Statistics and Probability Commons^™

The Distribution Of The Significance Level, Paul O. Monnu

Electronic Theses and Dissertations

Reporting the p-value is customary when conducting a test of hypothesis or significance. The likelihood of getting a fictitious second sample and presuming the null hypothesis is correct is the p-value. The significance level is a statistic that interests us to investigate. Being a statistic, it has a distribution. For the F-test in a one-way ANOVA and the t-tests for population means, we define the significance level, its observed value, and the observed significance level. It is possible to derive the significance level distribution. The t-test and the F-test are not without controversy. Specifically, we demonstrate that as sample size …

Microplate-Like Metal Pyrophosphate Engineered On Ni-Foam Towards Multifunctional Electrode Material For Energy Conversion And Storage, Rishabh Srivastava

Electronic Theses & Dissertations

High clean energy demand, dire need for sustainable development, and low carbon footprints are the few intuitive challenges, leading researchers to aim for research and development for high-performance energy devices. The development of materials used in energy devices is currently focused on enhancing the performance, electronic properties, and durability of devices. Tunning the attributes of transition metals using pyrophosphate (P₂O₇) ligand moieties can be a promising approach to meet the requirements of energy devices such as water electrolyzers and supercapacitors, although such a material’s configuration is rarely exposed for this purpose of study.

Herein, we grow …

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 …

The Private Pilot Check Ride: Applying The Spacing Effect Theory To Predict Time To Proficiency For The Practical Test, Michael Scott Harwin

Theses and Dissertations

This study examined the relationship between a set of targeted factors and the total flight time students needed to become ready to take the private pilot check ride. The study was grounded in Ebbinghaus’s (1885/1913/2013) forgetting curve theory and spacing effect, and Ausubel’s (1963) theory of meaningful learning. The research factors included (a) training time to proficiency, which represented the number of training days needed to become check-ride ready; (b) flight training program (Part 61 vs. Part 141); (c) organization offering the training program (2- or 4-year college/university vs. FBO); (d) scheduling policy (mandated vs. student-driven); and demographical variables, which …

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 …

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), …

High-Dimensional Variable Selection Via Knockoffs Using Gradient Boosting, Amr Essam Mohamed

Dissertations

As data continue to grow rapidly in size and complexity, efficient and effective statistical methods are needed to detect the important variables/features. Variable selection is one of the most crucial problems in statistical applications. This problem arises when one wants to model the relationship between the response and the predictors. The goal is to reduce the number of variables to a minimal set of explanatory variables that are truly associated with the response of interest to improve the model accuracy. Effectively choosing the true influential variables and controlling the False Discovery Rate (FDR) without sacrificing power has been a challenge …

High Dimensional Data Analysis: Variable Screening And Inference, Lei Fang

Theses and Dissertations--Statistics

This dissertation focuses on the problem of high dimensional data analysis, which arises in many fields including genomics, finance, and social sciences. In such settings, the number of features or variables is much larger than the number of observations, posing significant challenges to traditional statistical methods.

To address these challenges, this dissertation proposes novel methods for variable screening and inference. The first part of the dissertation focuses on variable screening, which aims to identify a subset of important variables that are strongly associated with the response variable. Specifically, we propose a robust nonparametric screening method to effectively select the predictors …

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. …

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 …

Functional Data Analysis Of Covid-19, Nichole L. Fluke

Mathematics & Statistics ETDs

This thesis deals with Functional Data Analysis (FDA) on COVID data. The Data involves counts for new COVID cases, hospitalized COVID patients, and new COVID deaths. The data used is for all the states and regions in the United States. The data starts in March 1^st, 2020 and goes through March 31^st, 2021. The FDA smooths the data and looks to see if there are similarities or differences between the states and regions in the data. The data also shows which states and regions stand out from the others and which ones are similar. Also shown …

Statistical Roles Of The G-Expectation Framework In Model Uncertainty: The Semi-G-Structure As A Stepping Stone, Yifan Li

Electronic Thesis and Dissertation Repository

The G-expectation framework is a generalization of the classical probability system based on the sublinear expectation to deal with phenomena that cannot be described by a single probabilistic model. These phenomena are closely related to the long-existing concern about model uncertainty in statistics. However, the distributions and independence in the G-framework are quite different from the classical setup. These distinctions bring difficulty when applying the idea of this framework to general statistical practice. Therefore, a fundamental and unavoidable problem is how to better understand G-version concepts from a statistical perspective.

