Applied Mathematics Commons^™

Quantitative Validation Of Simulated Sea Ice Displacements, Bryan R. Mccormick

Mathematics & Statistics ETDs

Accurate simulations of Arctic sea ice are important for forecasting as well as for understanding the global climate. However, quantitative measures for simulation displacements are underutilized. We present five such measures proposed as being useful in the validation of simulated sea ice displacements. Using drifting buoy and satellite measurements of sea ice motion as observation, we apply the metrics in a comparison of observed displacements and predicted displacements from the Arctic sea ice simulation MPM\_ice. We find the metric scores are useful for comparing simulations and observations. The metrics also brought to light problems in the simulation MPM_ice, demonstrating their …

Decision Making In A Changing Environment, Alan Veliz-Cuba

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Understanding Sexual Violence Against Women, Maria Martinez

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Identification Of Hostile Hemodynamics And Geometries Of Cerebral Aneurysms: A Case-Control Study, Bong Jae Chung, F. Mut, C. M. Putman, F. Hamzei-Sichani, W. Brinjikji, D. Kallmes, C. M. Jimenez, Juan R. Cebral

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

BACKGROUND AND PURPOSE: Hostile hemodynamic conditions and geometries are thought to predispose aneurysms for instability and rupture. This study compares stable, unstable, and ruptured aneurysms while controlling for location and patient characteristics. MATERIALS AND METHODS: The hemodynamics and geometries of 165 stable, 65 unstable, and 554 ruptured aneurysms were compared. Hemodynamics was modeled using image-based computational fluid dynamics. Case-control pairs were selected matching aneurysm location, patient age, and sex. Paired Wilcoxon tests were used to compare hemodynamic and geometric variables among different aneurysm groups. The pairing was repeated 100 times, and the combined P values were calculated and adjusted for …

Yelp’S Review Filtering Algorithm, Yao Yao, Ivelin Angelov, Jack Rasmus-Vorrath, Mooyoung Lee, Daniel W. Engels

SMU Data Science Review

In this paper, we present an analysis of features influencing Yelp's proprietary review filtering algorithm. Classifying or misclassifying reviews as recommended or non-recommended affects average ratings, consumer decisions, and ultimately, business revenue. Our analysis involves systematically sampling and scraping Yelp restaurant reviews. Features are extracted from review metadata and engineered from metrics and scores generated using text classifiers and sentiment analysis. The coefficients of a multivariate logistic regression model were interpreted as quantifications of the relative importance of features in classifying reviews as recommended or non-recommended. The model classified review recommendations with an accuracy of 78%. We found that reviews …

Development Of A Statistical Model For Discrimination Of Rupture Status In Posterior Communicating Artery Aneurysms, Felicitas J. Detmer, Bong Jae Chung, Fernando Mut, Michael Pritz, Martin Slawski, Farid Hamzei-Sichani, David Kallmes, Christopher Putman, Carlos Jimenez, Juan R. Cebral

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Background: Intracranial aneurysms at the posterior communicating artery (PCOM) are known to have high rupture rates compared to other locations. We developed and internally validated a statistical model discriminating between ruptured and unruptured PCOM aneurysms based on hemodynamic and geometric parameters, angio-architectures, and patient age with the objective of its future use for aneurysm risk assessment. Methods: A total of 289 PCOM aneurysms in 272 patients modeled with image-based computational fluid dynamics (CFD) were used to construct statistical models using logistic group lasso regression. These models were evaluated with respect to discrimination power and goodness of fit using tenfold nested …

Clustering Mixed Data: An Extension Of The Gower Coefficient With Weighted L2 Distance, Augustine Oppong

Electronic Theses and Dissertations

Sorting out data into partitions is increasing becoming complex as the constituents of data is growing outward everyday. Mixed data comprises continuous, categorical, directional functional and other types of variables. Clustering mixed data is based on special dissimilarities of the variables. Some data types may influence the clustering solution. Assigning appropriate weight to the functional data may improve the performance of the clustering algorithm. In this paper we use the extension of the Gower coefficient with judciously chosen weight for the L2 to cluster mixed data.The benefits of weighting are demonstrated both in in applications to the Buoy data set …

Calculus Of The Impossible: Review Of The Improbability Principle (2014) By David Hand And The Logic Of Miracles (2018) By Lásló Mérő, Samuel L. Tunstall

Numeracy

David J. Hand. 2014. The Improbability Principle: Why Coincidences, Miracles, and Rare Events Happen Every Day (New York, NY: Scientific American/Farrar, Straus and Giroux) 288 pp. ISBN: 978-0374175344.

Lásló Mérő. 2018. The Logic of Miracles: Making Sense of Rare, Really Rare, and Impossibly Rare Events (New Haven, CT: Yale University Press) 288 pp. ISBN: 978-0300224153.

