Statistics and Probability Commons^™

Mathematics Versus Statistics, Mindy B. Capaldi

Journal of Humanistic Mathematics

Mathematics and statistics are both important and useful subjects, but the former has maintained prominence in the American education system. On the other hand, statistics is more prevalent in daily life and is an increasingly marketable subject to know. This article gives a personal history of one mathematician’s bumpy road to learning and teaching statistics. Additionally, arguments for how and why to include statistics in the K-12 and college curricula are provided.

Choose Your Own Adventure: An Analysis Of Interactive Gamebooks Using Graph Theory, D'Andre Adams, Daniela Beckelhymer, Alison Marr

Journal of Humanistic Mathematics

"BEWARE and WARNING! This book is different from other books. You and YOU ALONE are in charge of what happens in this story." This is the captivating introduction to every book in the interactive novel series, Choose Your Own Adventure (CYOA). Our project uses the mathematical field of graph theory to analyze forty books from the CYOA book series for ages 9-12. We first began by drawing the digraphs of each book. Then we analyzed these digraphs by collecting structural data such as longest path length (i.e. longest story length) and number of vertices with outdegree zero (i.e. number …

Practical Modelling Of The Vanilla Option Volatility Smile, Jacob E. Shanley

Mathematics & Statistics ETDs

Many discussions on how best to model the standard American Option derivative focus solely upon the volatility smile modelling itself from a mathematical perspective. This thesis instead closely examines both the practical and mathematical implications of processing market data, modelling the volatility smile, and making real-world trading decisions from the results. In particular, it contains an analysis of market data processing algorithms, new volatility smile models, multiple empirically-driven weighting schemes, Gauss-Newton and Levenberg-Marquardt optimization algorithms, and various trading strategies. The top performing combinations found were those that involved the Smile and Twist volatility smile models, Volatility Width Vega Multiplier weighting …

One And Two-Step Estimation Of Time Variant Parameters And Nonparametric Quantiles, Bogdan Gadidov

Doctor of Data Science and Analytics Dissertations

This dissertation develops and discusses several one-step and two-step smoothing methods of time variant nonparametric quantiles and time variant parameters from probability models. First, we investigate and develop nonparametric techniques for measuring extreme quantiles. The method involves aggregating data by an explanatory variable such as time and smoothing the resulting data with a nonparametric method like kernel, local polynomial or spline smoothing. We demonstrate both in application and simulation that this two-step procedure of quantile estimation is superior to the parametric quantile regression. We then develop a one-step method which combines the strength of maximum likelihood estimation with a local …

Estimation Of Association Between A Longitudinal Marker And Interval-Censored Progression Times, Naghmeh Daneshi

Dissertations and Theses

In longitudinal studies, we observe the subjects who are likely to progress to a new state during the study time. For example, in clinical trials the stage of a progressing disease is recorded at each follow-up visit. The primary goal is to estimate the relationship between the attributes and the subject's progression state. In such studies, some subjects complete all their follow-up visits and their progression state are observed without any missingness. However, others miss their follow-up visits and when they come back, they learn that they have progressed to a new state. In this case, not only are their …

Constraining The Oxygen Values Of The Late Cretaceous Western Interior Seaway Using Marine Bivalves, Camille H. Dwyer

Earth and Planetary Sciences ETDs

The Western Interior Seaway (WIS) remains an oceanographic enigma, including its circulation, similarity to the open ocean, and the fidelity of geochemical proxies to reconstruct paleoenvironments. Across the late Campanian and early Maastrichtian I test whether: 1) the WIS had unique δ¹⁸O_VPDB compared to other marine settings, 2) increasing oceanographic restriction changed the stable isotope composition, and 3) biases, e.g., taxonomy or diagenesis, influenced stable isotope compositions. Results indicate distinct δ¹⁸O_VPDB in the WIS compared to other marine settings. δ¹⁸O_VPDB values were stable through time, suggesting insignificant oceanographic restriction and a …

A Deep Learning Approach To Uncertainty Quantification, Mst Afroja Akter

Mathematics & Statistics ETDs

In this thesis we consider ordinary differential equations (ODEs) with random parameters. We focus on Monte Carlo (MC) sampling for computing the statistics of some quantities of interest (QoIs) given by the solution of the ODE problems. We use the 4th order accurate Runge-Kutta (RK4) method as the deterministic ODE solver. We then develop a hybrid MC sampling method that combines RK4 with neural network models to efficiently compute the statistics of QoIs within a desired accuracy. We present several numerical examples to verify the accuracy and efficiency of the proposed hybrid method compared to classical MC sampling. The hybrid …

