Statistics and Probability Commons^™

A Two-Strain Tb Model With Multiple Latent Stages, Azizeh Jabbari, Carlos Castillo-Chavez, Fereshteh Nazari, Baojun Song, Hossein Kheiri

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

A two-strain tuberculosis (TB) transmission model incorporating antibiotic-generated TB resistant strains and long and variable waiting periods within the latently infected class is introduced. The mathematical analysis is carried out when the waiting periods are modeled via parametrically friendly gamma distributions, a reasonable alternative to the use of exponential distributed waiting periods or to integral equations involving "arbitrary" distributions. The model supports a globally-asymptotically stable disease-free equilibrium when the reproduction number is less than one and an endemic equilibriums, shown to be locally asymptotically stable, or l.a.s., whenever the basic reproduction number is greater than one. Conditions for the existence …

Is There A Symmetric Version Of Hindman's Theorem?, Ethan Akin, Eli Glasner

Mathematics and Statistics Faculty Research & Creative Works

We show that there does not exist a symmetric version of Hindman's Theorem, or more explicitly, that the property of containing a symmetric IP-set is not divisible. We consider several related dynamics questions.

Model-Free Variable Screening, Sparse Regression Analysis And Other Applications With Optimal Transformations, Qiming Huang

Open Access Dissertations

Variable screening and variable selection methods play important roles in modeling high dimensional data. Variable screening is the process of filtering out irrelevant variables, with the aim to reduce the dimensionality from ultrahigh to high while retaining all important variables. Variable selection is the process of selecting a subset of relevant variables for use in model construction. The main theme of this thesis is to develop variable screening and variable selection methods for high dimensional data analysis. In particular, we will present two relevant methods for variable screening and selection under a unified framework based on optimal transformations.

In the …

Maximum Empirical Likelihood Estimation In U-Statistics Based General Estimating Equations, Lingnan Li

Open Access Dissertations

In the first part of this thesis, we study maximum empirical likelihood estimates (MELE's) in U-statistics based general estimating equations (UGEE's). Our technical maneuver is the jackknife empirical likelihood (JEL) approach. We give the local uniform asymptotic normality condition for the log-JEL for UGEE's. We derive the estimating equations for finding MELE's and provide their asymptotic normality. We obtain easy MELE's which have less computational burden than the usual MELE's and can be easily implemented using existing software. We investigate the use of side information of the data to improve efficiency. We exhibit that the MELE's are fully efficient, and …

Controlling For Confounding Network Properties In Hypothesis Testing And Anomaly Detection, Timothy La Fond

Open Access Dissertations

An important task in network analysis is the detection of anomalous events in a network time series. These events could merely be times of interest in the network timeline or they could be examples of malicious activity or network malfunction. Hypothesis testing using network statistics to summarize the behavior of the network provides a robust framework for the anomaly detection decision process. Unfortunately, choosing network statistics that are dependent on confounding factors like the total number of nodes or edges can lead to incorrect conclusions (e.g., false positives and false negatives). In this dissertation we describe the challenges that face …

Learning From Data: Plant Breeding Applications Of Machine Learning, Alencar Xavier

Open Access Dissertations

Increasingly, new sources of data are being incorporated into plant breeding pipelines. Enormous amounts of data from field phenomics and genotyping technologies places data mining and analysis into a completely different level that is challenging from practical and theoretical standpoints. Intelligent decision-making relies on our capability of extracting from data useful information that may help us to achieve our goals more efficiently. Many plant breeders, agronomists and geneticists perform analyses without knowing relevant underlying assumptions, strengths or pitfalls of the employed methods. The study endeavors to assess statistical learning properties and plant breeding applications of supervised and unsupervised machine learning …

Extreme-Strike And Small-Time Asymptotics For Gaussian Stochastic Volatility Models, Xin Zhang

Open Access Dissertations

Asymptotic behavior of implied volatility is of our interest in this dissertation. For extreme strike, we consider a stochastic volatility asset price model in which the volatility is the absolute value of a continuous Gaussian process with arbitrary prescribed mean and covariance. By exhibiting a Karhunen-Loève expansion for the integrated variance, and using sharp estimates of the density of a general second-chaos variable, we derive asymptotics for the asset price density for large or small values of the variable, and study the wing behavior of the implied volatility in these models. Our main result provides explicit expressions for the first …

