Statistics and Probability Commons^™

Roles Of A Teacher And Researcher During In Situ Professional Development Around The Implementation Of Mathematical Modeling Tasks, Hyunyi Jung, Corey Brady

Mathematics, Statistics and Computer Science Faculty Research and Publications

Partnership with teachers for professional development has been considered beneficial because of the potential of collaborative work in the teacher’s own classroom to be relevant to practice. From this perspective, both teachers and researchers can draw on their own expertise and work as authentic partners. In this study, we address the need for such collaboration and focus on how a teacher and a researcher performed their roles when collaboratively implementing mathematical modeling tasks within a context of in situ professional development. Using multi-tier design-based research, as a framework, a researcher worked in a teacher’s classroom to implement a series of …

Bivariate Negative Binomial Hurdle With Random Spatial Effects, Robert Mcnutt

Dissertations

Count data with excess zeros widely occur in ecology, epidemiology, marketing, and many other disciplines. Mixture distributions consisting of a point mass at zero and a separate discrete distribution are often employed in regression models to account for excessive zero observations in the data. While Poisson models are very popular for count data, Negative Binomial models provide greater flexibility due to their ability to account for overdispersion.

This research focuses on developing a method for analyzing bivariate count data with excess zeros collected over a lattice. A bivariate Zero-Inflated Negative Binomial Hurdle (ZINBH) regression model with spatial random effects is …

Bayesian Rank Based Methods For Linear And Generalized Linear Models, James Kodzo Dzikunu

Dissertations

A Bayesian Rank Based Method for linear models is developed in this research. The estimation of the regression coefficients is based on the full conditional distributions utilizing a rank based initial fit. The data likelihood is based on the asymptotic distribution of the gradient function and the asymptotic linearity of this rank-based procedure. Prior distributions are put on regression coefficient(s) and scale parameter(s). The effects of different priors on this scale parameter(s) are studied. Using these full conditional distributions, the estimates are obtained by a Markov Chain Monte-Carlo (MCMC) procedure. The results of our simulation studies show that these Bayesian …

Uncovering Local Trends In Genetic Effects Of Multiple Phenotypes Via Functional Linear Models, Olga A. Vsevolozhskaya, Dmitri V. Zaykin, David A. Barondess, Xiaoren Tong, Sneha Jadhav, Qing Lu

Biostatistics Faculty Publications

Recent technological advances equipped researchers with capabilities that go beyond traditional genotyping of loci known to be polymorphic in a general population. Genetic sequences of study participants can now be assessed directly. This capability removed technology-driven bias toward scoring predominantly common polymorphisms and let researchers reveal a wealth of rare and sample-specific variants. Although the relative contributions of rare and common polymorphisms to trait variation are being debated, researchers are faced with the need for new statistical tools for simultaneous evaluation of all variants within a region. Several research groups demonstrated flexibility and good statistical power of the functional linear …

Implementation And Validation Of A Probabilistic Open Source Baseball Engine (Posbe): Modeling Hitters And Pitchers, Rhett Tracy Schaefer

Open Access Theses

This manuscript details the implementation and validation of an open source probabilistic baseball engine (POSBE) that focuses on the hitter and pitcher model of the simulation. The simulation produced outcomes that parallel those observed in actual professional Major League Baseball games. The observed data were taken from the nineteen games played between the New York Yankees (NYY) and Boston Red Sox (BOS) during the 2015 season. The potential hitter/pitcher outcomes of interest were singles, doubles, triples, homeruns, walks, hit-by-pitch, and strikeouts. The nineteen game series was simulated 1000 times, resulting in a total of 19,000 simulations. The eighteen hitters and …

Case-Oriented Pathways Analysis In Pancreatic Adenocarcinoma Using Data From A Sleeping Beauty Transposon Mutagenesis Screen, Yen Yi Ho, Timothy K. Starr, Rebecca S. Larue, David A. Largaespada

Faculty Publications

Background: Mutation studies of pancreatic ductal adenocarcinoma (PDA) have revealed complicated heterogeneous genomic landscapes of the disease. These studies cataloged a number of genes mutated at high frequencies, but also report a very large number of genes mutated in lower percentages of tumors. Taking advantage of a well-established forward genetic screening technique, with the Sleeping Beauty (SB) transposon, several studies produced PDA and discovered a number of common insertion sites (CIS) and associated genes that are recurrently mutated at high frequencies. As with human mutation studies, a very large number of genes were found to be altered by transposon insertion …

Empirical Evaluation Of Different Features Of Design In Confirmatory Factor Analysis, Deyab Almaleki

Dissertations

Factor analysis (FA) is the study of variance within a group. Within-subject variance (WSV) is affected by multiple features in a study context, such as: the study experimental design (ED) and sampling design (SD), thus anything that influences or changes variance may affect the conclusions related to FA.

