Statistics and Probability Commons^™

A Probability Model For Strategic Bidding On The Price Is Right, Paul H. Kvam

Department of Math & Statistics Faculty Publications

The TV game show “The Price is Right” features a bidding auction called “Contestants’ Row” that rewards the player (out of 4) who bids closest to an item’s value, without overbidding. This paper considers ways in which players can maximize a winning probability based on the player's bidding order. We consider marginal strategies in which players assume opponents are bidding individually perceived values of the merchandise. Based on preceding bids of others, players have information available to create strategies. We consider conditional strategies in which players adjust bids knowing other players are using strategies. The last bidder has a large …

Step-Selection Functions For Modeling Animal Movement -- Case Study: African Buffalo, Maia Adar

CMC Senior Theses

Understanding what factors influence wildlife movement allows landscape planners to make informed decisions that benefit both animals and humans. New quantitative methods, such as step-selection functions, provide valuable objective analyses of wildlife connectivity. This paper provides a framework for creating a step-selection function and demonstrates its use in a case study. The first section provides a general introduction about wildlife connectivity research. The second section explains the math behind the step-selection function using a simple example. The last section gives the results of a step-selection model for African buffalo in the Kavango Zambezi Transfrontier Conservation Area. Buffalo were found to …

Predictive Golf Analytics Versus The Daily Fantasy Sports Market, John O'Malley

CMC Senior Theses

This study examines the different skills necessary for PGA tour players to succeed at specific annual tournaments, in order to create a predictive model for DraftKings PGA contests. The model takes into account data from the PGA Tour ShotLink Intelligence Program. The predictive model is created each week based on past results from the specific tournament in question, with the hope of predicting a group of twenty-five players who should be successful based on their statistical profile. The results of the model are detailed in this paper, which covers the first nine weeks of the 2017 PGA Tour season, with …

Characterizations And Infinite Divisibility Of Certain Recently Introduced Distributions Iii, Gholamhossein G. Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Certain characterizations of recently proposed univariate continuous distributions are presented in different directions. This work may be a source of preventing reinventing and duplicating the existing distributions and calling them newly proposed distributions.

On The Mixtures Of Weibull And Pareto (Iv) Distribution: An Alternative To Pareto Distribution, I. Ghosh, Gholamhossein G. Hamedani, Naveen K. Bansal, Mehdi Maadooliat

Mathematics, Statistics and Computer Science Faculty Research and Publications

Finite mixture models have provided a reasonable tool to model various types of observed phenomena, specially those which are random in nature. In this article, a finite mixture of Weibull and Pareto (IV) distribution is considered and studied. Some structural properties of the resulting model are discussed including estimation of the model parameters via expectation maximization (EM) algorithm. A real-life data application exhibits the fact that in certain situations, this mixture model might be a better alternative than the rival popular models.

On Characterizations Of Mcllog, Ellogw, Pthl And K-Ge Distributions, Gholamhossein G. Hamedani, Nadeem Shafique Butt

Mathematics, Statistics and Computer Science Faculty Research and Publications

Huang S. and Oluyede (2016), Oluyede et al. (2016), Krishnarani (2016) and Rather and Rather (2017) consider the "McDonald Log-Logistic", the "Exponentiated Log-Logistic Weibull", the "Power Transformation Half-Logistic" and "k-Generalized Exponential" distributions, respectively, and study certain properties and applications of these distributions. The present short note is intended to complete, in some way, the above mentioned works via establishing certain characterizations of these distributions in different directions.