David Hand and Lásló Mérő both grapple with the occurrence of seemingly impossible events in these two popular science books. In this comparative review, I describe the two books, and explain why I prefer Hand's treatment of the impossible.

Extended Poisson Models For Count Data With Inflated Frequencies, Monika Arora

Mathematics & Statistics Theses & Dissertations

Count data often exhibits inflated counts for zero. There are numerous papers in the literature that show how to fit Poisson regression models that account for the zero inflation. However, in many situations the frequencies of zero and of some other value k tends to be higher than the Poisson model can fit appropriately. Recently, Sheth-Chandra (2011), Lin and Tsai (2012) introduced a mixture model to account for the inflated frequencies of zero and k. In this dissertation, we study basic properties of this mixture model and parameter estimation for grouped and ungrouped data. Using stochastic representation we show …

Masked Instability: Within-Sector Financial Risk In The Presence Of Wealth Inequality, Youngna Choi

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

We investigate masked financial instability caused by wealth inequality. When an economic sector is decomposed into two subsectors that possess a severe wealth inequality, the sector in entirety can look financially stable while the two subsectors possess extreme financially instabilities of opposite nature, one from excessive equity, the other from lack thereof. The unstable subsector can result in further financial distress and even trigger a financial crisis. The market instability indicator, an early warning system derived from dynamical systems applied to agent-based models, is used to analyze the subsectoral financial instabilities. Detailed mathematical analysis is provided to explain what financial …

Quantitative Electroencephalography For Detecting Concussions, Sara Krehbiel, Kathy Hoke, Joanna Wares

Biology and Medicine Through Mathematics Conference

No abstract provided.

Estimation Of The Burr Xii-Exponential Distribution Parameters, Gholamhossein Yari, Zahra Tondpour

Applications and Applied Mathematics: An International Journal (AAM)

The Burr XII distribution is one of the most important distributions in Survival analysis. In this article, we introduce the new wider Burr XII-G family of distributions. A special model in the new family called Burr XII-exponential distribution that has constant, decreasing and unimodal hazard rate functions is investigated. We discuss the estimation of this distribution parameters by maximum likelihood, three modifications of maximum likelihood and Bayes methods. In Bayes method, we use the uniform, triangular and Burr XII-uniform priors for posterior analysis and obtain Bayes estimations under two different loss functions. We obtain two approximations of the Bayes estimations, …

Profit Analysis Of A Two Unit Cold Standby System Operating Under Different Weather Conditions Subject T O Inspection, M. S. Barak, Neeraj _, Sudesh Kumari

Applications and Applied Mathematics: An International Journal (AAM)

A system, or unit, is said to be working under normal weather conditions if the system is working under prescribed conditions as defined/stated by the definition of reliability of system/unit, otherwise the system is said to be working in abnormal weather conditions. For example, if a car with the capacity for five persons is carrying more than five persons, it will be said to be working under abnormal weather conditions. Another example, if a hydraulic machine having the capacity to lift a maximum weight of 500 tons is lifting a weight of 600 tons, then the machine is working under …

Risk Assessment Of Dropped Cylindrical Objects In Offshore Operations, Adelina Steven

LSU New Orleans Theses and Dissertations

Dropped object are defined as any object that fall under its own weight from a previously static position or fell due to an applied force from equipment or a moving object. It is among the top ten causes of injuries and fatality in oil and gas industry. To solve this problem, several in-house tools and guidelines is developed over time to assess the risk of dropped objects on the sub-sea structures. This thesis focuses on compiling and comparing those methods in hope to improve the recommended practices available in the market. A simple modification is done on the in-house tools …

Fundamental Tradeoffs In Estimation Of Finite-State Hidden Markov Models, Justin Le

UNLV Theses, Dissertations, Professional Papers, and Capstones

Hidden Markov models (HMMs) constitute a broad and flexible class of statistical models that are widely used in studying processes that evolve over time and are only observable through the collection of noisy data. Two problems are essential to the use of HMMs: state estimation and parameter estimation. In state estimation, an algorithm estimates the sequence of states of the process that most likely generated a certain sequence of observations in the data. In parameter estimation, an algorithm computes the probability distributions that govern the time-evolution of states and the sampling of data. Although algorithms for the two problems are …

A Practical Guide To Big Data, Ekaterina Smirnova, Andrada Ivanescu, Jiawei Bai, Ciprian M. Crainiceanu

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Big Data is increasingly prevalent in science and data analysis. We provide a short tutorial for adapting to these changes and making the necessary adjustments to the academic culture to keep Biostatistics truly impactful in scientific research.

