construct four different types of confidence intervals, Wald, likelihood ratio, score, and higher-order asymptotic intervals for both the simple local level model and the general time-invariant state space models (ssm). We show that for a simple local level model, both the …

Addressing The Impact Of Time-Dependent Social Groupings On Animal Survival And Recapture Rates In Mark-Recapture Studies, Alexandru M. Draghici

Electronic Thesis and Dissertation Repository

Mark-recapture (MR) models typically assume that individuals under study have independent survival and recapture outcomes. One such model of interest is known as the Cormack-Jolly-Seber (CJS) model. In this dissertation, we conduct three major research projects focused on studying the impact of violating the independence assumption in MR models along with presenting extensions which relax the independence assumption. In the first project, we conduct a simulation study to address the impact of failing to account for pair-bonded animals having correlated recapture and survival fates on the CJS model. We examined the impact of correlation on the likelihood ratio test (LRT), …

Optimizing Tumor Xenograft Experiments Using Bayesian Linear And Nonlinear Mixed Modelling And Reinforcement Learning, Mary Lena Bleile

Statistical Science Theses and Dissertations

Tumor xenograft experiments are a popular tool of cancer biology research. In a typical such experiment, one implants a set of animals with an aliquot of the human tumor of interest, applies various treatments of interest, and observes the subsequent response. Efficient analysis of the data from these experiments is therefore of utmost importance. This dissertation proposes three methods for optimizing cancer treatment and data analysis in the tumor xenograft context. The first of these is applicable to tumor xenograft experiments in general, and the second two seek to optimize the combination of radiotherapy with immunotherapy in the tumor xenograft …

Time Series Analysis Of Longitudinally Collected Standard Autoperimetry Data In Glaucoma Patients, Carlyn Childress

Honors College Theses

Glaucoma is a group of eye diseases in which damage gradually occurs to the optic nerve, which often leads to partial or complete loss of vision. As the second leading cause of blindness, there is no cure for glaucoma. Early detection and the tracking of its progression is key to managing the effects of glaucoma. Ordinary Least Squares Regression (OLSR), the most commonly used methodology for tracking glaucoma progression, is inappropriate as the longitudinally collected perimetry data from the glaucoma patients appears to be temporally correlated. Time series models, that account for temporal correlation, are better methods to analyze Mean …

On Partially Observed Tensor Regression, Dinara Miftyakhetdinova

Major Papers

Tensor data is widely used in modern data science. The interest lies in identifying and characterizing the relationship between tensor datasets and external covariates. These datasets, though, are often incomplete. An efficient nonconvex alternating updating algorithm proposed by J. Zhou et al. in the paper "Partially Observed Dynamic Tensor Response Regression" provides a novel approach. The algorithm handles the problem of unobserved entries by solving an optimization problem of a loss function under the low-rankness, sparsity, and fusion constraints. This analysis aims to understand in detail the proposed algorithms and their theoretical proofs with, potentially, dropping some of the assumptions …

The Impact Of Subjective Risk Analysis On Real Estate Prices In The Nisqually Region Following The 2001 Nisqually Earthquake, Ryan Espedal

All Master's Theses

Earthquakes are an environmental hazard that pose great risks to communities almost every day. With earthquakes, the main cause of concern is physical destruction of property, however, there are also psychological effects that are researched and discussed much less. In 2001, the Nisqually area of western Washington experienced a substantial earthquake that produced minimal physical damage but caused a significant decrease in real estate prices. Studying single-family homes from 1986-2012, this research utilizes hedonic property models to measure the change in consumer’s subjective risk calculations with reference to real estate purchases after the Nisqually earthquake, measure the relationship between earthquake …

The Birds And The Trees: Quantifying The Drivers Of Whitebark Pine Decline And Clark's Nutcracker Habitat Use In Glacier National Park, Vladimir Kovalenko

Graduate Student Theses, Dissertations, & Professional Papers

Whitebark pine (Pinus albicaulis), recently listed as threatened under the Endangered Species Act, is in steep decline in Glacier National Park, Montana, USA due to the non-native pathogen Cronartium ribicola, causal agent of the fatal disease white pine blister rust. A sample of the park’s population suggests that approximately 70 percent of whitebark pines have died, while 65 percent of the remaining trees are infected. Using landscape and climate variables, we show how geographic location, elevation, aspect, solar radiation, relative humidity, and snowpack interact with tree diameter to affect mortality, disease incidence, cone production, and regeneration. We also examine how …