A Bayesian Variable Selection Approach Yields Improved Detection Of Brain Activation From Complex-Valued Fmri, Cheng-Han Yu, Raquel Prado, Hernando Ombao, Daniel B. Rowe

Mathematics, Statistics and Computer Science Faculty Research and Publications

Voxel functional magnetic resonance imaging (fMRI) time courses are complex-valued signals giving rise to magnitude and phase data. Nevertheless, most studies use only the magnitude signals and thus discard half of the data that could potentially contain important information. Methods that make use of complex-valued fMRI (CV-fMRI) data have been shown to lead to superior power in detecting active voxels when compared to magnitude-only methods, particularly for small signal-to-noise ratios (SNRs). We present a new Bayesian variable selection approach for detecting brain activation at the voxel level from CV-fMRI data. We develop models with complex-valued spike-and-slab priors on the activation …

Approximation Of Quantiles Of Rank Test Statistics Using Almost Sure Limit Theorems, Mark Ledbetter

Mathematics & Statistics Theses & Dissertations

There are many problems in statistics where the analysis is based on asymptotic distributions. In some cases, the asymptotic distribution is in an open form or is intractable. One possible solution is the logarithmic quantile estimation (LQE) method introduced by Thangavelu (2005) for rank tests and Fridline (2010) for the correlation coefficient. LQE is derived from an almost sure version of the central limit theorem using the results of Berkes and Csaki (2001), and it estimates the quantiles of a test statistic using only the data. To date, LQE has been used in only a few applications. We extend the …

Adaptive Methods For Point Cloud And Mesh Processing, Zinat Afrose

Computational Modeling & Simulation Engineering Theses & Dissertations

Point clouds and 3D meshes are widely used in numerous applications ranging from games to virtual reality to autonomous vehicles. This dissertation proposes several approaches for noise removal and calibration of noisy point cloud data and 3D mesh sharpening methods. Order statistic filters have been proven to be very successful in image processing and other domains as well. Different variations of order statistics filters originally proposed for image processing are extended to point cloud filtering in this dissertation. A brand-new adaptive vector median is proposed in this dissertation for removing noise and outliers from noisy point cloud data.

The major …

The Effect Of Rare Variants In Trem2 And Pld3 On Longitudinal Cognitive Function In The Wisconsin Registry For Alzheimer's Prevention, Corinne D. Engelman, Burcu F. Darst, Murat Bilgel, Eva Vasiljevic, Rebecca L. Koscik, Bruno M. Jedynak, Sterling C. Johnson

Mathematics and Statistics Faculty Publications and Presentations

Recent studies have found an association between functional variants in TREM2 and PLD3 and Alzheimer's disease (AD), but their effect on cognitive function is unknown. We examined the effect of these variants on cognitive function in 1449 participants from the Wisconsin Registry for Alzheimer's Prevention, a longitudinal study of initially asymptomatic adults, aged 36–73 years at baseline, enriched for a parental history of AD. A comprehensive cognitive test battery was performed at up to 5 visits. A factor analysis resulted in 6 cognitive factors that were standardized into z scores (∼N [0, 1]); the mean of these z scores was …

Simulations For Designing And Interpreting Intervention Trials In Infectious Diseases., M Elizabeth Halloran, Kari Auranen, Sarah Baird, Nicole E Basta, Steven E Bellan, +Several Additional Authors

Global Health Faculty Publications

BACKGROUND: Interventions in infectious diseases can have both direct effects on individuals who receive the intervention as well as indirect effects in the population. In addition, intervention combinations can have complex interactions at the population level, which are often difficult to adequately assess with standard study designs and analytical methods.

DISCUSSION: Herein, we urge the adoption of a new paradigm for the design and interpretation of intervention trials in infectious diseases, particularly with regard to emerging infectious diseases, one that more accurately reflects the dynamics of the transmission process. In an increasingly complex world, simulations can explicitly represent transmission dynamics, …

Long-Term Outcomes After Elective Sterilization Procedures — A Comparative Retrospective Cohort Study Of Medicaid Patients, Rachel Steward, Patricia Carney, Amy Law, Lin Xie, Yuexi Wang, Huseyin Yuce

Publications and Research

Objectives: The objectives were to compare the long-termoutcomes, including hysterectomy, chronic pelvic pain (CPP) and abnormal uterine bleeding (AUB), in women post hysteroscopic sterilization (HS) and laparoscopic tubal ligation (TL) in the Medicaid population.