To explore this problem, this thesis establishes a new substructure …

Bayesian Estimation Of The Intensity Function Of A Non-Homogeneous Poisson Process, James Jensen

Theses

In this paper we explore Bayesian inference and its application to the problem of estimating the intensity function of a non-homogeneous Poisson process. These processes model the behavior of phenomena in which one or more events, known as arrivals, occur independently of one another over a certain period of time. We are concerned with the number of events occurring during particular time intervals across several realizations of the process. We show that given sufficient data, we are able to construct a piecewise-constant function which accurately estimates the mean rates on particular intervals. Further, we show that as we reduce these …

To Logit Or Not To Logit Data In The Unit Interval: A Simulation Study, Kayode Idris Hamzat

Major Papers

In this paper, we recommend a mechanism for determining whether to logit or not to logit data in the unit interval which is based on quantile estimation of data between 0 and 1. By using a simulated dataset generated from a Beta regression model, the estimated quantile for this model perform better than those based on the linear quantile regression with logit transformation.

Further, we investigate the performance of the quantile regression estimators based on the LQR and we conclude that it is better than those based on the Beta regression when the distribution is contaminated with 10% uniform numbers …

New Developments On The Estimability And The Estimation Of Phase-Type Actuarial Models, Cong Nie

Electronic Thesis and Dissertation Repository

This thesis studies the estimability and the estimation methods for two models based on Markov processes: the phase-type aging model (PTAM), which models the human aging process, and the discrete multivariate phase-type model (DMPTM), which can be used to model multivariate insurance claim processes.

The principal contributions of this thesis can be categorized into two areas. First, an objective measure of estimability is proposed to quantify estimability in the context of statistical models. Existing methods for assessing estimability require the subjective specification of thresholds, which potentially limits their usefulness. Unlike these methods, the proposed measure of estimability is objective. In …

How Blockchain Solutions Enable Better Decision Making Through Blockchain Analytics, Sammy Ter Haar

Information Systems Undergraduate Honors Theses

Since the founding of computers, data scientists have been able to engineer devices that increase individuals’ opportunities to communicate with each other. In the 1990s, the internet took over with many people not understanding its utility. Flash forward 30 years, and we cannot live without our connection to the internet. The internet of information is what we called early adopters with individuals posting blogs for others to read, this was known as Web 1.0. As we progress, platforms became social allowing individuals in different areas to communicate and engage with each other, this was known as Web 2.0. As Dr. …

Advancements In Gaussian Process Learning For Uncertainty Quantification, John C. Nicholson

All Dissertations

Gaussian processes are among the most useful tools in modeling continuous processes in machine learning and statistics. The research presented provides advancements in uncertainty quantification using Gaussian processes from two distinct perspectives. The first provides a more fundamental means of constructing Gaussian processes which take on arbitrary linear operator constraints in much more general framework than its predecessors, and the other from the perspective of calibration of state-aware parameters in computer models. If the value of a process is known at a finite collection of points, one may use Gaussian processes to construct a surface which interpolates these values to …

Aberrant Responding With Underlying Dominance And Unfolding Response Processes: Examining Model Fit And Performance Of Person-Fit Statistics, Jennifer A. Reimers

Graduate Theses and Dissertations

Researchers have recognized that respondents may not answer items in a way that accurately reflects their attitude or trait level being measured. The resulting response data that deviates from what would be expected has been shown to have significant effects on the psychometric properties of a scale and analytical results. However, many studies that have investigated the detection of aberrant data and its effects have done so using dominance item response theory (IRT) models. It is unknown whether the impacts of aberrant data and the methodology used to identify aberrant responding when using dominance IRT models apply similarly when scales …

Early-Warning Alert Systems For Financial-Instability Detection: An Hmm-Driven Approach, Xing Gu

Electronic Thesis and Dissertation Repository

Regulators’ early intervention is crucial when the financial system is experiencing difficulties. Financial stability must be preserved to avert banks’ bailouts, which hugely drain government's financial resources. Detecting in advance periods of financial crisis entails the development and customisation of accurate and robust quantitative techniques. The goal of this thesis is to construct automated systems via the interplay of various mathematical and statistical methodologies to signal financial instability episodes in the near-term horizon. These signal alerts could provide regulatory bodies with the capacity to initiate appropriate response that will thwart or at least minimise the occurrence of a financial crisis. …

Confidence Interval For The Mean Of A Beta Distribution, Sean Rangel

Electronic Theses and Dissertations

Statistical inference for the mean of a beta distribution has become increasingly popular in various fields of academic research. In this study, we developed a novel statistical model from likelihood-based techniques to evaluate various confidence interval techniques for the mean of a beta distribution. Simulation studies will be implemented to compare the performance of the confidence intervals. In addition to the development and study involving confidence intervals, we will also apply the confidence intervals to real biological data that was gathered by the Department of Biology at Stephen F. Austin State University and provide recommendations on the best practice.

