Statistics and Probability Commons^™

Parameter Estimation And Inference Of Spatial Autoregressive Model By Stochastic Gradient Descent, Gan Luan

Dissertations

Stochastic gradient descent (SGD) is a popular iterative method for model parameter estimation in large-scale data and online learning settings since it goes through the data in only one pass. While SGD has been well studied for independent data, its application to spatially-correlated data largely remains unexplored. This dissertation develops SGD-based parameter estimation and statistical inference algorithms for the spatial autoregressive (SAR) model, a common model for spatial lattice data.

This research contains three parts. (I) The first part concerns SGD estimation and inference for the SAR mean regression model. A new SGD algorithm based on maximum likelihood estimator (MLE) …

Dependent Censoring In Survival Analysis, Zhongcheng Lin

Dissertations

This dissertation mainly consists of two parts. In the first part, some properties of bivariate Archimedean Copulas formed by two time-to-event random variables are discussed under the setting of left censoring, where these two variables are subject to one left-censored independent variable respectively. Some distributional results for their joint cdf under different censoring patterns are presented. Those results are expected to be useful in both model fitting and checking procedures for Archimedean copula models with bivariate left-censored data. As an application of the theoretical results that are obtained, a moment estimator of the dependence parameter in Archimedean copula models is …

A Poisson-Akash Inrar(1) Model For Over Dispersed Count Time Series, Emmanuel W. Okereke, Sunday N. Gideon

BAU Journal - Science and Technology

In this paper, a Poisson-Akash INAR(1) model was proposed in order to improve on the modelling of overdispersed stationary count time series. The estimators of the parameters of the model were derived using the Yule-Walker (YW) method and the conditional least squares (CLS) method. An expression for the conditional log-likelihood and the r-step ahead forecast were obtained for the model. Three overdispersed nonseasonal stationary count time series were modelled to illustrate the applicability of the proposed model as well as its capacity to outperform the competing INAR (1) models in modelling overdispersed stationary count time series and the result showed …

Genetic Contributors Of Incident Stroke In 10,700 African Americans With Hypertension: A Meta-Analysis From The Genetics Of Hypertension Associated Treatments And Reasons For Geographic And Racial Differences In Stroke Studies, Nicole D. Armstrong, Vinodh Srinivasasainagendra, Amit Patki, Rikki M. Tanner, Bertha A. Hidalgo, Hemant K. Tiwari, Nita A. Limdi, Ethan M. Lange, Leslie A. Lange, Donna K. Arnett, Marguerite R. Irvin

Epidemiology and Environmental Health Faculty Publications

Background: African Americans (AAs) suffer a higher stroke burden due to hypertension. Identifying genetic contributors to stroke among AAs with hypertension is critical to understanding the genetic basis of the disease, as well as detecting at-risk individuals.

Methods: In a population comprising over 10,700 AAs treated for hypertension from the Genetics of Hypertension Associated Treatments (GenHAT) and Reasons for Geographic and Racial Differences in Stroke (REGARDS) studies, we performed an inverse variance-weighted meta-analysis of incident stroke. Additionally, we tested the predictive accuracy of a polygenic risk score (PRS) derived from a European ancestral population in both GenHAT and REGARDS AAs …

Dysregulation Of Dna Methylation And Epigenetic Clocks In Prostate Cancer Among Puerto Rican Men, Anders Berglund, Jaime Matta, Jarline Encarnación-Medina, Carmen Ortiz-Sanchéz, Julie Dutil, Raymond Linares, Joshua Marcial, Caren Abreu-Takemura, Natasha Moreno, Ryan Putney, Ratna Chakrabarti, Hui Yi Lin, Kosj Yamoah, Carlos Diaz Osterman, Liang Wang, Jasreman Dhillon, Youngchul Kim, Seung Joon Kim, Gilberto Ruiz-Deya, Jong Y. Park

School of Public Health Faculty Publications

In 2021, approximately 248,530 new prostate cancer (PCa) cases are estimated in the United States. Hispanic/Latinos (H/L) are the second largest racial/ethnic group in the US. The objective of this study was to assess DNA methylation patterns between aggressive and indolent PCa along with ancestry proportions in 49 H/L men from Puerto Rico (PR). Prostate tumors were classified as aggressive (n = 17) and indolent (n = 32) based on the Gleason score. Genomic DNA samples were extracted by macro-dissection. DNA methylation patterns were assessed using the Illumina EPIC DNA methylation platform. We used ADMIXTURE to estimate global ancestry proportions. …

