Statistics and Probability Commons^™

Extremal H-Colorings Of Trees And 2-Connected Graphs, John Engbers, David Galvin

Mathematics, Statistics and Computer Science Faculty Research and Publications

For graphs G and H, an H-coloring of G is an adjacency preserving map from the vertices of G to the vertices of H. H-colorings generalize such notions as independent sets and proper colorings in graphs. There has been much recent research on the extremal question of finding the graph(s) among a fixed family that maximize or minimize the number of H-colorings. In this paper, we prove several results in this area.

First, we find a class of graphs H with the property that for each H∈H, the n-vertex tree that minimizes the number of …

Varieties Of Restriction Semigroups And Varieties Of Categories, Peter R. Jones

Mathematics, Statistics and Computer Science Faculty Research and Publications

The variety of restriction semigroups may be most simply described as that generated from inverse semigroups (S, ·, −1) by forgetting the inverse operation and retaining the two operations x+ = xx−1 and x* = x−1x. The subvariety B of strictrestriction semigroups is that generated by the Brandt semigroups. At the top of its lattice of subvarieties are the two intervals [B2, B2M = B] and [B0, B0M]. Here, B2and B0 are, respectively, generated by the five-element Brandt semigroup and that obtained …

Protein Structure Classification And Loop Modeling Using Multiple Ramachandran Distributions, Seyed Morteza Najibi, Mehdi Maadooliat, Lan Zhou, Jianhua Z. Huang, Xin Gao

Mathematics, Statistics and Computer Science Faculty Research and Publications

Recently, the study of protein structures using angular representations has attracted much attention among structural biologists. The main challenge is how to efficiently model the continuous conformational space of the protein structures based on the differences and similarities between different Ramachandran plots. Despite the presence of statistical methods for modeling angular data of proteins, there is still a substantial need for more sophisticated and faster statistical tools to model the large-scale circular datasets. To address this need, we have developed a nonparametric method for collective estimation of multiple bivariate density functions for a collection of populations of protein backbone angles. …

K-8 Pre-Service Teachers’ Algebraic Thinking: Exploring The Habit Of Mind Building Rules To Represent Functions, Marta T. Magiera, John C. Moyer, Leigh A. Van Den Kieboom

Mathematics, Statistics and Computer Science Faculty Research and Publications

In this study, through the lens of the algebraic habit of mind Building Rules to Represent Functions, we examined 18 pre-service middle school teachers' ability to use algebraic thinking to solve problems. The data revealed that pre-service teachers' ability to use different features of the habit of mind Building Rules to Represent Functions varied across the features. Significant correlations existed between 8 pairs of the features. The ability to justify a rule was the weakest of the seven features and it was correlated with the ability to chunk information. Implications for mathematics teacher education are discussed.

06. Sas Program Files For Design And Analysis Of Experiments, Angela Dean, Dan Voss, Danel Draguljic

Design and Analysis of Experiments

SAS program files for use with Design and Analysis of Experiments.

08. R Program Files For Design And Analysis Of Experiments, Angela Dean, Dan Voss, Danel Draguljic

Design and Analysis of Experiments

R program files for use with Design and Analysis of Experiments.

07. Sas Data Files For Design And Analysis Of Experiments, Angela Dean, Dan Voss, Danel Draguljic

Design and Analysis of Experiments

SAS Data files for use with Design and Analysis of Experiments.

Flexibility Of Projective-Planar Embeddings, John Maharry, Neil Robertson, Vaidy Sivaraman, Dan Slilaty

Mathematics and Statistics Faculty Publications

Given two embeddings σ1 and σ2 of a labeled nonplanar graph in the projective plane, we give a collection of maneuvers on projective-planar embeddings that can be used to take σ1 to σ2

The Nonparametric Estimation Of Elliptical Distributions, Panfeng Liang

Open Access Theses & Dissertations

In practice, many multivariate datasets have identical marginal distributions. Elliptical distributions can be used to model many of those datasets. In this Thesis, we will propose a Bayesian method using Markov chain Monte Carlo (MCMC) methods to estimate the density function underlying multivariate datasets assuming it is an elliptical distribution.

Advance Care Planning As A Shared Endeavor: Completion Of Acp Documents In A Multidisciplinary Cancer Program, Melissa A. Clark, Miles Q. Ott, Michelle L. Rogers, Mary C. Politi, Susan C. Miller, Laura Moynihan, Katina Robison, Ashley Stuckey, Don Dizon

Statistical and Data Sciences: Faculty Publications

Objective—We examined the roles of oncology providers in advance care planning (ACP) delivery in the context of a multidisciplinary cancer program.