Graphicacy For Numeracy: Review Of Fundamentals Of Data Visualization: A Primer On Making Informative And Compelling Figures By Claus O. Wilke (2019), Christy M. Bebeau

Numeracy

Wilke, Claus O. 2019. Fundamentals of Data Visualization: A Primer on Making Informative and Compelling Figures. (Sebastopol, CA: O’Reilly Media, Inc.). 390 pp. ISBN 978-1-492-03108-6. First edition. First release: 03-15-2019.

Claus O. Wilke has authored an excellent reference about producing and understanding static figures, figures used online, in print, and for presentations. His book is neither a statistics nor programming text, but familiarity with basic statistical concepts is helpful. Written in three parts, the book presents both the math and artistic design aspects of telling a story through figures. Wilke makes extensive use of examples, labels them good, bad, …

Taking Multiple Regression Analysis To Task: A Review Of Mindware: Tools For Smart Thinking, By Richard Nisbett (2015), Jason Makansi

Numeracy

Richard Nisbett. 2015. Mindware: Tools for Smart Thinking.(New York, NY: Farrar, Strauss, and Giroux). 336 pp. ISBN: 9780374536244

Nisbett, a psychologist, may not achieve his stated goal of teaching readers to “effortlessly” extend their common sense when it comes to quantitative analysis applied to everyday issues, but his critique of multiple regression analysis (MRA) in the middle chapters of Mindware is worth attention from, and contemplation by, the QL/QR and Numeracy community. While in at least one other source, Nisbett’s critique has been called a “crusade” against MRA, what he really advocates is that it not be used as …

Using Meta-Analysis To Assess Affective Outcomes In A Multi-Course Qr Module Intervention, James Friedrich, Kelley D. Strawn

Numeracy

When quantitative reasoning(QR) interventions share a common hypothesis or goal, a promising approach for evaluation involves integrating separate analyses through the use of meta-analysis. This paper reports an assessment of a module-based QR intervention distributed across 20 courses at a single institution. Topics and participating courses were diverse, including arts & humanities, quantitative behavioral sciences, and natural sciences & mathematics groupings, but all addressed the shared affective goals of reducing student QR self-doubt and increasing appreciation for QR value and utility. With a local framework to guide module development, we assess these outcomes using reliable self-report measures in a pre-post …

Sickle Cell Disease Complications: Prevalence And Resource Utilization, Nirmish Shah, Menaka Bhor, Lin Xi, Jincy Paulose, Huseyin Yuce

Publications and Research

Objectives: This study evaluated the prevalence rate of vaso-occlusive crisis (VOC) episodes, rates of uncomplicated and complicated VOC episodes, and the primary reasons for emergency room (ER) visits and inpatient admissions for sickle cell disease (SCD) patients.

Methods: The Medicaid Analytic extracts database was used to identify adult SCD patients using claims from 01JUL2009-31DEC2012. The date of the first observed SCD claim was designated as the index date. Patients were required to have continuous medical and pharmacy benefits for .6 months baseline and .12 months follow-up period. Patient demographics, baseline clinical characteristics, the rate of uncomplicated and complicated VOC (VOC …

Statistical Learning Of Biomedical Non-Stationary Signals And Quality Of Life Modeling, Mahdi Goudarzi

USF Tampa Graduate Theses and Dissertations

Statistical learning is a set of tools for modeling and understanding complex datasets. It is a recently developed area in statistics and blends with parallel developments in computer science and, in particular, machine learning.

The classification of biomedical non-stationary signals such as Electroencephalogram (EEG) is always a challenging problem due to their complexity. The low spatial resolution on the scalp, curse of dimensionality, poor signal-to-noise ratio are disadvantages of working with biomedical signals. EEG signals are unstructured data which needs preprocessing steps to extract informative features which are measurable and predictive. In the first two chapters of this dissertation, EEG …

Regression To The Mean, Dominic Klyve

Statistics and Probability

No abstract provided.