Potential Alzheimer's Disease Plasma Biomarkers, Taylor Estepp

Theses and Dissertations--Epidemiology and Biostatistics

In this series of studies, we examined the potential of a variety of blood-based plasma biomarkers for the identification of Alzheimer's disease (AD) progression and cognitive decline. With the end goal of studying these biomarkers via mixture modeling, we began with a literature review of the methodology. An examination of the biomarkers with demographics and other health factors found evidence of minimal risk of confounding along the causal pathway from biomarkers to cognitive performance. Further study examined the usefulness of linear combinations of biomarkers, achieved via partial least squares (PLS) analysis, as predictors of various cognitive assessment scores and clinical …

Statistical Models For Decision-Making In Professional Soccer, Sean Hellingman

Theses and Dissertations (Comprehensive)

As soccer is widely regarded as the most popular sport in the world there is high interest in methods of improving team performances. There are many ways teams and individual athletes can influence their own performances during competition. This thesis focuses on developing statistical methodologies for improving competition-based decision-making for soccer so as to allow professional soccer teams to make better informed decisions regarding player selection and in-game decision-making.

To properly capture the dynamic actions of professional soccer, Markov chains with increasing complexity are proposed. These models allow for the inclusion of potential changes in the process caused by goals …

Network Intrusion Detection Using Deep Reinforcement Learning, Hamed T. Sanusi

Electronic Theses and Dissertations

This thesis delves into cybersecurity by applying Deep Reinforcement(DRL) Learning in network intrusion detection. One advantage of DRL is the ability to adapt to changing network conditions and evolving attack methods, making it a promising solution for addressing the challenges involved in intrusion detection. The thesis will also discuss the obstacles and benefits of using Classification methods for network intrusion detection and the need for high-quality training data. To train and test our proposed method, the NSL-KDD dataset was used and then adjusted by converting it from a multi-classification to a binary classification, achieved by joining all attacks into one. …

Modeling Growth And Stress Factors For Converted Silvopasture Systems In The Missouri Ozarks, Bailee N. Suedmeyer

MSU Graduate Theses

Silvopasture systems are becoming increasingly popular among sustainable agriculture ranchers, due to the increase in knowledge of benefits to the cattle and ability to grow cool season grasses beneath the canopy. This project focuses on the forest crop aspect of silvopasture systems from monitoring of the health of the trees over time to recommendations for thinning management to keep it functioning as viable silvopasture. The study site consists of five acres of upland hardwood forest area in Southern Missouri with 18 monumented fixed area plots. Arial and ground data was collected at each plot throughout the growing season, along with …

Statistical Intervals For Neural Network And Its Relationship With Generalized Linear Model, Sheng Yuan

Theses and Dissertations--Statistics

Neural networks have experienced widespread adoption and have become integral in cutting-edge domains like computer vision, natural language processing, and various contemporary fields. However, addressing the statistical aspects of neural networks has been a persistent challenge, with limited satisfactory results. In my research, I focused on exploring statistical intervals applied to neural networks, specifically confidence intervals and tolerance intervals. I employed variance estimation methods, such as direct estimation and resampling, to assess neural networks and their performance under outlier scenarios. Remarkably, when outliers were present, the resampling method with infinitesimal jackknife estimation yielded confidence intervals that closely aligned with nominal …

Towards Structured Planning And Learning At The State Fisheries Agency Scale, Caleb A. Aldridge

Theses and Dissertations

Inland recreational fisheries has grown philosophically and scientifically to consider economic and sociopolitical aspects (non-biological) in addition to the biological. However, integrating biological and non-biological aspects of inland fisheries has been challenging. Thus, an opportunity exists to develop approaches and tools which operationalize planning and decision-making processes which include biological and non-biological aspects of a fishery. This dissertation expands the idea that a core set of goals and objectives is shared among and within inland fisheries agencies; that many routine operations of inland fisheries managers can be regimented or standardized; and the novel concept that current information and operations can …

Statistical Methods For Modern Threats, Brandon Lumsden

All Dissertations

More than ever before, technology is evolving at a rapid pace across the broad spectrum of biological sciences. As data collection becomes more precise, efficient, and standardized, a demand for appropriate statistical modeling grows as well. Throughout this dissertation, we examine a variety of new age data arising from modern technology of the 21st century. We begin by employing a suite of existing statistical techniques to address research questions surrounding three medical conditions presenting in public health sciences. Here we describe the techniques used, including generalized linear models and longitudinal models, and we summarize the significant associations identified between research …

Learning Graphical Models Of Multivariate Functional Data With Applications To Neuroimaging, Jiajing Niu

All Dissertations

This dissertation investigates the functional graphical models that infer the functional connectivity based on neuroimaging data, which is noisy, high dimensional and has limited samples. The dissertation provides two recipes to infer the functional graphical model: 1) a fully Bayesian framework 2) an end-to-end deep model.