Study design: This was a retrospective observational cohort analysis using data from the US Medicaid Analytic Extracts Encounters database.Women aged 18 to 49 years with at least one claimfor HS (n=3929) or TL (n=10,875) between July 1, 2009, through December 31, 2010, were included. Main outcome measures were hysterectomy, CPP or AUB in the 24 months poststerilization. Propensity score matching was used to control for patient …

Of Rats And Men, Thomas S. Walsh

Capstones

This capstone is a data-driven investigation into New York City's rat problem. By using publicly available government data to map rat activity in NYC, I identified several socio-economic variables that correlate with rat populations at the community district, borough, and city-scale. I used these findings (mainly that rat problems are linked to lower incomes) as the basis of an investigation, which includes interviews with residents, experts, and city officials. Prof. Bobby Corrigan, urban rodentologist and formerly with the NYC Department of Health criticizes the city's efforts for the first time on the record.

https://thomasseiyawalsh.wixsite.com/ratstone

Seasonal Resource Selection And Habitat Treatment Use By A Fringe Population Of Greater Sage-Grouse, Rhett Boswell

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Movement and habitat selection by Greater Sage-grouse (Centrocercus uropasianus) is of great interest to wildlife managers tasked with applying conservation measures for this iconic western species. Current technology has created small and lightweight GPS (Global Positioning Systems) transmitters that can be attached to sage-grouse. Using GIS software and statistical programs such as Program R, land managers can analyze GPS location data to assess how sage-grouse are geospatially interacting with their habitats. Within the Panguitch Sage-Grouse Management Area (SGMA) thousands of acres of land have been restored or manipulated to enhance sage-grouse habitat; this usually involves removal of pinyon pine …

Long-Term Follow-Up Of Cardiac Function And Quality Of Life For Patients In Nsabp Protocol B-31/Nrg Oncology: A Randomized Trial Comparing The Safety And Efficacy Of Doxorubicin And Cyclophosphamide (Ac) Followed By Paclitaxel With Ac Followed By Paclitaxel And Trastuzumab In Patients With Node-Positive Breast Cancer With Tumors Overexpressing Human Epidermal Growth Factor Receptor 2, Patricia A. Ganz, Edward H. Romond, Reena S. Cecchini, Priya Rastogi, Charles E. Geyer Jr., Sandra M. Swain, Jong-Hyeon Jeong, Louis Fehrenbacher, Howard M. Gross, Adam M. Brufsky, Patrick J. Flynn, Tanya A. Wahl, Thomas E. Seay, James L. Wade Iii, David D. Biggs, James N. Atkins, Jonathan Polikoff, John L. Zapas, Eleftherios P. Mamounas, Norman Wolmark

Markey Cancer Center Faculty Publications

Purpose

Early cardiac toxicity is a risk associated with adjuvant chemotherapy plus trastuzumab. However, objective measures of cardiac function and health-related quality of life are lacking in long-term follow-up of patients who remain cancer free after completion of adjuvant treatment.

Patients and Methods

Patients in NSABP Protocol B-31 received anthracycline and taxane chemotherapy with or without trastuzumab for adjuvant treatment of node-positive, human epidermal growth factor receptor 2–positive early-stage breast cancer. A long-term follow-up assessment was undertaken for patients who were alive and disease free, which included measurement of left ventricular ejection fraction by multigated acquisition scan along with patient-reported …

Using Mixed Effects Modeling To Quantify Difference Between Patient Groups With Diabetic Foot Ulcers, Rachel French

Mahurin Honors College Capstone Experience/Thesis Projects

When diabetes progresses, many patients suffer from chronic foot ulcers. In a study described in Matrix Metalloproteinases and Diabetic Foot Ulcers (Muller et al., 2008), sixteen patients with diabetic foot ulcers were examined throughout a twelve week healing period. During this period, levels of matrix metalloproteinases (MMP-1), their inhibitors (TIMP-1), and the extracellular matrix in a wound area were measured at distinct time intervals for each patient. The ratios of these healing components are vital in determining whether a wound will heal or become chronic and never properly heal. Connecting Local and Global Sensitivities in a Mathematical Model for Wound …

Some Dimension Reduction Strategies For The Analysis Of Survey Data, Jiaying Weng, Derek S. Young