Methods—Semi-structured interviews were conducted with 200 women with recurrent and/or metastatic breast or gynecologic cancer. Participants were asked to name providers they deemed important in their cancer care and whether they had discussed and/or completed ACP documentation. Evidence of ACP documentation was obtained from chart reviews.

Results—Fifty percent of participants self-reported completing an advance directive (AD) and 48.5% had named a healthcare power of attorney (HPA), 38.5% had completed both, and 39.0% had completed neither document. Among women who …

Alcohol Perceptions And Behavior In A Residential Peer Social Network, Shannon R. Kenney, Miles Q. Ott, Matthew Meisel, Nancy P. Barnett

Statistical and Data Sciences: Faculty Publications

Personalized normative feedback is a recommended component of alcohol interventions targeting college students. However, normative data are commonly collected through campus-based surveys, not through actual participant-referent relationships. In the present investigation, we examined how misperceptions of residence hall peers, both overall using a global question and those designated as important peers using person-specific questions, were related to students’ personal drinking behaviors. Participants were 108 students (88% freshman, 54% White, 51% female) residing in a single campus residence hall. Participants completed an online baseline survey in which they reported their own alcohol use and perceptions of peer alcohol use using both …

Curriculum Guidelines For Undergraduate Programs In Data Science, Richard D. De Veaux, Mahesh Agarwal, Maia Averett, Benjamin Baumer, Andrew Bray, Thomas C. Bressoud, Lance Bryant, Lei Z. Cheng, Amanda Francis, Robert Gould, Albert Y. Kim, Matt Kretchmar, Qin Lu, Ann Moskol, Deborah Nolan, Roberto Pelayo, Sean Raleigh, Ricky J. Sethi, Mutiara Sondjaja, Neelesh Tiruviluamala, Paul X. Uhlig, Talitha M. Washington, Curtis L. Wesley, David White, Ping Ye

Statistical and Data Sciences: Faculty Publications

The Park City Math Institute 2016 Summer Undergraduate Faculty Program met for the purpose of composing guidelines for undergraduate programs in data science. The group consisted of 25 undergraduate faculty from a variety of institutions in the United States, primarily from the disciplines of mathematics, statistics, and computer science. These guidelines are meant to provide some structure for institutions planning for or revising a major in data science.

Augmenting Bottom-Up Metamodels With Predicates, Ross J. Gore, Saikou Diallo, Christopher Lynch, Jose Padilla

VMASC Publications

Metamodeling refers to modeling a model. There are two metamodeling approaches for ABMs: (1) top-down and (2) bottom-up. The top down approach enables users to decompose high-level mental models into behaviors and interactions of agents. In contrast, the bottom-up approach constructs a relatively small, simple model that approximates the structure and outcomes of a dataset gathered fromthe runs of an ABM. The bottom-up metamodel makes behavior of the ABM comprehensible and exploratory analyses feasible. Formost users the construction of a bottom-up metamodel entails: (1) creating an experimental design, (2) running the simulation for all cases specified by the design, (3) …

The Use Of The Pivot Pairwise Relative Criteria Importance Assessment Method For Determining The Weights Of Criteria, Florentin Smarandache, Dragisa Stanujkic, Edmundas Kazimieras Zavadskas, Darjan Karabasevic, Zenonas Turskis

Branch Mathematics and Statistics Faculty and Staff Publications

The weights of evaluation criteria could have a significant impact on the results obtained by applying multiple criteria decision-making methods. Therefore, the two extensions of the SWARA method that can be used in cases when it is not easy, or even is impossible to reach a consensus on the expected importance of the evaluation criteria are proposed in this paper. The primary objective of the proposed extensions is to provide an understandable and easy-to-use approach to the collecting of respondents’ real attitudes towards the significance of evaluation criteria and to also provide an approach to the checking of the reliability …

Improving The Computational Efficiency In Bayesian Fitting Of Cormack-Jolly-Seber Models With Individual, Continuous, Time-Varying Covariates, Woodrow Burchett

Theses and Dissertations--Statistics

The extension of the CJS model to include individual, continuous, time-varying covariates relies on the estimation of covariate values on occasions on which individuals were not captured. Fitting this model in a Bayesian framework typically involves the implementation of a Markov chain Monte Carlo (MCMC) algorithm, such as a Gibbs sampler, to sample from the posterior distribution. For large data sets with many missing covariate values that must be estimated, this creates a computational issue, as each iteration of the MCMC algorithm requires sampling from the full conditional distributions of each missing covariate value. This dissertation examines two solutions to …