The aim of this study was to provide empirical evaluation of the influence of different aspects of ED and SD on WSV in the context of FA in terms of model precision and model estimate stability. Four Monte Carlo population correlation matrices were hypothesized based on different communality magnitudes (high, moderate, low, …

One-Step Targeted Minimum Loss-Based Estimation Based On Universal Least Favorable One-Dimensional Submodels, Mark J. Van Der Laan, Susan Gruber

U.C. Berkeley Division of Biostatistics Working Paper Series

Consider a study in which one observes n independent and identically distributed random variables whose probability distribution is known to be an element of a particular statistical model, and one is concerned with estimation of a particular real valued pathwise differentiable target parameter of this data probability distribution. The targeted maximum likelihood estimator (TMLE) is an asymptotically efficient substitution estimator obtained by constructing a so called least favorable parametric submodel through an initial estimator with score, at zero fluctuation of the initial estimator, that spans the efficient influence curve, and iteratively maximizing the corresponding parametric likelihood till no more updates …

Modeling And Survival Analysis Of Breast Cancer: A Statistical, Artificial Neural Network, And Decision Tree Approach, Venkateswara Rao Mudunuru

USF Tampa Graduate Theses and Dissertations

Survival analysis today is widely implemented in the fields of medical and biological sciences, social sciences, econometrics, and engineering. The basic principle behind the survival analysis implies to a statistical approach designed to take into account the amount of time utilized for a study period, or the study of time between entry into observation and a subsequent event. The event of interest pertains to death and the analysis consists of following the subject until death. Events or outcomes are defined by a transition from one discrete state to another at an instantaneous moment in time. In the recent years, research …

Maximum Likelihood Based Analysis Of Equally Spaced Longitudinal Count Data With Specified Marginal Means, First-Order Antedependence, And Linear Conditional Expectations, Victoria Gamerman, Matthew Guerra, Justine Shults

UPenn Biostatistics Working Papers

This manuscript implements a maximum likelihood based approach that is appropriate for equally spaced longitudinal count data with over-dispersion, so that the variance of the outcome variable is larger than expected for the assumed Poisson distribution. We implement the proposed method in the analysis of two data sets and make comparisons with the semi-parametric generalized estimating equations (GEE) approach that incorrectly ignores the over-dispersion. The simulations demonstrate that the proposed method has better small sample efficiency than GEE. We also provide code in R that can be used to recreate the analysis results that we provide in this manuscript.

Marginal Structural Models With Counterfactual Effect Modifiers, Wenjing Zheng, Zhehui Luo, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

In health and social sciences, research questions often involve systematic assessment of the modification of treatment causal effect by patient characteristics, in longitudinal settings with time-varying or post-intervention effect modifiers of interest. In this work, we investigate the robust and efficient estimation of the so-called Counterfactual-History-Adjusted Marginal Structural Model (van der Laan and Petersen (2007)), which models the conditional intervention-specific mean outcome given modifier history in an ideal experiment where, possible contrary to fact, the subject was assigned the intervention of interest, including the treatment sequence in the conditioning history. We establish the semiparametric efficiency theory for these models, and …

Conditional Screening For Ultra-High Dimensional Covariates With Survival Outcomes, Hyokyoung Grace Hong, Jian Kang, Yi Li

The University of Michigan Department of Biostatistics Working Paper Series

Identifying important biomarkers that are predictive for cancer patients' prognosis is key in gaining better insights into the biological influences on the disease and has become a critical component of precision medicine. The emergence of large-scale biomedical survival studies, which typically involve excessive number of biomarkers, has brought high demand in designing efficient screening tools for selecting predictive biomarkers. The vast amount of biomarkers defies any existing variable selection methods via regularization. The recently developed variable screening methods, though powerful in many practical setting, fail to incorporate prior information on the importance of each biomarker and are less powerful in …

Determining The Optimal Work Breakdown Structure For Government Acquisition Contracts, Brian J. Fitzpatrick

