Physical Sciences and Mathematics Commons^™

Bayesian Model For Detection Of Outliers In Linear Regression With Application To Longitudinal Data, Zahraa Al-Sharea

Graduate Theses and Dissertations

Outlier detection is one of the most important challenges with many present-day applications. Outliers can occur due to uncertainty in data generating mechanisms or due to an error in data recording/processing. Outliers can drastically change the study's results and make predictions less reliable. Detecting outliers in longitudinal studies is quite challenging because this kind of study is working with observations that change over time. Therefore, the same subject can produce an outlier at one point in time produce regular observations at all other time points. A Bayesian hierarchical modeling assigns parameters that can quantify whether each observation is an outlier …

Data Analysis Methods Using Persistence Diagrams, Andrew Marchese

Doctoral Dissertations

In recent years, persistent homology techniques have been used to study data and dynamical systems. Using these techniques, information about the shape and geometry of the data and systems leads to important information regarding the periodicity, bistability, and chaos of the underlying systems. In this thesis, we study all aspects of the application of persistent homology to data analysis. In particular, we introduce a new distance on the space of persistence diagrams, and show that it is useful in detecting changes in geometry and topology, which is essential for the supervised learning problem. Moreover, we introduce a clustering framework directly …

Gilmore Girls And Instagram: A Statistical Look At The Popularity Of The Television Show Through The Lens Of An Instagram Page, Brittany Simmons

Student Scholar Symposium Abstracts and Posters

After going on the Warner Brothers Tour in December of 2015, I created a Gilmore Girls Instagram account. This account, which started off as a way for me to create edits of the show and post my photos from the tour turned into something bigger than I ever could have imagined. In just over a year I have over 55,000 followers. I post content including revival news, merchandise, and edits of the show that have been featured in Entertainment Weekly, Bustle, E! News, People Magazine, Yahoo News, & GilmoreNews.

I created a dataset of qualitative and quantitative outcomes from my …

The Battle Against Malaria: A Teachable Moment, Randy K. Schwartz

Journal of Humanistic Mathematics

Malaria has been humanity’s worst public health problem throughout recorded history. Mathematical methods are needed to understand which factors are relevant to the disease and to develop counter-measures against it. This article and the accompanying exercises provide examples of those methods for use in lower- or upper-level courses dealing with probability, statistics, or population modeling. These can be used to illustrate such concepts as correlation, causation, conditional probability, and independence. The article explains how the apparent link between sickle cell trait and resistance to malaria was first verified in Uganda using the chi-squared probability distribution. It goes on to explain …

Neural Network Predictions Of A Simulation-Based Statistical And Graph Theoretic Study Of The Board Game Risk, Jacob Munson

Murray State Theses and Dissertations

We translate the RISK board into a graph which undergoes updates as the game advances. The dissection of the game into a network model in discrete time is a novel approach to examining RISK. A review of the existing statistical findings of skirmishes in RISK is provided. The graphical changes are accompanied by an examination of the statistical properties of RISK. The game is modeled as a discrete time dynamic network graph, with the various features of the game modeled as properties of the network at a given time. As the network is computationally intensive to implement, results are produced …

An Exploratory Statistical Method For Finding Interactions In A Large Dataset With An Application Toward Periodontal Diseases, Joshua Lambert

Theses and Dissertations--Epidemiology and Biostatistics

It is estimated that Periodontal Diseases effects up to 90% of the adult population. Given the complexity of the host environment, many factors contribute to expression of the disease. Age, Gender, Socioeconomic Status, Smoking Status, and Race/Ethnicity are all known risk factors, as well as a handful of known comorbidities. Certain vitamins and minerals have been shown to be protective for the disease, while some toxins and chemicals have been associated with an increased prevalence. The role of toxins, chemicals, vitamins, and minerals in relation to disease is believed to be complex and potentially modified by known risk factors. A …

Quasi-Random Action Selection In Markov Decision Processes, Samuel D. Walker

Electronic Theses and Dissertations

In Markov decision processes an operator exploits known data regarding the environment it inhabits. The information exploited is learned from random exploration of the state-action space. This paper proposes to optimize exploration through the implementation of quasi-random sequences in both discrete and continuous state-action spaces. For the discrete case a permutation is applied to the indices of the action space to avoid repetitive behavior. In the continuous case sequences of low discrepancy, such as Halton sequences, are utilized to disperse the actions more uniformly.