Novel Computational Methods For Censored Data And Regression, Yifan Yang

Theses and Dissertations--Statistics

This dissertation can be divided into three topics. In the first topic, we derived a recursive algorithm for the constrained Kaplan-Meier estimator, which promotes the computation speed up to fifty times compared to the current method that uses EM algorithm. We also showed how this leads to the vast improvement of empirical likelihood analysis with right censored data. After a brief review of regularized regressions, we investigated the computational problems in the parametric/non-parametric hybrid accelerated failure time models and its regularization in a high dimensional setting. We also illustrated that, when the number of pieces increases, the discussed models are …

Nonparametric Compound Estimation, Derivative Estimation, And Change Point Detection, Sisheng Liu

Theses and Dissertations--Statistics

Firstly, we reviewed some popular nonparameteric regression methods during the past several decades. Then we extended the compound estimation (Charnigo and Srinivasan [2011]) to adapt random design points and heteroskedasticity and proposed a modified Cp criteria for tuning parameter selection. Moreover, we developed a DCp criteria for tuning paramter selection problem in general nonparametric derivative estimation. This extends GCp criteria in Charnigo, Hall and Srinivasan [2011] with random design points and heteroskedasticity. Next, we proposed a change point detection method via compound estimation for both fixed design and random design case, the adaptation of heteroskedasticity was considered for the method. …

A Predictive Probability Interim Design For Phase Ii Clinical Trials With Continuous Endpoints, Meng Liu

Theses and Dissertations--Epidemiology and Biostatistics

Phase II clinical trials aim to potentially screen out ineffective and identify effective therapies to move forward to randomized phase III trials. Single-arm studies remain the most utilized design in phase II oncology trials, especially in scenarios where a randomized design is simply not practical. Due to concerns regarding excessive toxicity or ineffective new treatment strategies, interim analyses are typically incorporated in the trial, and the choice of statistical methods mainly depends on the type of primary endpoints. For oncology trials, the most common primary objectives in phase II trials include tumor response rate (binary endpoint) and progression disease-free survival …

An Exploratory Statistical Method For Finding Interactions In A Large Dataset With An Application Toward Periodontal Diseases, Joshua Lambert

Theses and Dissertations--Epidemiology and Biostatistics

It is estimated that Periodontal Diseases effects up to 90% of the adult population. Given the complexity of the host environment, many factors contribute to expression of the disease. Age, Gender, Socioeconomic Status, Smoking Status, and Race/Ethnicity are all known risk factors, as well as a handful of known comorbidities. Certain vitamins and minerals have been shown to be protective for the disease, while some toxins and chemicals have been associated with an increased prevalence. The role of toxins, chemicals, vitamins, and minerals in relation to disease is believed to be complex and potentially modified by known risk factors. A …

Statistical Analyses To Detect And Refine Genetic Associations With Neurodegenerative Diseases, Yuriko Katsumata

Theses and Dissertations--Epidemiology and Biostatistics

Dementia is a clinical state caused by neurodegeneration and characterized by a loss of function in cognitive domains and behavior. Alzheimer’s disease (AD) is the most common form of dementia. Although the amyloid β (Aβ) protein and hyperphosphorylated tau aggregates in the brain are considered to be the key pathological hallmarks of AD, the exact cause of AD is yet to be identified. In addition, clinical diagnoses of AD can be error prone. Many previous studies have compared the clinical diagnosis of AD against the gold standard of autopsy confirmation and shown substantial AD misdiagnosis Hippocampal sclerosis of aging (HS-Aging) …

Barriers To Counseling Among Human Service Professionals: The Development And Validation Of The Fit, Stigma, & Value Scale, Edward S. Neukrug, Michael T. Kalkbrenner, Sandy-Ann M. Griffith

Counseling & Human Services Faculty Publications

This study sought to confirm rates of attendance in counseling of human service professionals and validate a 32-item questionnaire designed to identify barriers to counseling seeking behavior among this population. Results indicated that a large percentage of human service professionals attend counseling, with males and females attending at similar rates and non-Caucasians attending at lower rates. A multivariate analysis of variance and descriptive statistics identified the most common barriers to attendance in counseling and examined demographic differences in participants’ sensitivity towards barriers to attendance in counseling. A Principal Factor Analysis (PFA) revealed three subscales (fit, value, and stigma), which we …

Estimating The Coefficients Of A Linear Differential Operator, Maria Ivette Barraza

Open Access Theses & Dissertations

Principal Differential Analysis (PDA; Ramsay, 1996) is used to obtain low dimensional representations of functional data, where each observation is represented as a curve. PDA seeks to identify a Linear Differential Operator (LDO) L = ω0I + ω 1D + ... + ωmDm, where I denotes the identity function and D j the jth derivative, that satisfies as closely as possible that Lx = 0 for each functional observation x. A theorem from analysis establishes that the coefficients of the LDO are in the Sobolev space, and thus can be approximated by B-splines. Current PDA software used to estimate the …