Hierarchical Bayesian Regression With Application In Spatial Modeling And Outlier Detection, Ghadeer Mahdi

Graduate Theses and Dissertations

This dissertation makes two important contributions to the development of Bayesian hierarchical models. The first contribution is focused on spatial modeling. Spatial data observed on a group of areal units is common in scientific applications. The usual hierarchical approach for modeling this kind of dataset is to introduce a spatial random effect with an autoregressive prior. However, the usual Markov chain Monte Carlo scheme for this hierarchical framework requires the spatial effects to be sampled from their full conditional posteriors one-by-one resulting in poor mixing. More importantly, it makes the model computationally inefficient for datasets with large number of units. …

Physical Applications Of The Geometric Minimum Action Method, George L. Poppe Jr.

Dissertations, Theses, and Capstone Projects

This thesis extends the landscape of rare events problems solved on stochastic systems by means of the \textit{geometric minimum action method} (gMAM). These include partial differential equations (PDEs) such as the real Ginzburg-Landau equation (RGLE), the linear Schroedinger equation, along with various forms of the nonlinear Schroedinger equation (NLSE) including an application towards an ultra-short pulse mode-locked laser system (MLL).

Additionally we develop analytical tools that can be used alongside numerics to validate those solutions. This includes the use of instanton methods in deriving state transitions for the linear Schroedinger equation and the cubic diffusive NLSE.

These analytical solutions are …

Using Random Forests To Describe Equity In Higher Education: A Critical Quantitative Analysis Of Utah’S Postsecondary Pipelines, Tyler Mcdaniel

Butler Journal of Undergraduate Research

The following work examines the Random Forest (RF) algorithm as a tool for predicting student outcomes and interrogating the equity of postsecondary education pipelines. The RF model, created using longitudinal data of 41,303 students from Utah's 2008 high school graduation cohort, is compared to logistic and linear models, which are commonly used to predict college access and success. Substantially, this work finds High School GPA to be the best predictor of postsecondary GPA, whereas commonly used ACT and AP test scores are not nearly as important. Each model identified several demographic disparities in higher education access, most significantly the effects …

Score Test And Likelihood Ratio Test For Zero-Inflated Binomial Distribution And Geometric Distribution, Xiaogang Dai

Masters Theses & Specialist Projects

The main purpose of this thesis is to compare the performance of the score test and the likelihood ratio test by computing type I errors and type II errors when the tests are applied to the geometric distribution and inflated binomial distribution. We first derive test statistics of the score test and the likelihood ratio test for both distributions. We then use the software package R to perform a simulation to study the behavior of the two tests. We derive the R codes to calculate the two types of error for each distribution. We create lots of samples to approximate …

Pricing Asian Options: Volatility Forecasting As A Source Of Downside Risk, Adam T. Diehl

Undergraduate Economic Review

Asian options are a class of derivative securities whose payoffs average movements in the underlying asset as a means of hedging exposure to unexpected market behavior. We find that despite their volatility smoothing properties, the price of an Asian option is sensitive to the choice of volatility model employed to price them from market data. We estimate the errors induced by two common schemes of forecasting volatility and their potential impact upon trading.

General Stochastic Integral And Itô Formula With Application To Stochastic Differential Equations And Mathematical Finance, Jiayu Zhai

LSU Doctoral Dissertations

A general stochastic integration theory for adapted and instantly independent stochastic processes arises when we consider anticipative stochastic differential equations. In Part I of this thesis, we conduct a deeper research on the general stochastic integral introduced by W. Ayed and H.-H. Kuo in 2008. We provide a rigorous mathematical framework for the integral in Chapter 2, and prove that the integral is well-defined. Then a general Itô formula is given. In Chapter 3, we present an intrinsic property, near-martingale property, of the general stochastic integral, and Doob-Meyer's decomposition for near-submartigales. We apply the new stochastic integration theory to several …

Modeling Multimodal Failure Effects Of Complex Systems Using Polyweibull Distribution, Daniel A. Timme

Theses and Dissertations

The Department of Defense (DoD) enlists multiple complex systems across each of their departments. Between the aging systems going through an overhaul and emerging new systems, quality assurance to complete the mission and secure the nation‘s objectives is an absolute necessity. The U.S. Air Force‘s increased interest in Remotely Piloted Aircraft (RPA) and the Space Warfighting domain are current examples of complex systems that must maintain high reliability and sustainability in order to complete missions moving forward. DoD systems continue to grow in complexity with an increasing number of components and parts in more complex arrangements. Bathtub-shaped hazard functions arise …

Essentials Of Structural Equation Modeling, Mustafa Emre Civelek

Zea E-Books Collection

Structural Equation Modeling is a statistical method increasingly used in scientific studies in the fields of Social Sciences. It is currently a preferred analysis method, especially in doctoral dissertations and academic researches. However, since many universities do not include this method in the curriculum of undergraduate and graduate courses, students and scholars try to solve the problems they encounter by using various books and internet resources.