The Design And Statistical Analysis Of Single-Cell Rna-Sequencing Experiments, Faye H. Zheng

Open Access Dissertations

Next-generation DNA- and RNA-sequencing (RNA-seq) technologies have expanded rapidly in both throughput and accuracy within the last decade. The momentum continues as emerging techniques become increasingly capable of profiling molecular content at the level of individual cells. One goal of this research is to put forward best practices in the design of single-cell RNA-sequencing (scRNA-seq) experiments, specifically as it relates to choices regarding the trade-off between sequencing depth and sample size. In addition to general guidelines, an interactive tool is presented to aid researchers in making experiment-specific decisions that are informed by real data and practical constraints. Further, a new …

Diabetes Is Associated With Cerebrovascular But Not Alzheimer's Disease Neuropathology, Erin L. Abner, Peter T. Nelson, Richard J. Kryscio, Frederick A. Schmitt, David W. Fardo, Randall L. Woltjer, Nigel J. Cairns, Lei Yu, Hiroko H. Dodge, Chengjie Xiong, Kamal Masaki, Suzanne L. Tyas, David A. Bennett, Julie A. Schneider, Zoe Arvanitakis

Sanders-Brown Center on Aging Faculty Publications

INTRODUCTION: The relationship of diabetes to specific neuropathologic causes of dementia is incompletely understood.

METHODS: We used logistic regression to evaluate the association between diabetes and infarcts, Braak neurofibrillary tangle stage, and neuritic plaque score in 2365 autopsied persons. In a subset of >1300 persons with available cognitive data, we examined the association between diabetes and cognition using Poisson regression.

RESULTS: Diabetes increased odds of brain infarcts (odds ratio [OR] = 1.57, P < .0001), specifically lacunes (OR = 1.71, P < .0001), but not Alzheimer's disease neuropathology. Diabetes plus infarcts was associated with lower cognitive scores at end of life than infarcts or diabetes alone, and diabetes plus high level of Alzheimer's neuropathologic changes was associated with lower mini-mental state examination scores than the pathology alone.

DISCUSSION: This study supports the conclusions that diabetes increases the risk of cerebrovascular but not Alzheimer's disease pathology, and at least some of diabetes' relationship to …

Methods To Account For Breed Composition In A Bayesian Gwas Method Which Utilizes Haplotype Clusters, Danielle F. Wilson-Wells

Department of Statistics: Dissertations, Theses, and Student Research

In livestock, prediction of an animal’s genetic merit using genomic information is becoming increasingly common. The models used to make these predictions typically assume that we are sampling from a homogeneous population. However, in both commercial and experimental populations the sire and dam of an individual may be a mixture of different breeds. Haplotype models can capture this population structure.

Two models based on breed specific haplotype clusters where developed to account for differences across multiple breeds. The first model utilizes the breed composition of the individual, while the second utilizes the breed composition from the sire and dam. Haplotype …

Biomarkers For Radiation Pneumonitis Using Noninvasive Molecular Imaging, Meetha Medhora, Steven Haworth, Yu Liu, Jayashree Narayanan, Feng Gao, Ming Zhao, Said H. Audi, Elizabeth R. Jacobs, Brian L. Fish, Anne V. Clough

Mathematics, Statistics and Computer Science Faculty Research and Publications

Our goal is to develop minimally invasive biomarkers for predicting radiation-induced lung injury before symptoms develop. Currently, there are no biomarkers that can predict radiation pneumonitis. Radiation damage to the whole lung is a serious risk in nuclear accidents or in radiologic terrorism. Our previous studies have shown that a single dose of 15 Gy of x-rays to the thorax causes severe pneumonitis in rats by 6–8 wk. We have also developed a mitigator for radiation pneumonitis and fibrosis that can be started as late as 5 wk after radiation. Methods: We used 2 functional SPECT probes in vivo in …

Characterizations Of Pareto, Weibull And Power Function Distributions Based On Generalized Order Statistics, M. Ahsanullah, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Characterizations of probability distributions by different regression conditions on generalized order statistics has attracted the attention of many researchers. We present here, characterization of Pareto and Weibull distributions based on the conditional expectation of generalized order statistics extending the characterization results reported by Jin and Lee (2014). We also present a characterization of the power function distribution based on the conditional expectation of lower generalized order statistics.