Statistics Faculty Publications

In the era of big data, researchers interested in developing statistical models are challenged with how to achieve parsimony. Usually, some sort of dimension reduction strategy is employed. Classic strategies are often in the form of traditional inference procedures, such as hypothesis testing; however, the increase in computing capabilities has led to the development of more sophisticated methods. In particular, sufficient dimension reduction has emerged as an area of broad and current interest. While these types of dimension reduction strategies have been employed for numerous data problems, they are scantly discussed in the context of analyzing survey data. This …

Bayesian Prediction Intervals For Assessing P-Value Variability In Prospective Replication Studies, Olga A. Vsevolozhskaya, Gabriel Ruiz, Dmitri Zaykin

Biostatistics Faculty Publications

Increased availability of data and accessibility of computational tools in recent years have created an unprecedented upsurge of scientific studies driven by statistical analysis. Limitations inherent to statistics impose constraints on the reliability of conclusions drawn from data, so misuse of statistical methods is a growing concern. Hypothesis and significance testing, and the accompanying P-values are being scrutinized as representing the most widely applied and abused practices. One line of critique is that P-values are inherently unfit to fulfill their ostensible role as measures of credibility for scientific hypotheses. It has also been suggested that while P-values …

Flow Anisotropy Due To Thread-Like Nanoparticle Agglomerations In Dilute Ferrofluids, Alexander Cali, Wah-Keat Lee, A. David Trubatch, Philip Yecko

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Improved knowledge of the magnetic field dependent flow properties of nanoparticle-based magnetic fluids is critical to the design of biomedical applications, including drug delivery and cell sorting. To probe the rheology of ferrofluid on a sub-millimeter scale, we examine the paths of 550 μm diameter glass spheres falling due to gravity in dilute ferrofluid, imposing a uniform magnetic field at an angle with respect to the vertical. Visualization of the spheres’ trajectories is achieved using high resolution X-ray phase-contrast imaging, allowing measurement of a terminal velocity while simultaneously revealing the formation of an array of long thread-like accumulations of magnetic …

Analytics And Baseball's New Generation, John Roche

Essential Studies UNDergraduate Showcase

Major League Baseball has been a catalyst for making decisions in sports and competition from a purely mathematical viewpoint. We have seen teams utilize unique on-field player alignments and roster-building strategies based on statistical observations and applications of math. This project examines the advantages Sabermetrics and analytics present within the sport. Untapped statistical categories that could further the success of teams in the future is also briefly discussed.

The Most Important Statistics In Football, Jacob Holmen

Essential Studies UNDergraduate Showcase

This research is based on the Five Factors that were devised by Bill Connelly of SBNation. The Five Factors of football include Explosiveness, Efficiency, Field Position, Finishing Drives, and Turnovers. Each factor is composed of associated statistics that when put together make up the most important statistics in football. This research includes the analysis of all 857 FBS (the highest level of NCAA Division I football) games from the 2016 season. Data was analyzed through the use of an Excel spreadsheet. Five different statistics were looked at, each associated with one of the Five Factors. The statistics include Yards per …

How Is Your Productivity Affected Based On Your App Usage?, Colette Noghreian

Student Scholar Symposium Abstracts and Posters

As technology becomes more prominent in society, it is crucial to investigate its effect on day to day life. The purpose of this study is to determine how the amount of time spent on iPhone applications affects how productive students feel in the span of one week. Results are tested through a survey which first determines general information about the student, and then guides students to navigate their phone settings and record the battery usage of the top three applications which use up the most battery. It is hypothesized that productivity decreases as battery usage increases due to the substantial …

Statistical Analysis Of Momentum In Basketball, Mackenzi Stump

Honors Projects

The “hot hand” in sports has been debated for as long as sports have been around. The debate involves whether streaks and slumps in sports are true phenomena or just simply perceptions in the mind of the human viewer. This statistical analysis of momentum in basketball analyzes the distribution of time between scoring events for the BGSU Women’s Basketball team from 2011-2017. We discuss how the distribution of time between scoring events changes with normal game factors such as location of the game, game outcome, and several other factors. If scoring events during a game were always randomly distributed, or …