Acute Pediatric Chagas Disease In Antioquia, Colombia: A Geographic Location Of Suspected Oral Transmission, Lídia Gual-Gonzalez, Catalina Aango-Ferreira, Laura Camila Lopera-Restrepo, Omar Cantillo-Barraza, Daniela Velásquez Marín, Natalia Restrepo Bustamante, Omar Triana-Chavez, Melissa Nolan Ph.D., Mph

Faculty Publications

Chagas disease, Trypanosoma cruzi infection, is an insidious cause of heart failure in Latin America. Early diagnosis and treatment are critical to prevent irreversible myocardial damage that progressively accumulates over decades. Several structural barriers account for the less than 1% of cases in Colombia being treated, including poor physician knowledge, especially considering that some regions are considered non-endemic. The two cases reported here represent an emerging epidemiologic scenario associated with pediatric Chagas disease. Both cases are suspected oral transmitted parasitic infection in a geographic region of Colombia (Andean region of Antioquia) where no previous oral transmission of Chagas disease had …

Approximate Likelihood Based Estimations For Joint Models With Intractable Likelihoods, Karl Stessy M. Bisselou

Theses & Dissertations

This dissertation focuses on the development of approximation approaches for the joint modeling (JM) of repeated measures data and time-to-event data in the presence of analytically or numerically intractable likelihoods. Current likelihood-based inferences for JMs show several limitations including (i) intractability of integrals during marginal likelihood derivations due to the complexity in computations, and (ii) the large number of nuisance parameters (unobserved) posing a problem with convergence. The h-likelihood (HL) and synthetic likelihood (SL) are two computationally efficient estimation approaches that overcome these challenges.

In the presence of extremely high censoring rates, the HL can produce bias parameter estimates. We …

Smoking, Alcohol Consumption, And Depression In Association With Incidence Of Type 2 Diabetes Among Mexican Americans In Starr County, Texas, Gabriela Rubannelsonkumar

Honors Program Theses and Research Projects

Previous studies on conditions like obesity, hypertension, and type 2 diabetes mellitus (T2DM) have explored the correlations between them and various other human conditions, including aortic stiffness, left ventricular hypertrophy and sleep apnea, as they predict possibilities of developing certain diseases in Mexican Americans. This study aims to observe the correlation between lifestyle decisions that could relate to the onset of the depression in normal, prediabetic, and diabetic individuals. These include smoking habits and alcohol consumption. Many papers have previously conducted research on these lifestyle habits as they relate to obesity, hypertension, diabetes, however, have done so in a singular …

The Efficacy Of Plant-Based Dietary Program In Patients With Diabetes: A Pilot Study, Reuben Adatorwovor, Nisha Sharma, Dakota Mccoy, Sharon Wasserstrom, Matthew Robinson, Jacquelyn Nyenhuis, Sowmya Suryanarayanan

Biostatistics Faculty Publications

Dietary choices play a key role in insulin sensitivity among diabetes patients. An 8-week pilot study was conducted to evaluate whether a mostly plant-based dietary program will lead to improvement in biochemical markers in adults with diabetes. The dietary program included educational presentations, weekly cooking demonstrations and small group discussions. A sample of thirty-two adults with diabetes (types 1 and 2) were recruited and seventeen (53%) completed the study. Matched-pair tests and Fishers exact tests were used to compare the changes in means and proportion of the participants’ responses. There were changes in HbA1c, lipids, CRP (mg/L), cholesterol (mg/dL), HDL …

Aspect-Based Sentiment Analysis Of Movie Reviews, Samuel Onalaja, Eric Romero, Bosang Yun

SMU Data Science Review

This study investigates a comparison of classification models used to determine aspect based separated text sentiment and predict binary sentiments of movie reviews with genre and aspect specific driving factors. To gain a broader classification analysis, five machine and deep learning algorithms were compared: Logistic Regression (LR), Naive Bayes (NB), Support Vector Machine (SVM), and Recurrent Neural Network Long-Short-Term Memory (RNN LSTM). The various movie aspects that are utilized to separate the sentences are determined through aggregating aspect words from lexicon-base, supervised and unsupervised learning. The driving factors are randomly assigned to various movie aspects and their impact tied to …