The Influence Of The Electric Supply Industry On Economic Growth In Less Developed Countries, Edward Richard Bee

Dissertations

This study measures the impact that electrical outages have on manufacturing production in 135 less developed countries using stochastic frontier analysis and data from World Bank’s Investment Climate surveys. Outages of electricity, for firms with and without backup power sources, are the most frequently cited constraint on manufacturing growth in these surveys.

Outages are shown to reduce output below the production frontier by almost five percent in Africa and by a lower percentage in South Asia, Southeast Asia and the Middle East and North Africa. Production response to outages is quadratic in form. Outages also increase labor cost, reduce exports …

Tornado Density And Return Periods In The Southeastern United States: Communicating Risk And Vulnerability At The Regional And State Levels, Michelle Bradburn

Electronic Theses and Dissertations

Tornado intensity and impacts vary drastically across space, thus spatial and statistical analyses were used to identify patterns of tornado severity in the Southeastern United States and to assess the vulnerability and estimated recurrence of tornadic activity. Records from the Storm Prediction Center's tornado database (1950-2014) were used to estimate kernel density to identify areas of high and low tornado frequency at both the regional- and state-scales. Return periods (2-year, 5-year, 10-year, 25-year, 50-year, and 100-year) were calculated at both scales as well using a composite score that included EF-scale magnitude, injury counts, and fatality counts. Results showed that the …

Multilevel Models For Longitudinal Data, Aastha Khatiwada

Electronic Theses and Dissertations

Longitudinal data arise when individuals are measured several times during an ob- servation period and thus the data for each individual are not independent. There are several ways of analyzing longitudinal data when different treatments are com- pared. Multilevel models are used to analyze data that are clustered in some way. In this work, multilevel models are used to analyze longitudinal data from a case study. Results from other more commonly used methods are compared to multilevel models. Also, comparison in output between two software, SAS and R, is done. Finally a method consisting of fitting individual models for each …

Propensity Score Based Methods For Estimating The Treatment Effects Based On Observational Studies., Younathan Abdia

Electronic Theses and Dissertations

This dissertation consists of two interconnected research projects. The first project was a study of propensity scores based statistical methods for estimating the average treatment effect (ATE) and the average treatment effect among treated (ATT) when there are two treatment groups. The ATE is defined as the mean of the individual causal effects in the whole population, while ATT is defined as the treatment effect for the treated population. Propensity score based statistical methods, such as matching, regression, stratification, inverse probability weighting (IPW), and doubly robust (DR) methods were used to estimate the ATE and ATT. Simulation studies and case …

Wind Climatology: A Study Of Trends On Rodgers' Dry Lakebed, Dana Coppernoll-Houston

STAR Program Research Presentations

A number of smaller projects at the Armstrong Flight Research Center fly on or close to the ground and are subject to ground-level winds. Many of these are new prototype models, such as PRANDTL-D (Preliminary Research Aerodynamic Design to Lower Drag). Waiting for the right conditions on a day of variable winds can sometimes mean that teams fail to complete testing. A strategic analysis of wind behavior at a locations where winds can vary greatly due to terrain could lend insight into the best times to test for near-ground aircraft. The purpose of this project was to data mine historical …

Utilizing Computed To Mography Image Features To Advance Prediction Of Radiation Pneumonitis, Shane P. Krafft

Dissertations and Theses (Open Access)

Improving outcomes for non-small-cell lung cancer patients treated with radiation therapy (RT) requires optimizing the balance between local tumor control and risk of normal tissue toxicity. In approximately 20% of patients, severe acute symptomatic lung toxicity, termed radiation pneumonitis (RP), still occurs. Identifying the individuals at risk of RP prior to or early during treatment offers tremendous potential to improve RT by providing the physician with information to assist in making clinical decisions that enhance therapy. Our central goal for this work was to demonstrate the potential gain in predictive accuracy of normal tissue complication probability models for RP by …

Accuracy And Precision Of Occlusal Contacts Of Stereolithographic Casts Mounted By Digital Interocclusal Registrations, Jason T. Krahenbuhl, Seok-Hwan Cho, Jon Patrick Irelan, Naveen K. Bansal

Mathematics, Statistics and Computer Science Faculty Research and Publications

Statement of problem

Little peer-reviewed information is available regarding the accuracy and precision of the occlusal contact reproduction of digitally mounted stereolithographic casts.