Predicting Individualized Treatment Effects Via Random Forests Of Interaction Trees, Annette Pena Franco

Open Access Theses & Dissertations

Abstract Not Available

Analysis Of Bias-Corrected And Exact Estimators For Binomial Generalized Linear Model Parameters, Hamna Hannan

Open Access Theses & Dissertations

Typically, small samples have always been a problem for binomial generalized linear models. Though generalized linear models are widely popular in public health, social sciences etc. In small sample scenarios the non-existence of the maximum likelihood (ML) estimators is very common as well as separation occurs in the data. In logistic regression the maximum likelihood estimates are found to have biased away from origin. My work examines the bias-reduced and exact estimators that have been used to estimate the slope parameters and standard errors of the estimated slope parameters as compared to the traditional ML method.

The present work is …

Sample Size Estimation For Linear Mixed Models With Dependent End Points, Michael Nsiah-Nimo

Open Access Theses & Dissertations

The primary objective is sample size estimation in linear mixed model settings. Sample size estimation is an important component of planning a well thought out scientific experiment. Whenever sample size estimation is performed, taking into account a priori model based inferences will provide a sample size estimate that will achieve the desired power without inflating the type I error rate of the study.

One common practice is a traditional approach cited in the literature that uses the largest sample size after you Bonferroni the type I error rate to estimate sample sizes as such. We are going to take into …

Evaluating Binary Splits On Nominal Inputs, Isaac Xoese Ocloo

Open Access Theses & Dissertations

The maximally selected statistic approach in building tree models is shown to be a cause of variable selection bias. In this study we propose three methods to solve this problem in building regression trees with nominal predictor variables. Out of the three methods

proposed we explored only two in detail and defer one for further research. We developed an exact method to compute the p-value corresponding to the maximized splitting statistic in regression trees for nominal predictor variables with at most 10 distinct levels and a

method to estimate the best cutoff point as a parameter in a parametric nonlinear …

On The Equivalence Between Bayesian And Frequentist Nonparametric Hypothesis Testing, Qiuchen Hai

Dissertations, Master's Theses and Master's Reports

Testing of hypotheses about the population parameter is one of the most fundamental tasks in the empirical sciences and is often conducted by using parametric tests (e.g., the t-test and F-test), in which they assume that the samples are from populations that are normally distributed. When the normality assumption is violated, nonparametric tests are employed as alternatives for making statistical inference. In recent years, the Bayesian versions of parametric tests have been well studied in the literature, whereas in contrast, the Bayesian versions of nonparametric tests are quite scant (for exception, Yuan and Johnson (2008) ) in the literature, mainly …

Gamma/Hadron Separation For The Hawc Observatory, Michael J. Gerhardt

Dissertations, Master's Theses and Master's Reports

The High-Altitude Water Cherenkov (HAWC) Observatory is a gamma-ray observatory sensitive to gamma rays from 100 GeV to 100 TeV with an instantaneous field of view of ~2 sr. It is located on the Sierra Negra plateau in Mexico at an elevation of 4,100 m and began full operation in March 2015. The purpose of the detector is to study relativistic particles that are produced by interstellar and intergalactic objects such as: pulsars, supernova remnants, molecular clouds, black holes and more. To achieve optimal angular resolution, energy reconstruction and cosmic ray background suppression for the extensive air showers detected by …

A Meta-Analysis Of The Effects Of Incentives On Response Rate In Online Survey Studies, Amal Muhammad Asire

Electronic Theses and Dissertations

Meta-analysis was used to investigate the effect of incentives on response rates of web-based survey studies. Whereas numerous meta-analyses that address the effect of incentives on increasing response rates in survey studies are available in the literature, these analyses are based on mail surveys, so there is a need for an applied meta-analysis to examine the effect of incentives on response rates in online survey studies. A meta-analysis of an online method of survey administration was used because the use of online surveys has greatly increased, making web-based survey administration an important form of data collection in multiple fields of …

A Markov Decision Process Approach To Adaptive Contact Strategies, Artur Grygorian

College of Graduate Studies: Theses & Dissertations

In the field of survey methodology, optimizing contact strategies helps organizations increase response rates using their allocated budget. Markov Decision Processes (MDP) are widely used to model decision-making strategies in situations where the outcomes have a random component. In this research, we use MDPs and adaptive sampling techniques to construct a strategy that, based on target audience characteristics, suggests the best contact policy. The data we use comes from the First Destination Survey conducted by the Office of Career Services at Georgia Southern University. The constructed model is quite flexible and can be used by other organizations to optimize their …