Mathematics Commons^™

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 …

Making Models With Bayes, Pilar Olid

Electronic Theses, Projects, and Dissertations

Bayesian statistics is an important approach to modern statistical analyses. It allows us to use our prior knowledge of the unknown parameters to construct a model for our data set. The foundation of Bayesian analysis is Bayes' Rule, which in its proportional form indicates that the posterior is proportional to the prior times the likelihood. We will demonstrate how we can apply Bayesian statistical techniques to fit a linear regression model and a hierarchical linear regression model to a data set. We will show how to apply different distributions to Bayesian analyses and how the use of a prior affects …

Application Of Inverse Problems In Imaging, Xiaoyue Luo

Post-Grant Reports

In this project, we studied how to enhance image quality by denoising and deblurring a given image mathematically. We compared some existing state-of-the-art methods for image denoising and deblurring. We implemented the algorithms numerically using Matlab.

We studied the possibility of combining statistical analysis with the traditional image restoration methods including using wavelets and framelets and we derived some encouraging preliminary results.

My research student Alleta Maier gave a sequence of talks on the project including the Pacific Northwest Mathematical Association of America conference at Oregon State University in April, 2016; Linfield College Taylor Series in March, 2016, and Linfield …

A Comprehensive Analysis Of Team Streakiness In Major League Baseball: 1962-2016, Paul H. Kvam, Zezhong Chen

Department of Math & Statistics Faculty Publications

A baseball team would be considered “streaky” if its record exhibits an unusually high number of consecutive wins or losses, compared to what might be expected if the team’s performance does not really depend on whether or not they won their previous game. If an average team in Major League Baseball (i.e., with a record of 81-81) is not streaky, we assume its win probability would be stable at around 50% for most games, outside of peculiar details of day-to-day outcomes, such as whether the game is home or away, who is the starting pitcher, and so on.

In this …

Flexibility Of Projective-Planar Embeddings, John Maharry, Neil Robertson, Vaidy Sivaraman, Dan Slilaty

Mathematics and Statistics Faculty Publications

Given two embeddings σ1 and σ2 of a labeled nonplanar graph in the projective plane, we give a collection of maneuvers on projective-planar embeddings that can be used to take σ1 to σ2

Bounding And Stabilizing Realizations Of Biased Graphs With A Fixed Group, Nancy Ann Neudauer, Dan Slilaty

Mathematics and Statistics Faculty Publications

Given a group Γ and a biased graph (G, B), we define a what is meant by a Γ-realization of (G, B) and a notion of equivalence of Γ-realizations. We prove that for a finite group Γ and t ≥ 3, that there are numbers n(Γ) and n(Γ, t) such that the number of Γ-realizations of a vertically 3-connected biased graph is at most n(Γ) and that the number of Γ-realizations of a nonseparable biased graph without a (2Ct , ∅)-minor is at most n(Γ, t). Other results pertaining to contrabalanced biased graphs are presented as well as an analogue …

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 …

The Document Similarity Network: A Novel Technique For Visualizing Relationships In Text Corpora, Dylan Baker

HMC Senior Theses

With the abundance of written information available online, it is useful to be able to automatically synthesize and extract meaningful information from text corpora. We present a unique method for visualizing relationships between documents in a text corpus. By using Latent Dirichlet Allocation to extract topics from the corpus, we create a graph whose nodes represent individual documents and whose edge weights indicate the distance between topic distributions in documents. These edge lengths are then scaled using multidimensional scaling techniques, such that more similar documents are clustered together. Applying this method to several datasets, we demonstrate that these graphs are …