Statistics and Probability Commons^™

Em Estimation For Zero- And K-Inflated Poisson Regression Model, Monika Arora, N. Rao Chaganty

Mathematics & Statistics Faculty Publications

Count data with excessive zeros are ubiquitous in healthcare, medical, and scientific studies. There are numerous articles that show how to fit Poisson and other models which account for the excessive zeros. However, in many situations, besides zero, the frequency of another count k tends to be higher in the data. The zero- and k-inflated Poisson distribution model (ZkIP) is appropriate in such situations The ZkIP distribution essentially is a mixture distribution of Poisson and degenerate distributions at points zero and k. In this article, we study the fundamental properties of this mixture distribution. Using stochastic representation, we …

Novel Statistical Analysis In The Context Of A Comprehensive Needs Assessment For Secondary Stem Recruitment, Norou Diawara, Sarah Ferguson, Melva Grant, Kumer Das

Mathematics & Statistics Faculty Publications

There is a myriad of career opportunities stemming from science, technology, engineering, and mathematics (STEM) disciplines. In addition to careers in corporate settings, teaching is a viable career option for individuals pursuing degrees in STEM disciplines. With national shortages of secondary STEM teachers, efforts to recruit, train, and retain quality STEM teachers is greatly important. Prior to exploring ways to attract potential STEM teacher candidates to pursue teacher training programs, it is important to understand the perceived value that potential recruits place on STEM careers, disciplines, and the teaching profession. The purpose of this study was to explore students’ perceptions …

Principal Components Analysis Corrects Collider Bias In Polygenic Risk Score Effect Size Estimation, Nathaniel S. Thomas, Peter B. Barr, Fazil Aliev, Sally I. Kuo, Danielle M. Dick, Jessica E. Salvatore

Graduate Research Posters

BACKGROUND: Genome-wide polygenic scoring has emerged as a way to predict psychiatric and behavioral outcomes and identify environments that promote the expression of genetic risks. An increasing number of studies demonstrate that the effects of polygenic risk scores (PRS) may be biased by the inclusion of heritable environments as covariates when the environment is influenced by unmeasured confounding variables, an example of collider bias. Inclusion of the principal components of observed confounders as covariates may correct for the effect of unmeasured confounders.

METHODS: A simulation study was conducted to test principal components analysis (PCA) as a correction for collider bias. …

Modeling Longitudinal Change In Cervical Length Across Pregnancy, Hope M. Wolf, Shawn J. Latendresse, Jerome F. Strauss Iii, Timothy P. York

Graduate Research Posters

Introduction: A short cervix (cervical length < 25 mm) in the mid-trimester (18 to 24 weeks) of pregnancy is a powerful predictor of spontaneous preterm delivery (gestational age at delivery < 37 weeks). Although the biological mechanisms of cervical remodeling have been the subject of extensive investigation, very little is known about the rate of change in cervical length over the course of a pregnancy, or the extent to which rapid cervical shortening increases maternal risk for spontaneous preterm delivery.

Methods: A cohort of 5,160 unique women carrying 5,971 singleton pregnancies provided two or more measurements of cervical length during pregnancy. Cervical length was measured in millimeters using a transvaginal 12-3 MHz ultrasound endocavity probe (SuperSonic Imagine). Maternal characteristics, including relevant medical history and birth outcome data, were collected for each participant. Gestational age at delivery was measured from the first day of each woman’s last menstrual period and confirmed by ultrasound. Repeated measurements of cervical length during pregnancy were modeled as a longitudinal, multilevel growth curve in MPlus. A three-level variance structure was …

Bayesian Tail Probability Estimation And Model Selection, Nan Shen

Graduate Research Theses & Dissertations

Bayesian statistics is a prevalent and important field in statistics that assigns Bayesian probabilities, which represent a state of knowledge, to unknown quantities. We study Bayesian statistics with its applications through two projects in this report.

In the first project, we investigate the reasons that the Bayesian estimator of the tail probability is always higher than the frequentist estimator. Sufficient conditions for this phenomenon are established by looking at Taylor series approximations about the tail and by using Jensen's Inequality, both of which point to the convexity of the distribution function.