Model-Free Descriptive Modeling For Multivariate Categorical Data With An Ordinal Dependent Variable, Li Wang

Doctoral Dissertations

In the process of statistical modeling, the descriptive modeling plays an essential role in accelerating the formulation of plausible hypotheses in the subsequent explanatory modeling and facilitating the selection of potential variables in the subsequent predictive modeling. Especially, for multivariate categorical data analysis, it is desirable to use the descriptive modeling methods for uncovering and summarizing the potential association structure among multiple categorical variables in a compact manner. However, many classical methods in this case either rely on strong assumptions for parametric models or become infeasible when the data dimension is higher. To this end, we propose a model-free method …

Upper-Sided Ewma-Based Distribution-Specific Tolerance Limits, Owen Visser

UNF Graduate Theses and Dissertations

Tolerance limits are constructed from sample data to ascertain if a proportion of a process is within specification limits. There exists multiple methods of calculating the sample size requirements for tolerance limits under various assumptions. In this research, a distribution-specific algorithm that utilizes the exponentially weighted moving average technique (EWMA), first introduced by Sa and Razaila (2004), is reconstructed. The algorithm is used to calculate the required sample sizes for continuous construction of upper-sided tolerance limits. The sample sizes and intervals constructed from them are compared to three existing methods for various distributions. The distribution-specific algorithm was observed to reduce …

Bias Of Rank Correlation Under A Mixture Model, Russell Land

Electronic Theses and Dissertations

This thesis project will analyze the bias in mixture models when contaminated data is present. Specifically, we will analyze the relationship between the bias and the mixing proportion, p, for the rank correlation methods Spearman’s Rho and Kendall’s Tau. We will first look at the history of the two non-parametric rank correlation methods and the sample and population definitions will be introduced. Copulas will be introduced to show a few ways we can define these correlation methods. After that, mixture models will be defined and the main theorem will be stated and proved. As an example, we will apply this …

Use Of Research Tradition And Design In Program Evaluation: An Explanatory Mixed Methods Study Of Practitioners’ Methodological Choices, Margaret Schultz Patel

Electronic Theses and Dissertations

The goal of this explanatory sequential mixed method study was to assess whether there were observable trends, associations, or group differences in evaluation methodology by settings and content area in published evaluations from the past ten years (quantitative), to illuminate how evaluation practitioners selected these methodologies (qualitative), and assess how emergent findings from each phase fit together or helped contextualize each other. In this study, methodology was operationalized as research tradition and method was operationalized as research design. For phase one (quantitative), a systematized ten-year review of five peer-reviewed evaluation journals was conducted and coded by journal, research tradition, research …

Multi-Level Small Area Estimation Based On Calibrated Hierarchical Likelihood Approach Through Bias Correction With Applications To Covid-19 Data, Nirosha Rathnayake

Theses & Dissertations

Small area estimation (SAE) has been widely used in a variety of applications to draw estimates in geographic domains represented as a metropolitan area, district, county, or state. The direct estimation methods provide accurate estimates when the sample size of study participants within each area unit is sufficiently large, but it might not always be realistic to have large sample sizes of study participants when considering small geographical regions. Meanwhile, high dimensional socio-ecological data exist at the community level, providing an opportunity for model-based estimation by incorporating rich auxiliary information at the individual and area levels. Thus, it is critical …

Conditional Distance Correlation Test For Gene Expression Level, Dna Methylation Level And Copy Number, Shanshan Zhang

Graduate Theses and Dissertations

Over the past years, efforts have been devoted to the genome-wide analysis of genetic and epigenetic profiles to better understand the underlying biological mechanisms of complex diseases such as cancer. It is of great importance to unravel the complex dependence structure between biological factors, and many conditional dependence tests have been developed to meet this need. The traditional partial correlation method can only capture the linear partial correlation, but not the nonlinear correlation. To overcome this limitation, we propose to use the innovative conditional distance correlation (CDC), which measures the conditional dependence between random vectors and detect nonlinear relations. In …

Statistical Approaches Of Gene Set Analysis With Quantitative Trait Loci For High-Throughput Genomic Studies., Samarendra Das

Electronic Theses and Dissertations

Recently, gene set analysis has become the first choice for gaining insights into the underlying complex biology of diseases through high-throughput genomic studies, such as Microarrays, bulk RNA-Sequencing, single cell RNA-Sequencing, etc. It also reduces the complexity of statistical analysis and enhances the explanatory power of the obtained results. Further, the statistical structure and steps common to these approaches have not yet been comprehensively discussed, which limits their utility. Hence, a comprehensive overview of the available gene set analysis approaches used for different high-throughput genomic studies is provided. The analysis of gene sets is usually carried out based on …

Task Interrupted By A Poisson Process, Jarrett Christopher Nantais

Major Papers

We consider a task which has a completion time T (if not interrupted), which is a random variable with probability density function (pdf) f(t), t>0. Before it is complete, the task may be interrupted by a Poisson process with rate lambda. If that happens, then the task must begin again, with the same completion time random variable T, but with a potentially different realization. These interruptions can reoccur, until eventually the task is finished, with a total time of W. In this paper, we will find the Laplace Transform of W in several special cases.