Statistical Methodology Commons^™

Determining Malignancy: Can Mammogram Results Help Predict The Diagnosis Of Breast Tumors?, Taylor Behrens

Symposium of Student Scholars

Even with advancements in treatment and preventative care, breast cancer remains an epidemic claiming more than 40,000 American male and female lives each year. The mammogram dataset that I am analyzing was initially complied in the early 1990s by a team from the University of Wisconsin - Madison. Past research diagnoses breast cancer from fine-needle aspirates. My research focuses on predicting whether we can determine breast cancer diagnoses without the use of invasive procedures and, in particular, whether we can predict breast cancer based on mammogram data. Do measures of gray-scale texture, radius, concavity, perimeter, compactness, area, and smoothness of …

Accidental Overdoses: Insights To Aid In Prevention, Annabel Nganga

Symposium of Student Scholars

Having lost a friend six years ago to an accidental cocaine overdose, I am very passionate about spreading awareness of accidental drug overdoses that have affected thousands of families countrywide. According to past research, deaths resulting from opiates specifically have been on the rise, and a significant number of deaths in the United States for those below fifty years are caused by drug overdoses. Data exists indicating which states have more overdoses. The data set I will be using includes variables on race, sex, age, drug with which person overdosed, location of the overdose, ultimate cause of death and year …

Death By Police: When “Protecting And Serving” Goes Wrong, Hesper Mallis

Symposium of Student Scholars

The recent cases of law enforcement using lethal force in the United States have gained massive public attention. My dataset is from the Mapping Police Violence website. The website’s focus was to create a heat map to display where police killings occurred most frequently. The website has a dataset with information on 7,664 deaths of suspects. The variables in the dataset include age, sex and race of the suspect; geographic location; alleged threat level; alleged weapon; cause of death; and criminal charges against the officer. In addition, the variables include whether the individual had a mental illness, was armed or …

Are There Predictors Of A Running Back’S Success?, Joshua Price

Symposium of Student Scholars

People who analyze football have concentrated in the past on a running back’s 40-yard dash, shuffle, broad jump, vertical jump, and bench press measures. My research will test if the following variables can predict a running back’s success in the NFL: height, weight, conference, offensive line ranking for their team, the running back’s total yards for the season, their average yards for each attempt, the number of times the running back has entered the end zone for a touchdown that season, the running back’s time average time behind the line of scrimmage (TLOS), the percentage of times the running back …

Sources And Aftermaths Of Pipeline Related Leaks And Spills, Justin Smith

Symposium of Student Scholars

The escape of oil and other hazardous materials have been shown to pollute and destroy ecosystems. As an aspiring chemist, I am adamant about the secure handling and transportation of oil and other hazardous materials. In the past, researchers have concentrated on oil’s high viscosity. Oil’s high viscosity physically smothers wildlife, affecting their ability to continue critical functions such as respiration, feeding, and thermoregulation. My research focuses on the source of these oil spills, as well as natural gas leaks, for the purpose of risk assessment. In addition, I compare recovery efforts based on the cause of the leak/spill, the …

On The Front Lines Of Fire: How Do We Save Their Lives?, Cathrine Jatta

Symposium of Student Scholars

The National Institute for Occupational Safety and Health (NIOSH) reports that the United States depends on about 1.1 million firefighters to protect its citizens and property from fire. NIOSH adds that approximately 336,000 are career firefighters; 812,000 are volunteers; and 80 to 100 die in the line of duty each year. NIOSH investigates each fatality individually for the cause and prevention. In contrast, my research will look at a complete dataset of 2005 firefighter fatalities and see if any of the following variables may predict firefighter death: age, cause of death, property type, type of duty (e.g. on-duty, training), and …

Cervical Cancer: Are There Ways To Reduce The Risks?, Madelyn Dorn

Symposium of Student Scholars

History has shown us that when caught early, cervical cancer is curable. Past research has found that the sexually transmitted diseases (STDs), herpes and human papillomavirus (HPV), have been associated with cervical cancer. In contrast, my dataset on 859 women has many more STDs and lifestyle choices compiled on 36 variables. The diagnoses in the dataset are many: cervical condylomatosis, vaginal condylomatosis, vulvo-perineral condylomatosis, syphilis, pelvic inflammatory disease, genital herpes, molluscum contagiosum, acquired immune deficiency syndrome (AIDS), human immunodeficiency virus (HIV), hepatitis B, HPV, and cervical cancer. In addition to the demographic variable on age, there are many lifestyle choice …