The second project is about redefining the Bayesian information …

Gene-Based Disease Classification Using Bayesian Self-Organizing Map Neural Networks, Guangting Zhou

Graduate Research Theses & Dissertations

Genes perform vital roles in living beings. By taking charges of protein synthesis, genes are able to take control of the expression of living traits. There are a lot of diseases associated closely to our genes. By analyzing genetic information, we are able to detect or classify gene based diseases. Among genetic disease information technologies, microarray can be one of the widely used ones. Usually, microarray data records thousands of gene expression features from a small number of samples including both normal and abnormal expressed tissues. It provides standardized comparison information between normal and diseased tissues, so as to provide …

Robust Determinants Of Happiness: High-Dimensional Bayesian Treatment Of Model Uncertainty, Milivoje Davidovic

Graduate Research Theses & Dissertations

The thesis investigates the most relevant economic and institutional determinants of happiness in some 93 countries worldwide, covering the period 2006-2019. We employ the Bayesian Model Averaging (BMA) fixed effect model (country demeaned and time demeaned) using a working panel data set with 651 observations. Our initial goal is to address the problem of model uncertainty in panel data models of happiness, aiming at selecting a set variables that are likely to be included in as "true" model of happiness. In addition, we aim to investigate the causal relationship running from selected economic and institutional variable to index of happiness. …

Frequentist Methods In Handling Misrepresentation Risk, Rexford Mawunyegah Akakpo

Graduate Research Theses & Dissertations

A commonly encountered risk in insurance business is misrepresentation risk. Misrepresentation is a type of insurance fraud where a policyholder or a policy applicant falsifies his or her risk status in order to pay cheaper premiums for more expensive future risks. It is difficult and expensive for insurance companies to detect this kind of risk. With high cost of sophisticated underwriting, it becomes a norm for insurance companies to regularly rely on the policy applicant to self-report most of their risk statuses. We employ a frequentist approach by using expectation-maximization (EM) algorithm to carry out maximum likelihood estimation of the …

A New Generalized Modified Weibull Distribution, Morad Alizadeh, Muhammad Nauman Khan, Mahdi Rasekhi, Gholamhossein Hamedani

Mathematical and Statistical Science Faculty Research and Publications

We introduce a new distribution, so called A new generalized modified Weibull (NGMW) distribution. Various structural properties of the distribution are obtained in terms of Meijer’s G–function, such as moments, moment generating function, conditional moments, mean deviations, order statistics and maximum likelihood estimators. The distribution exhibits a wide range of shapes with varying skewness and assumes all possible forms of hazard rate function. The NGMW distribution along with other distributions are fitted to two sets of data, arising in hydrology and in reliability. It is shown that the proposed distribution has a superior performance among the compared distributions as …

Addressing The Ecological Fallacy With Lagrangian Inference, Michael Schwob

Calvert Undergraduate Research Awards

Most epidemiologists elect to use statistical models that use population-level data to make inference on the spread of some virus or disease. This has become commonplace in the fields of epidemiology and biostatistics since most data used to construct and verify epidemic models are recorded at the population-level. Obtaining inference from a population-level model may be beneficial in studying the spread of disease in a homogeneous population, but the use of such models to describe a heterogeneous population results in inadequate inference. The inaccuracy of these models is further amplified when one tries to make individual-level inference from these population-level …

Planning Algorithms Under Uncertainty For A Team Of A Uav And A Ugv For Underground Exploration, Matteo De Petrillo

Graduate Theses, Dissertations, and Problem Reports (ETD)

Robots’ autonomy has been studied for decades in different environments, but only recently, thanks to the advance in technology and interests, robots for underground exploration gained more attention. Due to the many challenges that any robot must face in such harsh environments, this remains an challenging and complex problem to solve.