We first propose a fully Bayesian regularization scheme to estimate functional graphical models. We consider a direct Bayesian analog of the functional graphical lasso proposed by Qiao et al. (2019).. We then propose a regularization strategy via the graphical horseshoe. We compare both Bayesian approaches to the frequentist functional graphical lasso, and compare the …

Bayesian Methods For Graphical Models With Neighborhood Selection., Sagnik Bhadury

Electronic Theses and Dissertations

Graphical models determine associations between variables through the notion of conditional independence. Gaussian graphical models are a widely used class of such models, where the relationships are formalized by non-null entries of the precision matrix. However, in high-dimensional cases, covariance estimates are typically unstable. Moreover, it is natural to expect only a few significant associations to be present in many realistic applications. This necessitates the injection of sparsity techniques into the estimation method. Classical frequentist methods, like GLASSO, use penalization techniques for this purpose. Fully Bayesian methods, on the contrary, are slow because they require iteratively sampling over a quadratic …

Understanding Consumers' Use Experience On Electrically Heated Jacket: A Study On Online Review Using Topic Modeling, Md Nakib-Ul Hasan

LSU Doctoral Dissertations

The demand for heated jackets is anticipated to be fuelled by frequent temperature drops, severe winter weather, and increasing outdoor activities. Electrically heated jackets (EHJ) are primarily marketed through online distribution channels and expansion of online sales channels is expected to boost the global market. Consumers are increasingly relying on online reviews from other consumers to help them decide what to buy. Businesses also actively monitor and manage their online reviews to build trust in their brand and make it more likely that customers will buy. Traditional approaches for assessing customer behavior, such as market research surveys and focus groups, …

Dynamic Prediction For Alternating Recurrent Events Using A Semiparametric Joint Frailty Model, Jaehyeon Yun

Statistical Science Theses and Dissertations

Alternating recurrent events data arise commonly in health research; examples include hospital admissions and discharges of diabetes patients; exacerbations and remissions of chronic bronchitis; and quitting and restarting smoking. Recent work has involved formulating and estimating joint models for the recurrent event times considering non-negligible event durations. However, prediction models for transition between recurrent events are lacking. We consider the development and evaluation of methods for predicting future events within these models. Specifically, we propose a tool for dynamically predicting transition between alternating recurrent events in real time. Under a flexible joint frailty model, we derive the predictive probability of …

Statistical Methods For Personalized Treatment Selection And Survival Data Analysis Based On Observational Data With High-Dimensional Covariates., Don Ramesh Dinendra Sudaraka Tholkage

Electronic Theses and Dissertations

Due to the wide availability of functional data from multiple disciplines, the studies of functional data analysis have become popular in the recent literature. However, the related development in censored survival data has been relatively sparse. In Chapter 2, we consider the problem of analyzing time-to-event data in the presence of functional predictors. We develop a conditional generalized Kaplan Meier (KM) estimator that incorporates functional predictors using kernel weights and rigorously establishes its asymptotic properties. In addition, we propose to select the optimal bandwidth based on a time-dependent Brier score. We then carry out extensive numerical studies to examine the …

Advanced High Dimensional Regression Techniques, Yuan Yang

All Dissertations

This dissertation focuses on developing high dimensional regression techniques to analyze large scale data using both Bayesian and frequentist approaches, motivated by data sets from various disciplines, such as public health and genetics. More specifically, Chapters 2 and Chapter 4 take a Bayesian approach to achieve modeling and parameter estimation simultaneously while Chapter 3 takes a frequentist approach. The main aspects of these techniques are that they perform variable selection and parameter estimation simultaneously, while also being easily adaptable to large-scale data. In particular, by embedding a logistic model into traditional spike and slab framework and selecting of proper prior …

Impact Of Climate Oscillations/Indices On Hydrological Variables In The Mississippi River Valley Alluvial Aquifer., Meena Raju

Theses and Dissertations

The Mississippi River Valley Alluvial Aquifer (MRVAA) is one of the most productive agricultural regions in the United States. The main objectives of this research are to identify long term trends and change points in hydrological variables (streamflow and rainfall), to assess the relationship between hydrological variables, and to evaluate the influence of global climate indices on hydrological variables. Non-parametric tests, MMK and Pettitt’s tests were used to analyze trend and change points. PCC and Streamflow elasticity analysis were used to analyze the relationship between streamflow and rainfall and the sensitivity of streamflow to rainfall changes. PCC and MLR analysis …