Theses and Dissertations

The optimal level of Government Contract Work Breakdown Structure (G-CWBS) reporting for the purposes of Earned Value Management was inspected. The G-Score Metric was proposed, which can quantitatively grade a G-CWBS, based on a new method of calculating an Estimate At Completion (EAC) cost for each reported element. A random program generator created in R replicated the characteristics of DOD program artifacts retrieved from the Cost Analysis Data Enterprise (CADE) system. The generated artifacts were validated as a population, however validation at the demographic combination level using an artificial neural network was inconclusive. Comparative WBS forms were created for a …

Analysis And Modeling Of U.S. Army Recruiting Markets, Joshua L. Mcdonald

Theses and Dissertations

The United States Army Recruiting Command (USAREC) is charged with finding, engaging, and ultimately enlisting young Americans for service as Soldiers in the U.S. Army. USAREC must decide how to allocate monthly enlistment goals, by aptitude and education level, across its 38 subordinate recruiting battalions in order to maximize the number of enlistment contracts produced each year. In our research, we model the production of enlistment contracts as a function of recruiting supply and demand factors which vary over the recruiting battalion areas of responsibility. Using county-level data for the period of recruiting year RY2010 through RY2013 mapped to recruiting …

Predicting Schedule Duration For Defense Acquisition Programs: Program Initiation To Initial Operational Capability, Christopher A. Jimenez

Theses and Dissertations

Accurately predicting the most realistic schedule for a defense acquisitions program is an extremely difficult task considering the inherent risk and uncertainties present in the early stages of a program. We use a multiple regression analysis to predict schedule duration in a defense acquisition program. The prediction scope of our research is limited to predicting schedule duration from program initiation to initial operation capability (IOC).We use the data from 56 programs across all services, which was acquired from a SAR database created by RAND. We were able to achieve an R2 of 0.429 and an Adjusted R2 of 0.384 in …

Clustering Theory And Data Driven Health Care Strategies, Takayuki Iguchi

Theses and Dissertations

DoD health care requires reform with growing costs causing concerns of decreased military capability. One proposed radical strategy to fix current health care delivery systems is to organize medical teams around patients with similar treatment requirements. This is a clustering problem; how do you partition the set of patients so that each group has similar treatment needs? We provide advances in clustering theory relevant to this new health care strategy. In particular, we create fast certifiably optimal k-means clustering using what is known as Probably Certifiably Correct (PCC) algorithms which achieves state-of-the-art performance under certain models. Inspired by the health …

Application Of Non-Rated Line Officer Attrition Levels And Career Field Stability, Christine L. Zens

Theses and Dissertations

The Air Force monitors the strength of its active duty officer force and attempts to achieve the difficult challenge of employing a diversity of talent among career specialties and experience levels. This study completes two objectives, predicting future manning levels for 23 career fields, and providing a statistical framework to assess the stability of these fields. The first part of the study applies regression and survival analysis to subpopulations within the active duty Air Force officer corps, and then aggregates them by year to forecast future personnel levels. Four career fields are considered, including Acquisitions (ACQ), Logistics (LOG), Support (SPT), …

Correlation Of Maximal Inspiratory Pressure To Transdiaphragmatic Twitch Pressure In Intensive Care Unit Patients, Gerald S. Supinski, Philip M. Westgate, Leigh Ann Callahan

Internal Medicine Faculty Publications

Background: Respiratory muscle weakness contributes to respiratory failure in ICU patients. Unfortunately, assessment of weakness is difficult since the most objective test, transdiaphragmatic pressure in response to phrenic nerve stimulation (PdiTw), is difficult to perform. While most clinicians utilize maximum inspiratory pressure (Pimax) to assess strength, the relationship of this index to PdiTw has not been evaluated in a large ICU population. The purpose of the present study was to assess both PdiTw and Pimax in ICU patients to determine how these indices correlate with each other, what factors influence these indices, and how well these indices predict outcomes.

Methods: …

Asymptotically Periodic Solutions Of Volterra Integral Equations, Muhammad Islam

Mathematics Faculty Publications

We study the existence of asymptotically periodic solutions of a nonlinear Volterra integral equation. In the process, we obtain the existence of periodic solutions of an associated nonlinear integral equation with infinite delay. Schauder's fixed point theorem is used in the analysis.

Smallest Eigenvalues For A Right Focal Boundary Value Problem, Paul W. Eloe, Jeffrey T. Neugebauer

Mathematics Faculty Publications

We establish the existence of smallest eigenvalues for the fractional linear boundary value problems D^α₀₊u+λ₁p(t)u = 0 and D^α₀₊u+λ₂q(t)u = 0, 0