As technology became cheaper and more accessible, the use of robots for underground ex- ploration increased. One of the main challenges is concerned with robot localization, which is not easily provided by any Global Navigation Services System (GNSS). Many developments have been achieved for indoor mobile ground robots, making …

Review Of Forecasting Univariate Time-Series Data With Application To Water-Energy Nexus Studies & Proposal Of Parallel Hybrid Sarima-Ann Model, Cory Sumner Yarrington

Graduate Theses, Dissertations, and Problem Reports (ETD)

The necessary materials for most human activities are water and energy. Integrated analysis to accurately forecast water and energy consumption enables the implementation of efficient short and long-term resource management planning as well as expanding policy and research possibilities for the supportive infrastructure. However, the integral relationship between water and energy (water-energy nexus) poses a difficult problem for modeling. The accessibility and physical overlay of data sets related to water-energy nexus is another main issue for a reliable water-energy consumption forecast. The framework of urban metabolism (UM) uses several types of data to build a global view and highlight issues …

Characterization Of Modern Ammunition And Background Profiles: A Novel Approach And Probabilistic Interpretation Of Inorganic Gunshot Residue, Korina Layli Menking-Hoggatt

Graduate Theses, Dissertations, and Problem Reports (ETD)

Gunshot residue (GSR) can provide essential clues in gun-related investigations. The standard practice for GSR analysis uses SEM-EDS, with the capability for single particle elemental and morphological analysis. However, the method is time-consuming and based on categorical classification models without considering case circumstances. Therefore, complementary and more encompassing methods are needed to improve evidence interpretation of modern ammunition. This research aims to fill these demands by developing standard materials and alternative methods to characterize and interpret IGSR.

This study developed primer GSR (pGSR) standards from sixty discharged primers that were fully characterized by three techniques. The number of GSR particles, …

Methods For Developing A Machine Learning Framework For Precise 3d Domain Boundary Prediction At Base-Level Resolution, Spiro C. Stilianoudakis

Theses and Dissertations

High-throughput chromosome conformation capture technology (Hi-C) has revealed extensive DNA looping and folding into discrete 3D domains. These include Topologically Associating Domains (TADs) and chromatin loops, the 3D domains critical for cellular processes like gene regulation and cell differentiation. The relatively low resolution of Hi-C data (regions of several kilobases in size) prevents precise mapping of domain boundaries by conventional TAD/loop-callers. However, high resolution genomic annotations associated with boundaries, such as CTCF and members of cohesin complex, suggest a computational approach for precise location of domain boundaries.

We developed preciseTAD, an optimized machine learning framework that leverages a random …

Analyzing Electronic Health Records With Time-To-Event Endpoints: Propensity Scores And Semiparametric Approaches, Jonathan W. Yu

Theses and Dissertations

For analyzing large electronic health records (EHR) with time-to-event endpoints, such as in kidney transplantation, a major challenge is to provide an accurate risk analyses, while accounting for a multitude of epidemiological and statistical complexities. Motivated by a right-censored kidney transplantation EHR dataset derived from the United Network of Organ Sharing (UNOS), this dissertation, through a culmination of two interrelated yet distinctly different projects, focuses on developments of novel statistical procedures and methodologies to address some pressing issues arising in EHR-based research. In the first project, we aim to decouple the causal effects of treatments (here, studying subgroups, such as …

The Relevance Of Credit Risk In The Determination Of Commercial Banks’ Profitability: Evidence From Ghana, Godwin Kwabla Ekpe

Graduate Research Theses & Dissertations

Existing empirical literature on the relationship between credit risk and bank’s profitability is replete with mixed results. This research investigates the probable effect of credit risk on banks’ profitability by examining the nature of the relationship between two measures of credit risk (Loss provisioning rate and Actual provisioning charge rate) and two measures ofprofitability (Return on assets and Return on Equity). The investigation is conducted using data on the Ghanaian banking industry. Various modeling techniques are used to fit the data, including frequentist beta regression and Bayesian beta regression models. The results across all models suggest negative linear relationship between …

Traffic Fatality Rate Prediction Based On Deep Neural Network And Bayesian Neural Network, Yiqun Hu

Graduate Research Theses & Dissertations

There have been numerous studies on traffic accidents and their fatality rate. For this challenging machine learning regression problem, Neural Networks (NNs) have produced state-of-the-art data. Despite their success, they are often used in a fre- quentist scheme, which means they cannot account for uncertainty in their forecasts. BNNs are comprised of a Probabilistic Model and a Neural Network. The aim of such a design is to bring together the benefits of Neural Networks and stochastic modeling. Neural networks have the ability to approximate continuous functions uni- versally. Statistical models allow for the direct definition of a model with known …