This book aims to guide the researcher who wants to use this method in a way that is free from math expressions. It teaches the steps of a research program using structured equality modeling …

Predicting The Next Us President By Simulating The Electoral College, Boyan Kostadinov

Publications and Research

We develop a simulation model for predicting the outcome of the US Presidential election based on simulating the distribution of the Electoral College. The simulation model has two parts: (a) estimating the probabilities for a given candidate to win each state and DC, based on state polls, and (b) estimating the probability that a given candidate will win at least 270 electoral votes, and thus win the White House. All simulations are coded using the high-level, open-source programming language R. One of the goals of this paper is to promote computational thinking in any STEM field by illustrating how probabilistic …

Modeling Mayfly Nymph Length Distribution And Population Dynamics Across A Gradient Of Stream Temperatures And Stream Types, Jeremy Anthony, Jennifer Baccam, Imanuel Bier, Emily Gregg, Leif Halverson, Ryan Mulcahy, Emmanuel Okanla, Samira A. Osman, Adam R. Pancoast, Kevin C. Schultz, Alex Sushko, Jennifer Vorarath, Yia Vue, Austin Wagner, Emily Gaenzle Schilling, John M. Zobitz

Spora: A Journal of Biomathematics

We analyze a process-based temperature model for the length distribution and population over time of mayfly nymphs. Model parameters are estimated using a Markov Chain Monte Carlo parameter estimation method utilizing length distribution data at five different stream sites. Two different models (a standard exponential model and a modified Weibull model) of mayfly mortality are evaluated, where in both cases mayfly length growth is a function of stream temperature. Based on model-data comparisons to the modeled length distribution and the Bayesian Information Criterion, we found that approaches that length distribution data can reliably estimate 2–3 model parameters. Future model development …

Modeling Mayfly Nymph Length Distribution And Population Dynamics Across A Gradient Of Stream Temperatures And Stream Types, Jeremy Anthony, Jennifer Baccam, Imanuel Bier, Emily Gregg, Leif Halverson, Ryan Mulcahy, Emmanuel Okanla, Samira A. Osman, Adam R. Pancoast, Kevin C. Schultz, Alex Sushko, Jennifer Vorarath, Yia Vue, Austin Wagner, Emily Gaenzle Schilling, John Zobitz

Faculty Authored Articles

We analyze a process-based temperature model for the length distribution and population over time of mayfly nymphs. Model parameters are estimated using a Markov Chain Monte Carlo parameter estimation method utilizing length distribution data at five different stream sites. Two different models (a standard exponential model and a modified Weibull model) of mayfly mortality are evaluated, where in both cases mayfly length growth is a function of stream temperature. Based on model-data comparisons to the modeled length distribution and the Bayesian Information Criterion, we found that approaches that length distribution data can reliably estimate 2–3 model parameters. Future model development …

Sequential Probing With A Random Start, Joshua Miller

HMC Senior Theses

Processing user requests quickly requires not only fast servers, but also demands methods to quickly locate idle servers to process those requests. Methods of finding idle servers are analogous to open addressing in hash tables, but with the key difference that servers may return to an idle state after having been busy rather than staying busy. Probing sequences for open addressing are well-studied, but algorithms for locating idle servers are less understood. We investigate sequential probing with a random start as a method for finding idle servers, especially in cases of heavy traffic. We present a procedure for finding the …

Iterative Matrix Factorization Method For Social Media Data Location Prediction, Natchanon Suaysom

HMC Senior Theses

Since some of the location of where the users posted their tweets collected by social media company have varied accuracy, and some are missing. We want to use those tweets with highest accuracy to help fill in the data of those tweets with incomplete information. To test our algorithm, we used the sets of social media data from a city, we separated them into training sets, where we know all the information, and the testing sets, where we intentionally pretend to not know the location. One prediction method that was used in (Dukler, Han and Wang, 2016) requires appending one-hot …

Borrowing Capacity, Financial Instability, And Contagion: Case Study Of The U.S. Subprime Mortgage Crisis, Youngna Choi

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

We use the case of the 2007 United States subprime mortgage crisis to investigate the impact of borrowing capacity limitations on financial instability and contagion. We divide an economy into agents that interact via flow of funds and express the financial instability level of each agent as a function of time derivatives of its wealth, cash inflows, and borrowing capacity. We show that among these factors, the borrowing capacity, which is determined by other economic constraints, has the largest impact on financial instability. It is suggested that borrowing capacity limitations could even cause contagion through feedback loop formed by flow …