Marijuana Arrests In Toronto Canada: A Look Into The Canadian Criminal Justice System, Steven Tully

Symposium of Student Scholars

Marijuana related drug offenses made up fifty-eight percent of all Controlled Drugs and Substances Act offenses in Canada in 2016. On October 17, 2018, Canada legalized marijuana. As part of the efforts to legalize marijuana, descriptive statistics of single variables, like the age of the arrestees and the number of people arrested per year, were reported by the Toronto Star newspaper. The dataset analyzed in this research predates the legalization of marijuana and was collected from 1997 to 2002 on 5,226 individuals arrested in Toronto, Canada for simple possession of small quantities of marijuana. When an offender was arrested for …

Who Is Next? Evaluating Factors That May Contribute To Heart Failure, Davon Broadwater

Symposium of Student Scholars

Cardiovascular diseases are the number one causes of death globally, and for African Americans those risks are even higher. As an African American university student studying Biology, I am passionate about researching the diseases that affect my race. Current research states that behavioral factors such as obesity, tobacco use, unhealthy diet, and harmful use of alcohol should be avoided. I have chosen to research predictors of what helps patients survive if they already have heart failure. Heart failure develops gradually, where the heart becomes weaker over time and has trouble pumping blood to nourish the cells in the body. Data …

Eradicating Zebra Mussels: What Works?, Elijah Davies

Symposium of Student Scholars

The invasion of U.S lakes and rivers by the invasive species of zebra mussels called Dreissena polymorpha has caused catastrophic harm to the local ecosystem by reproducing and outcompeting native mussel species as well as harm to pipes leading into water sources by binding to surfaces and reproducing to the point that the mussels clog pipes. In addition, recreation areas must be closed due to the sharp shells making areas unusable. In the past, research has focused on individual molluscicides and their eradication of zebra mussels, as well as their effect on native flora and fauna. My research will contrast …

Bias In Police Shootings: Is It Just An Opinion?, Phuong Ho

Symposium of Student Scholars

The claims of racism have drawn public attention toward police brutality and its impact on minorities. Is this just an opinion or is there any statistical evidence? Recent studies from The Atlantic have investigated the average age and ethnicity of victims from police killings in 2015-2016. As an Asian-American, I am motivated to examine the issue of police killings among races and other demographics to find any bias that is present. Using the dataset of 2,204 victims of police killings (2015-2016) collected by The Guardian, I will examine the following variables for bias: age, cause of death, armed/unarmed, race/ethnicity, and …

Do Environmental Toxins Predict Violent Crimes?, Tyler Stahl

Symposium of Student Scholars

Do chemical pollutants that persistent in the environment and bioaccumulate in the body affect human health and behavior? Could these Persistent, Bioaccumulative, and Toxic (PBT) chemicals play a role in the cause of violent crimes due to deterioration of mental and cognitive functions? In the past, Mercury, a PBT chemical, has been shown in salmon to be associated with aggression. Could similar aggression occur in humans exposed to mercury through a toxic spill? Two sources of data are utilized in this analysis. The Environmental Protection Agency’s (EPA) Annual Toxic Release Inventory publishes data on toxic releases into the environment and …

From Mathematics To Medicine: A Practical Primer On Topological Data Analysis (Tda) And The Development Of Related Analytic Tools For The Functional Discovery Of Latent Structure In Fmri Data, Andrew Salch, Adam Regalski, Hassan Abdallah, Raviteja Suryadevara, Michael J. Catanzaro, Vaibhav A. Diwadkar

Mathematics Faculty Research Publications

fMRI is the preeminent method for collecting signals from the human brain in vivo, for using these signals in the service of functional discovery, and relating these discoveries to anatomical structure. Numerous computational and mathematical techniques have been deployed to extract information from the fMRI signal. Yet, the application of Topological Data Analyses (TDA) remain limited to certain sub-areas such as connectomics (that is, with summarized versions of fMRI data). While connectomics is a natural and important area of application of TDA, applications of TDA in the service of extracting structure from the (non-summarized) fMRI data itself are heretofore nonexistent. …