A Time Series Analysis Approach To Forecasting Covid-19 Cases And Deaths: An Analysis Of Covid-19 Data In Colombia, Andrea Jackson-Sagredo

Graduate Research Theses & Dissertations

The novel Coronavirus, known as COVID-19 is a highly contagious and transmissible infectious disease that has taken a toll throughout the entire world for over a year. The inner workings and long term effects of COVID-19 continue to be misunderstood. While COVID-19 has impacted all countries tremendously, Latin American countries and specifically Colombia have been impacted significantly by the virus. This thesis investigates the potential to forecast COVID-19 cases and deaths using Time Series Analysis methods and models for the South American country of Colombia. Time series analysis on Colombian COVID-19 data begins with data processing on a data set …

Stochastic Infection In Network Models With Applications To Pollution Analysis, Alexander Thor Wold

Graduate Research Theses & Dissertations

The continued adoption and escalation of commercial surface extraction techniques threatens to contaminate adjacent river networks across the coal mining landscape. We look to simulate the movement of this pollution across connected graph structures using stochastic block model methodologies, fueled from work and theory derived from exponential random graph models. We begin our study by applying our virtual experiment to the motivating material, later offering an exhaustive walk through of the simulation itself. Afterwards, we present our findings and their implications to water pollution analysis, emphasizing a need for this research and expanding on some inferential statistics left for later …

The Simulation Extrapolation Method With Differential Measurement Error, Dominic Partipilo

Graduate Research Theses & Dissertations

Most of statistical theory operates under the assumption that the true values of covariates have been measured correctly, but it is not always possible to obtain the true values of these covariates. A common issue, specifically in regression models, is that predictors are misclassified or measured with systematic measurement error. There have been many methods developed for handling measurement error, specifically in the case where measurement error is nondifferential, where the measurement error can be treated as independent from the covariates. The frequentist method known as simulation extrapolation (SIMEX) is one of these methods that specifically handles the case for …

Optimization Of Dynamic Objective Functions Using Path Integrals, Paramahansa Pramanik

Graduate Research Theses & Dissertations

Path integrals are used to find an optimal strategy for a firm under a Walrasian system. We define dynamic optimal strategies and develop an integration method to capture all non-additive non-convex strategies. We also show that the method can solve the non-linear case, for example Merton-Garman-Hamiltonian system, which the traditional Pontryagin maximum principle cannot solve in closed form. Furthermore, we assume that the strategy space and time are inseparable with respect to a contract. Under this assumption we show that the strategy spacetime is a dynamic curved Liouville-like 2-brane quantum gravity surface under asymmetric information and that traditional Euclidean geometry …

Methods For High-Dimensional Spatial Data: Dimension Reduction And Covariance Approximation, Paul May

Electronic Theses and Dissertations

In spatial statistics, because quantities are correlated based on their relative positions in space, data is modeled as a single realization of a multivariate stochastic process. Spatial data can be high-dimensional either through a large number of observed variables per location, or through a large number of observed locations. The two are often handled differently, with the former addressed through dimension reduction and the latter addressed through appropriate modeling of the spatial correlation between locations. The main body of this dissertation is a three-part work. Parts 2 and 3 pertain to the "many variables" problem, proposing novel methods of dimension …

Statistical And Machine Learning Approaches To Depressive Disorders Among Adults In The United States: From Factor Discovery To Prediction Evaluation, Minhwa Lee

Senior Independent Study Theses

According to the National Institutes of Mental Health (NIMH), depressive disorders (or major depression) are considered one of the most common and serious health risks in the United States. Our study focuses on extracting non-medical factors of depressive disorders diagnosis, such as overall health states, health risk behaviors, demography, and healthcare access, using the Behavioral Risk Factor Surveillance System (BRFSS) data set collected by the Centers for Disease Control and Prevention (CDC) in 2018.