Predicting Power Using Time Series Analysis Of Power Generation And Consumption In Texas, Joshua Eysenbach, Bodie Franklin, Andrew J. Larsen, Joel Lindsey

SMU Data Science Review

Due to the recent power events in Texas, power forecasting has been brought national attention. Accurate demand forecasting is necessary to be sure that there is adequate power supply to meet consumer's needs. While Texas has a forecasting model created by the Electricity Reliability Council of Texas (ERCOT), constant efforts are required to ensure that the model stays at the state-of-the-art and is producing the most reliable forecasts possible. This research seeks to provide improved short- and medium-term forecasting models, bringing in state-of-the-art deep learning models to compare to ERCOT’s forecasts. A model that is more accurate than ERCOT’s own …

Identification And Characterization Of Forest Fire Risk Zones Leveraging Machine Learning Methods, Joshua Balson, Matt Chinchilla, Cam Lu, Jeff Washburn, Nibhrat Lohia

SMU Data Science Review

Across the United States, record numbers of wildfires are observed costing billions of dollars in property damage, polluting the environment, and putting lives at risk. The ability of emergency management professionals, city planners, and private entities such as insurance companies to determine if an area is at higher risk of a fire breaking out has never been greater. This paper proposes a novel methodology for identifying and characterizing zones with increased risks of forest fires. Methods involving machine learning techniques use the widely available and recorded data, thus making it possible to implement the tool quickly.

Basis For Changes In The Disease Burden Estimates Related To Vitamin A And Zinc Deficiencies In The 2017 And 2019 Global Burden Of Disease Studies, Sonja Y. Hess, Alexander C. Mclain, Haley Lescinsky, Kenneth H. Brown, Ashkan Afshin, Reed Atkin, Saskia Jm Osendarp

Faculty Publications

Background:

The Global Burden of Disease (GBD) Study provides estimates of death and disability from eighty-seven risk factors, including some micronutrient deficiencies. Objectives:

To review methodological changes that led to large differences in the disease burden estimates for vitamin A and Zn deficiencies between the GBD 2017 and 2019 Studies. Methods:

GBD publications were reviewed; additional information was provided by GBD researchers. Results:

Vitamin A deficiency prevalence is based on plasma retinol concentration, whereas the estimate for Zn deficiency prevalence uses dietary adequacy as a proxy. The estimated global prevalence of vitamin A deficiency for children aged 1–4 years in …

The Development Of Authentic Virtual Reality Scenarios To Measure Individuals’ Level Of Systems Thinking Skills And Learning Abilities, Vidanelage L. Dayarathna

Theses and Dissertations

This dissertation develops virtual reality modules to capture individuals’ learning abilities and systems thinking skills in dynamic environments. In the first chapter, an immersive queuing theory teaching module is developed using virtual reality technology. The objective of the study is to present systems engineering concepts in a more sophisticated environment and measure students learning abilities. Furthermore, the study explores the performance gaps between male and female students in manufacturing systems concepts. To investigate the gender biases toward the performance of developed VR module, three efficacy measures (simulation sickness questionnaire, systems usability scale, and presence questionnaire) and two effectiveness measures (NASA …

Measuring Irregularity Via Approximate Entropy: How Does Perceived Human Instability Affect One's Own Stability?, Madi Braunersrither

Fall Student Research Symposium 2021

In a study performed at Utah State University, participants were prompted to evaluate the stability of pictured human postures while standing on a force plate. The force plate was used to collect the center of pressure of the subjects by recording measurements in the vertical and horizontal directions. The way these factors fluctuate over time and the irregularity in this fluctuation, specifically, can give insight into the subject’s postural stability. Rather than working with summary statistics such as means and variances of fitting parameters of a distribution as commonly done in statistics, we want to measure irregularity through analyzing the …

Creating Transparent And Accessible Methods For Approximating The Composite Strength Of Concrete Sandwich Wall Panels, Ruth Taylor

Fall Student Research Symposium 2021

Background: The method of designing partially composite sandwich wall panels (SWPs) relies strongly on the use of percent of composite action. Calculating these values proves to be a complex and virtually inaccessible process for practicing engineers, resulting in the reliance on proprietary software or connector-system manufacturers for the necessary values. We simulated percent composite action data, including several relevant variables, to examine the relationship and determine if simple and accessible methods of calculation could be created. Methods: Code from collaborating engineers used to calculate percent composite action with the Iterative Sandwich Beam Theory (ISBT) method was translated into R, a …