Bayesian Variable Selection Strategies In Longitudinal Mixture Models And Categorical Regression Problems., Md Nazir Uddin

Electronic Theses and Dissertations

In this work, we seek to develop a variable screening and selection method for Bayesian mixture models with longitudinal data. To develop this method, we consider data from the Health and Retirement Survey (HRS) conducted by University of Michigan. Considering yearly out-of-pocket expenditures as the longitudinal response variable, we consider a Bayesian mixture model with $K$ components. The data consist of a large collection of demographic, financial, and health-related baseline characteristics, and we wish to find a subset of these that impact cluster membership. An initial mixture model without any cluster-level predictors is fit to the data through an MCMC …

On The Use Of Minimum Penalties In Statistical Learning, Ben Sherwood, Bradley S. Price

Faculty & Staff Scholarship

Modern multivariate machine learning and statistical methodologies estimate parameters of interest while leveraging prior knowledge of the association between outcome variables. The methods that do allow for estimation of relationships do so typically through an error covariance matrix in multivariate regression which does not scale to other types of models. In this article we proposed the MinPEN framework to simultaneously estimate regression coefficients associated with the multivariate regression model and the relationships between outcome variables using mild assumptions. The MinPen framework utilizes a novel penalty based on the minimum function to exploit detected relationships between responses. An iterative algorithm that …

Evaluating The Efficiency Of Markov Chain Monte Carlo Algorithms, Thuy Scanlon

Graduate Theses and Dissertations

Markov chain Monte Carlo (MCMC) is a simulation technique that produces a Markov chain designed to converge to a stationary distribution. In Bayesian statistics, MCMC is used to obtain samples from a posterior distribution for inference. To ensure the accuracy of estimates using MCMC samples, the convergence to the stationary distribution of an MCMC algorithm has to be checked. As computation time is a resource, optimizing the efficiency of an MCMC algorithm in terms of effective sample size (ESS) per time unit is an important goal for statisticians. In this paper, we use simulation studies to demonstrate how the Gibbs …

Statistical Modeling For High-Dimensional Compositional Data With Applications To The Human Microbiome, Thy Dao

Graduate Theses and Dissertations

Compositional data refer to the data that lie on a simplex, which are common in many scientific domains such as genomics, geology, and economics. As the components in a composition must sum to one, traditional tests based on unconstrained data become inappropriate, and new statistical methods are needed to analyze this special type of data. This dissertation is motivated by some statistical problems arising in the analysis of compositional data. In particular, we focus on the high-dimensional and over-dispersed setting, where the dimensionality of compositions is greater than the sample size and the dispersion parameter is moderate or large. In …

A Geometric Approach To Conditioning And The Search For Minimum Variance Unbiased Estimators, David L. Farnsworth, James E. Marengo

Articles

Our purpose is twofold: to present a prototypical example of the conditioning technique to obtain the best estimator of a parameter and to show that this technique resides in the structure of an inner product space. The technique uses conditioning of an unbiased estimator on a sufficient statistic. This procedure is founded upon the conditional variance formula, which leads to an inner product space and a geometric interpretation. The example clearly illustrates the dependence on the sampling methodology. These advantages show the power and centrality of this process.

Modeling And Solving The Outsourcing Risk Management Problem In Multi-Echelon Supply Chains, Arian A. Nahangi

Master's Theses

Worldwide globalization has made supply chains more vulnerable to risk factors, increasing the associated costs of outsourcing goods. Outsourcing is highly beneficial for any company that values building upon its core competencies, but the emergence of the COVID-19 pandemic and other crises have exposed significant vulnerabilities within supply chains. These disruptions forced a shift in the production of goods from outsourcing to domestic methods.

This paper considers a multi-echelon supply chain model with global and domestic raw material suppliers, manufacturing plants, warehouses, and markets. All levels within the supply chain network are evaluated from a holistic perspective, calculating a total …

Pivot Points In Bivariate Linear Regression, David L. Farnsworth, Carl V. Lutzer

Articles

There are little-noticed points in the plane, which are artifacts of linear regression. The points, which are called pivot points, are the intersections of sets of regression lines. We derive the coordinates of the pivot point and explain its sources. We show how a pivot point arises in a certain notable data set, which has been analyzed often for points of high leverage. We obtain the application of pivot points that shortens calculations when updating a set of bivariate observations by adding a new point.