Purpose

The purpose of this in vitro study was to evaluate the accuracy and precision of occlusal contacts among stereolithographic casts mounted by digital occlusal registrations.

Material and methods

Four complete anatomic dentoforms were arbitrarily mounted on a semi-adjustable articulator in maximal intercuspal position and served as the 4 different simulated patients (SP). A total of 60 digital impressions and digital interocclusal registrations were made with a digital intraoral scanner to fabricate 15 sets of mounted stereolithographic …

Spatio-Temporal Analysis Of Point Patterns, Abdul-Nasah Soale

Electronic Theses and Dissertations

In this thesis, the basic tools of spatial statistics and time series analysis are applied to the case study of the earthquakes in a certain geographical region and time frame. Then some of the existing methods for joint analysis of time and space are described and applied. Finally, additional research questions about the spatial-temporal distribution of the earthquakes are posed and explored using statistical plots and models. The focus in the last section is in the relationship between number of events per year and maximum magnitude and its effect on how clustered the spatial distribution is and the relationship between …

Newsvendor Models With Monte Carlo Sampling, Ijeoma W. Ekwegh

Electronic Theses and Dissertations

Newsvendor Models with Monte Carlo Sampling by Ijeoma Winifred Ekwegh The newsvendor model is used in solving inventory problems in which demand is random. In this thesis, we will focus on a method of using Monte Carlo sampling to estimate the order quantity that will either maximizes revenue or minimizes cost given that demand is uncertain. Given data, the Monte Carlo approach will be used in sampling data over scenarios and also estimating the probability density function. A bootstrapping process yields an empirical distribution for the order quantity that will maximize the expected profit. Finally, this method will be used …

Some Nonparametric Ordered Restricted Inference Problems In The Context Of A Statistical Education Study, Bradford M. Dykes

Dissertations

Over the past 10 years, the Department of Statistics at Western Michigan University has developed a question generating system that can be used for creating multiple forms of exams, quizzes and homework for online and face-to-face use. This system can also be used to provide students with a form of instantaneous feedback. With the goal of analyzing how different levels of feedback in an online learning environment impacts students' performance on assignments, this study presents data collected on two semesters of students enrolled in three different meeting types (strictly online, typical face-to-face, and honors face-to-face) of an introductory Statistics course. …

Teaching The Quandary Of Statistical Jurisprudence: A Review-Essay On Math On Trial By Schneps And Colmez, Noah Giansiracusa

Journal of Humanistic Mathematics

This review-essay on the mother-and-daughter collaboration Math on Trial stems from my recent experience using this book as the basis for a college freshman seminar on the interactions between math and law. I discuss the strengths and weaknesses of this book as an accessible introduction to this enigmatic yet deeply important topic. For those considering teaching from this text (a highly recommended endeavor) I offer some curricular suggestions.

Simple Tools With Nontrivial Implications For Assessment Of Hypothesis-Evidence Relationships: The Interrogator’S Fallacy, Justus R. Riek

Journal of Humanistic Mathematics

This paper takes a mathematical analysis technique derived from the Interrogator’s Fallacy (in a legal context), expands upon it to identify a set of three interrelated probabilistic tools with wide applicability, and demonstrates their ability to assess hypothesis-evidence relationships associated with important problems

Apoe Ε4 Allele Modifies The Association Of Lead Exposure With Age-Related Cognitive Decline In Older Individuals, Diddier Prada, Elena Colicino, Melinda C. Power, Marc G Weisskopf, Jia Zhong, Lifang Hou, Avron Spiro, Pantel Vokonas, Plus 4 Others...

Epidemiology Faculty Publications

BACKGROUND: Continuing chronic and sporadic high-level of lead exposure in some regions in the U.S. has directed public attention to the effects of lead on human health. Long-term lead exposure has been associated with faster cognitive decline in older individuals; however, genetic susceptibility to lead-related cognitive decline during aging has been poorly studied.