Nutrient Intake And Dietary Inflammatory Potential In Current And Recovered Anorexia Nervosa, Olivia Patsalos, Bethan Dalton, Christia Kyprianou, Joseph Firth, Nitin Shivappa Mbbs, Mph, Ph.D., James Hébert Scd, Ulrike Schmidt, Hubertus Himmerich

Faculty Publications

Anorexia nervosa (AN) is characterised by disrupted and restrictive eating patterns. Recent investigations and meta-analyses have found altered concentrations of inflammatory markers in people with current AN. We aimed to assess nutrient intake in participants with current or recovered AN, as compared to healthy individuals, and explore group differences in dietary inflammatory potential as a possible explanation for the observed alterations in inflammatory markers. We recruited participants with current AN (n = 51), those recovered from AN (n = 23), and healthy controls (n = 49). We used the Food Frequency Questionnaire (FFQ), to calculate a Dietary …

Teacher Education Programs Of Top Pisa Scoring Countries, Stephanie Kafer

Honors Projects

This research paper aims to investigate the teacher education programs of four different countries that have consistently scored high on the international Programme for International Student Assessment (PISA) test. This project intends to answer two questions: What locations consistently perform high on the Programme for International Student Assessment (PISA) test? What do the teacher training programs look like for these locations and are there commonalities between programs of different locations? The first question is answered using statistics of PISA scores from the past twenty years and from those statistics, the top four countries that this paper focuses on are Finland, …

Non-Parametric Tests For Testing Of Scale Parameters, Manish Goyal, Narinder Kumar

Journal of Modern Applied Statistical Methods

One of the fundamental problems in testing of equality of populations is of testing the equality of scale parameters. The subsequent usages for scale are dispersion, spread and variability. In this paper, we proposed non-parametric tests based on U-Statistics for the testing of equality of scale parameters. The null distribution of proposed tests is developed and its Pitman efficiency is worked out to compare proposed tests with respect to some existing tests. Simulation study is carried out to compute the asymptotic power of proposed tests. An illustrative example is also provided.

Oscillation Of Nonlinear Third-Order Difference Equations With Mixed Neutral Terms, Jehad Alzabut, Martin Bohner, Said R. Grace

Mathematics and Statistics Faculty Research & Creative Works

In this paper, new oscillation results for nonlinear third-order difference equations with mixed neutral terms are established. Unlike previously used techniques, which often were based on Riccati transformation and involve limsup or liminf conditions for the oscillation, the main results are obtained by means of a new approach, which is based on a comparison technique. Our new results extend, simplify, and improve existing results in the literature. Two examples with specific values of parameters are offered.

(R1505) A Note On Large Deviations In Insurance Risk, Stefan Gerhold

Applications and Applied Mathematics: An International Journal (AAM)

We study large and moderate deviations for an insurance portfolio, with the number of claims tending to infinity, without assuming identically distributed claims. The crucial assumption is that the centered claims are bounded, and that variances are bounded below. From a general large deviations upper bound, we obtain an exponential bound for the probability of the average loss exceeding a threshold. A counterexample shows that a full large deviation principle, including also a lower bound, does not follow from our assumptions. We argue that our assumptions make sense, in particular, for life insurance portfolios and discuss how to apply our …

(R1463) On The Central Limit Theorem For Conditional Density Estimator In The Single Functional Index Model, Abbes Rabhi, Nadia Kadiri, Fatima Akkal

Applications and Applied Mathematics: An International Journal (AAM)

The main objective of this paper is to investigate the nonparametric estimation of the conditional density of a scalar response variable Y, given the explanatory variable X taking value in a Hilbert space when the sample of observations is considered as an independent random variables with identical distribution (i.i.d.) and are linked with a single functional index structure. First of all, a kernel type estimator for the conditional density function (cond-df) is introduced. Afterwards, the asymptotic properties are stated for a conditional density estimator when the observations are linked with a single-index structure from which we derive an central …

Predicting Lifespan Of Drosophila Melanogaster: A Novel Application Of Convolutional Neural Networks And Zero-Inflated Autoregressive Conditional Poisson Model, Yi Zhang, V. A. Samaranayake, Gayla R. Olbricht, Matthew S. Thimgan