Extending Statistical Learning For Aneurysm Rupture Assessment To Finnish And Japanese Populations Using Morphology, Hemodynamics, And Patient Characteristics, Felicitas J. Detmer, Sara Hadad, Bong Jae Chung, Fernando Mut, Martin Slawski, Norman Juchler, Vartan Kurtcuoglu, Sven Hirsch, Philippe Bijlenga, Yuya Uchiyama, Soichiro Fujimura, Makoto Yamamoto, Yuichi Murayama, Hiroyuki Takao, Timo Koivisto, Juhana Frösen, Juan R. Cebral

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

OBJECTIVE: Incidental aneurysms pose a challenge for physicians, who need to weigh the rupture risk against the risks associated with treatment and its complications. A statistical model could potentially support such treatment decisions. A recently developed aneurysm rupture probability model performed well in the US data used for model training and in data from two European cohorts for external validation. Because Japanese and Finnish patients are known to have a higher aneurysm rupture risk, the authors' goals in the present study were to evaluate this model using data from Japanese and Finnish patients and to compare it with new models …

Maquiladoras In Central America: An Analysis Of Workforce Schedule, Productivity And Fatigue., Jose L. Barahona

Masters Theses & Specialist Projects

Textile factories or Maquiladoras are very abundant and predominant in Central American economies. However, they all do not have the same standardized work schedule or routines. Most of the Maquiladoras only follow schedules and regulations established by the current labor laws without taking into consideration many variables within their organization that could affect their overall performance. As a result, the purpose of the study is to analyze the current working structure of a textile Maquiladora and determine the most suitable schedule that will abide with the current working structure but also increase production levels, employee morale and decrease employee fatigue. …

A First Look At Sublimation Rates In Toss Island Region, Antarctica, Rebecca Baiman, Scott Landolt

STAR Program Research Presentations

70% of Earth’s fresh water is held in Antarctica ice sheet. If the sheet melts, it has the potential to raise global sea levels by 190 feet (Klekociuk and Wiennecke, 2016). As the climate changes, it is imperative that to understand precipitation systems of Antarctica in order to measure and predict weather around the world. One aspect of precipitation events that we do not understand fully in Antarctica is sublimation. Data was collected from four Ott Pluvio Precipitation Gauges with Belfort Double Alter Shields placed in and around the Ross Ice Shelf from November of 2017 to present. An R …

Extension Of Risk-Based Measure Of Time-Varying Prognostic Discrimination For Survival Models, Shujie Chen

Theses and Dissertations

The Cox proportional hazards (PH) model and time dependent PH model are the most popular survival models in survival analysis. The hazard discrimination summary HDS(t) proposed by Liang and Heagerty [2017] is used to evaluate the mean hazard difference between cases and controls at time t. Liang and Heagerty [2017] evaluated the discrimination performance under the PH model and time dependent PH model with right censoring.

In this thesis, first, we further investigate their method via comprehensive simulations including 1) We extend the simulation in Liang and Heagerty [2017] under the PH model by adding more scenarios such as different …

Investigations On Multiple Interval Estimators, Taeho Kim

Theses and Dissertations

Multiple interval estimation for a set of parameters is investigated. To begin, a strategy of optimization for a multiple interval estimator (MIE) is introduced. This approach allocates distinct optimized levels to individual interval estimators so that the global expected content can be minimized while the global coverage probability is still maintained at a global level. This optimal allocation is achieved by a decision theoretic procedure which consists of two global risk functions. The major part of this manuscript is devoted to two multiple interval estimation procedures. Both procedures adopt prior information added to the classical setting, but these procedures do …

Multivariate Probit Models For Interval-Censored Failure Time Data, Yifan Zhang

Theses and Dissertations

Survival analysis is an important branch of statistics that analyzes the time to event data. The events of interest can be death, disease occurrence, the failure of a machine part, etc.. One important feature of this type of data is censoring: information on time to event is not observed exactly due to loss to follow-up or non-occurrence of interested event before the trial ends. Censored data are commonly observed in clinical trials and epidemiological studies, since monitoring a person’s health over time after treatment is often required in medical or health studies. In this dissertation we focus on studying multivariate …

On Continuous Images Of Ultra-Arcs, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

Any space homeomorphic to one of the standard subcontinua of the Stone-Čech remainder of the real half-line is called an ultra-arc. Alternatively, an ultra-arc may be viewed as an ultracopower of the real unit interval via a free ultrafilter on a countable set. It is known that any continuum of weight is a continuous image of any ultra-arc; in this paper we address the problem of which continua are continuous images under special maps. Here are some of the results we present.