METHODS: We determined the interaction of APOE-epsilon variants and environmental lead exposure in relation to age-related cognitive decline. We measured tibia bone lead by K-shell-x-ray fluorescence, APOE-epsilon variants by multiplex PCR and global cognitive z-scores in 489 men from the VA-Normative Aging Study. To determine global cognitive …

Update On Schizophrenia And Bipolar Disorder: Focus On Cariprazine, Rona Jeannie Roberts, Lillian Jan Findlay, Peggy El-Mallakh, Rif S. El-Mallakh

Nursing Faculty Publications

Schizophrenia and bipolar disorder are severe psychiatric disorders that are frequently associated with persistent symptoms and significant dysfunction. While there are a multitude of psychopharmacologic agents are available for treatment of these illnesses, suboptimal response and significant adverse consequences limit their utility. Cariprazine is a new, novel antipsychotic medication with dopamine D2 and D3 partial agonist effects. Its safety and efficacy have been investigated in acute psychosis of schizophrenia, bipolar mania, bipolar depression, and unipolar depression. Efficacy has been demonstrated in schizophrenia and mania. It is unclear if cariprazine is effective in depression associated with unipolar or bipolar illness. Adverse …

Retention Of Mothers And Infants In The Prevention Of Mother-To-Child Transmission Of Hiv Programme Is Associated With Individual And Facility-Level Factors In Rwanda., Godfrey B Woelk, Dieudonne Ndatimana, Sally Behan, Martha Mukaminega, Epiphanie Nyirabahizi, Heather J. Hoffman, Placidie Mugwaneza, Muhayimpundu Ribakare, Anouk Amzel, B Ryan Phelps

Epidemiology Faculty Publications

OBJECTIVES: Investigate levels of retention at specified time periods along the prevention of mother-to-child transmission (PMTCT) cascade among mother-infant pairs as well as individual- and facility-level factors associated with retention.

METHODS: A retrospective cohort of HIV-positive pregnant women and their infants attending five health centres from November 2010 to February 2012 in the Option B programme in Rwanda was established. Data were collected from several health registers and patient follow-up files. Additionally, informant interviews were conducted to ascertain health facility characteristics. Generalized estimating equation methods and modelling were utilized to estimate the number of mothers attending each antenatal care visit …

Self-Similar Random Process And Chaotic Behavior In Serrated Flow Of High Entropy Alloys, Shuying Chen, Liping Yu, Jingli Ren, Xie Xie, Xueping Li, Ying Xu, Guangfeng Zhao, Peizhen Li, Fuqian Yang, Yang Ren, Peter K. Liaw

Chemical and Materials Engineering Faculty Publications

The statistical and dynamic analyses of the serrated-flow behavior in the nanoindentation of a high-entropy alloy, Al_0.5CoCrCuFeNi, at various holding times and temperatures, are performed to reveal the hidden order associated with the seemingly-irregular intermittent flow. Two distinct types of dynamics are identified in the high-entropy alloy, which are based on the chaotic time-series, approximate entropy, fractal dimension, and Hurst exponent. The dynamic plastic behavior at both room temperature and 200 °C exhibits a positive Lyapunov exponent, suggesting that the underlying dynamics is chaotic. The fractal dimension of the indentation depth increases with the increase of temperature, and …

Variable Selection For Estimating The Optimal Treatment Regimes In The Presence Of A Large Number Of Covariate, Baqun Zhang, Min Zhang

The University of Michigan Department of Biostatistics Working Paper Series

Most of existing methods for optimal treatment regimes, with few exceptions, focus on estimation and are not designed for variable selection with the objective of optimizing treatment decisions. In clinical trials and observational studies, often numerous baseline variables are collected and variable selection is essential for deriving reliable optimal treatment regimes. Although many variable selection methods exist, they mostly focus on selecting variables that are important for prediction (predictive variables) instead of variables that have a qualitative interaction with treatment (prescriptive variables) and hence are important for making treatment decisions. We propose a variable selection method within a general classification …

Theorems On Boundedness Of Solutions To Stochastic Delay Differential Equations, Youssef Raffoul, Dan Ren

Mathematics Faculty Publications

In this report, we provide general theorems about boundedness or bounded in probability of solutions to nonlinear delay stochastic differential systems. Our analysis is based on the successful construction of suitable Lyapunov functionals. We offer several examples as application of our theorems.