Mathematics and Statistics Faculty Research & Creative Works

A model to classify the lifespan of Drosophila, the fruit fly, into short- and long-lived categories based on a sleep characteristic, extracted from activity data, is developed using a two-stage process. Stage 1 models the per-minute activity counts of each fly using a zero-inflated autoregressive conditional Poisson model. These probabilities are allowed to vary hourly, reflecting the circadian and other cycles present in a fly's sleep architecture. A 5-day moving window is used to model data allowing the model parameters to vary over the course of the fly's life. The resulting probabilities capture information about changes in sleep patterns with …

Generalization Of Mitrinović–Pečarić Inequalities On Time Scales, Ahmed A. El-Deeb, Elvan Akin, Billur Kaymakçalan

Mathematics and Statistics Faculty Research & Creative Works

We prove some new inequalities of Mitrinović–Pečarić inequalities for convex functions on an arbitrary time scale using delta integrals. These inequalities extend and improve some known dynamic inequalities in the literature. The main results will be proved by using Hölder and Jensen inequalities and a simple consequence of Keller's and Poetzsche's chain rules on time scales.

(R1493) Discussion On Stability And Hopf-Bifurcation Of An Infected Prey Under Refuge And Predator, Moulipriya Sarkar, Tapasi Das

Applications and Applied Mathematics: An International Journal (AAM)

The paper deals with the case of non-selective predation in a partially infected prey-predator system, where both the susceptible prey and predator follow the law of logistic growth and some preys avoid predation by hiding. The disease-free preys get infected in due course of time by a certain rate. However, the carrying capacity of the predator population is considered proportional to the sum-total of the susceptible and infected prey. The positivity and boundedness of the solutions of the system are studied and the existence of the equilibrium points and stability of the system are analyzed at these points. The effect …

Discrete Fractional Boundary Value Problems And Inequalities, Martin Bohner, Nick Fewster-Young

Mathematics and Statistics Faculty Research & Creative Works

In this paper, a general nonlinear discrete fractional boundary value problem is considered, of order between one and two. The main result is an existence theorem, proving the existence of at least one solution to the boundary value problem, subject to validity of a certain key inequality that allows unrestricted growth in the problem. The proof of this existence theorem is accomplished by using Brouwer's fixed point theorem as well as two other main results of this paper, namely, first, a result showing that the solutions of the boundary value problem are exactly the solutions to a certain equivalent integral …

Estimating Average Treatment Effect On The Treated Via Sufficient Dimension Reduction, Lu Li, Wei Luo, Xuerong Meggie Wen, Zhou Yu

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we propose to use sufficient dimension reduction (SDR) in conjunction with nonparametric techniques to estimate the average treatment effect on the treated (ATT), a parameter of common interest in causal inference. The proposed method is applicable under a general low-dimensional structure in the data and avoids both the risk of model misspecification and the "curse of dimensionality," for which it often outperforms the existing parametric and nonparametric methods. We develop the theoretical properties of the proposed method, including its asymptotic normality, its asymptotic super-efficiency, and its equivalent form as an augmented inverse probability weighting estimator. We also …

Oscillation And Nonoscillation Criteria For Four-Dimensional Advanced And Delay Time-Scale Systems, Elvan Akin, Gülşah Yenpi

Mathematics and Statistics Faculty Research & Creative Works

We obtain oscillation and Non oscillation criteria for solutions to four-dimensional advanced and delay systems of first-order dynamic equations on time scales. To establish oscillation criteria, we eliminate Non oscillatory solutions of the systems based on the sign of components of the solutions. Furthermore, some of our results are new in the discrete case.

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.

Gps-Denied Navigation Using Synthetic Aperture Radar Images And Neural Networks, Teresa White

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Unmanned aerial vehicles (UAV) often rely on GPS for navigation. GPS signals, however, are very low in power and easily jammed or otherwise disrupted. This paper presents a method for determining the navigation errors present at the beginning of a GPS-denied period utilizing data from a synthetic aperture radar (SAR) system. This is accomplished by comparing an online-generated SAR image with a reference image obtained a priori. The distortions relative to the reference image are learned and exploited with a convolutional neural network to recover the initial navigational errors, which can be used to recover the true flight trajectory throughout …