We set the two objectives of our study about depressive disorders diagnosis in the United States as follows. First, we aim to utilize machine learning algorithms …

An Evaluation Of The Performance Of Proc Arima's Identify Statement: A Data-Driven Approach Using Covid-19 Cases And Deaths In Florida, Fahmida Akter Shahela

Electronic Theses and Dissertations, 2020-2023

Understanding data on novel coronavirus (COVID-19) pandemic, and modeling such data over time are crucial for decision making at managing, fighting, and controlling the spread of this emerging disease. This thesis work looks at some aspects of exploratory analysis and modeling of COVID-19 data obtained from the Florida Department of Health (FDOH). In particular, the present work is devoted to data collection, preparation, description, and modeling of COVID-19 cases and deaths reported by FDOH between March 12, 2020, and April 30, 2021. For modeling data on both cases and deaths, this thesis utilized an autoregressive integrated moving average (ARIMA) times …

Ensemble Protein Inference Evaluation, Kyle Lee Lucke

Graduate Student Theses, Dissertations, & Professional Papers

The Protein inference problem is becoming an increasingly important tool that aids in the characterization of complex proteomes and analysis of complex protein samples. In bottom-up shotgun proteomics experiments the metrics for evaluation (like AUC and calibration error) are based on an often imperfect target-decoy database. These metrics make the inherent assumption that all of the proteins in the target set are present in the sample being analyzed. In general, this is not the case, they are typically a mix of present and absent proteins. To objectively evaluate inference methods, protein standard datasets are used. These datasets are special in …

Impact Of Case Management On Childhood Lead Exposure In Marion County, Indiana, Maliki Yacouba

Walden Dissertations and Doctoral Studies

The Centers for Disease Control and Prevention recently declared that no amount of childhood blood lead level (BLL) is safe. The purpose of this quantitative study with a retrospective cohort design was to evaluate the effectiveness of case management intervention on children diagnosed with elevated BLL (EBLL; ≥ 5 μg/dL) in Marion, County, Indiana. The health belief model was used as the theoretical foundation for the study. A data set of 160 lead exposure case management records was analyzed to find whether: (a) BLL at post-case-management time significantly differ from BLL at baseline (b) BLL at post-case-management time is affected …

Prediction Intervals For Fractionally Integrated Time Series And Volatility Models, Rukman Ekanayake

Doctoral Dissertations

"The two of the main formulations for modeling long range dependence in volatilities associated with financial time series are fractionally integrated generalized autoregressive conditional heteroscedastic (FIGARCH) and hyperbolic generalized autoregressive conditional heteroscedastic (HYGARCH) models. The traditional methods of constructing prediction intervals for volatility models, either employ a Gaussian error assumption or are based on asymptotic theory. However, many empirical studies show that the distribution of errors exhibit leptokurtic behavior. Therefore, the traditional prediction intervals developed for conditional volatility models yield poor coverage. An alternative is to employ residual bootstrap-based prediction intervals. One goal of this dissertation research is to develop …

Modeling Time Series With Conditional Heteroscedastic Structure, Ratnayake Mudiyanselage Isuru Panduka Ratnayake

Doctoral Dissertations

"Models with a conditional heteroscedastic variance structure play a vital role in many applications, including modeling financial volatility. In this dissertation several existing formulations, motivated by the Generalized Autoregressive Conditional Heteroscedastic model, are further generalized to provide more effective modeling of price range data well as count data. First, the Conditional Autoregressive Range (CARR) model is generalized by introducing a composite range-based multiplicative component formulation named the Composite CARR model. This formulation enables a more effective modeling of the long and short-term volatility components present in price range data. It treats the long-term volatility as a stochastic component that in …

Depicting Bivariate Relationship With A Gaussian Ellipse, Mamunur Rashid, Jyotirmoy Sarkar

Mathematics Faculty Publications

For data on two continuous variables, how should one depict the summary statistics (means, SDs, correlation coefficient, coefficient of determination, regression lines) so that their values can be read off easily from the depiction and potential outliers can be flagged also? We propose the Gaussian covariance ellipse as an answer that will benefit all users of statistics.

Bias Of Rank Correlation Under A Mixture Model, Russell Land

College of Graduate Studies: Theses & 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 …