Fetal Growth Restriction: Case Definition & Guidelines For Data Collection, Analysis, And Presentation Of Immunization Safety Data, Sarah Rae Easter, Linda O. Eckert, Nansi Boghossian, Rebecca Spencer, Eugene Oteng-Ntim, Christos Ioannou, Manasi Patwardhan, Margo S. Harrison, Asma Khalil, Michael Gravett, Robert Goldenberg, Alastair Mckelvey, Manish Gupta, Vitali Pool, Stephen C. Robson, Jyoti Joshi, Sonali Kochhar, Tom Mcelrath

Faculty Publications

No abstract provided.

Small For Gestational Age: Case Definition & Guidelines For Data Collection, Analysis, And Presentation Of Maternal Immunisation Safety Data, Elizabeth P. Schlaudecker, Flor M. Munoz, Azucena Bardají, Nansi S. Boghossian, Asma Khalil, Hatem Mousa, Mirjana Nesin, Muhammad Imran Nisar, Vitali Pool, Hans M.L. Spiegel, Milagritos D. Tapia, Sonali Kochhar, Steven Black

Faculty Publications

No abstract provided.

Approximating The Distribution Of Indefinite Quadratic Forms In Normal Variables By Maximum Entropy Density Estimation, Ghasem Rekabdar, Rahim Chinipardaz

Journal of Modern Applied Statistical Methods

The quadratic form of non-central normal variables is presented based on a sum of weighted independent non-central chi-square variables. This presentation provides moments of quadratic form. The maximum entropy method is used to estimate the density function because distribution moments of quadratic forms are known. A Euclidean distance is proposed to select an appropriate maximum entropy density function. In order to compare with other methods some numerical examples were evaluated. Also, for discrimination between two groups by the Euclidean distances, we obtained a stochastic representation for the linear discriminant function using the quadratic form. The maximum entropy estimation was an …

Semi-Parametric Method To Estimate The Time-To-Failure Distribution And Its Percentiles For Simple Linear Degradation Model, Laila Naji Ba Dakhn, Mohammed Al-Haj Ebrahem, Omar Eidous

Journal of Modern Applied Statistical Methods

Most reliability studies obtained reliability information by using degradation measurements over time, which contains useful data about the product reliability. Parametric methods like the maximum likelihood (ML) estimator and the ordinary least square (OLS) estimator are used widely to estimate the time-to-failure distribution and its percentiles. In this article, we estimate the time-to-failure distribution and its percentiles by using a semi-parametric estimator that assumes the parametric function to have a half- normal distribution or an exponential distribution. The performance of the semi-parametric estimator is compared via simulation study with the ML and OLS estimators by using the mean square error …

Jmasm 48: The Pearson Product-Moment Correlation Coefficient And Adjustment Indices: The Fisher Approximate Unbiased Estimator And The Olkin-Pratt Adjustment (Spss), David A. Walker

Journal of Modern Applied Statistical Methods

This syntax program is intended to provide an application, not readily available, for users in SPSS who are interested in the Pearson product–moment correlation coefficient (r) and r biased adjustment indices such as the Fisher Approximate Unbiased estimator and the Olkin and Pratt adjustment.

Inferential Procedures For Log Logistic Distribution With Doubly Interval Censored Data, Yue Fang Loh, Jayanthi Arasan, Habshah Midi, M. R. Abu Bakar

Journal of Modern Applied Statistical Methods

The log logistic model with doubly interval censored data is examined. Three methods of constructing confidence interval estimates for the parameter of the model were compared and discussed. The results of the coverage probability study indicated that the Wald outperformed the likelihood ratio and jackknife inferential procedures.

On Poisson Quasi-Lindley Distribution And Its Applications, Razika Grine, Halim Zeghdoudi

Journal of Modern Applied Statistical Methods

This paper proposes a recent version of compound Poisson distributions named the Poisson quasi-Lindley (PQL) distribution by compounding Poisson and quasi-Lindley distributions. Some properties of the distributions are given with estimation and some illustrative examples.