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Articles 1 - 6 of 6
Full-Text Articles in Other Mathematics
Making Models With Bayes, Pilar Olid
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 …
Extending Difference Of Votes Rules On Three Voting Models., Sarah Schulz King
Extending Difference Of Votes Rules On Three Voting Models., Sarah Schulz King
Electronic Theses and Dissertations
In a voting situation where there are only two competing alternatives, simple majority rule outputs the alternatives with the most votes or declares a tie if both alternatives receive the same number of votes. For any non-negative integer k, the difference of votes rule Mk outputs the alternative that beats the competing alternative by more than k votes. Llamazares (2006) gives a characterization of the difference of votes rules in terms of five axioms. In this thesis, we extend Llamazares' result by completely describing the class of voting rules that satisfy only two out of his five axioms. …
Cayley Graphs Of Groups And Their Applications, Anna Tripi
Cayley Graphs Of Groups And Their Applications, Anna Tripi
MSU Graduate Theses
Cayley graphs are graphs associated to a group and a set of generators for that group (there is also an associated directed graph). The purpose of this study was to examine multiple examples of Cayley graphs through group theory, graph theory, and applications. We gave background material on groups and graphs and gave numerous examples of Cayley graphs and digraphs. This helped investigate the conjecture that the Cayley graph of any group (except Z_2) is hamiltonian. We found the conjecture to still be open. We found Cayley graphs and hamiltonian cycles could be applied to campanology (in particular, to the …
Krylov Subspace Spectral Methods For Pdes In Polar And Cylindrical Geometries, Megan Richardson
Krylov Subspace Spectral Methods For Pdes In Polar And Cylindrical Geometries, Megan Richardson
Dissertations
As a result of stiff systems of ODEs, difficulties arise when using time stepping methods for PDEs. Krylov subspace spectral (KSS) methods get around the difficulties caused by stiffness by computing each component of the solution independently. In this dissertation, we extend the KSS method to a circular domain using polar coordinates. In addition to using these coordinates, we will approximate the solution using Legendre polynomials instead of Fourier basis functions. We will also compare KSS methods on a time-independent PDE to other iterative methods. Then we will shift our focus to three families of orthogonal polynomials on the interval …
Neural Network Predictions Of A Simulation-Based Statistical And Graph Theoretic Study Of The Board Game Risk, Jacob Munson
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 …
Triple Non-Negative Matrix Factorization Technique For Sentiment Analysis And Topic Modeling, Alexander A. Waggoner
Triple Non-Negative Matrix Factorization Technique For Sentiment Analysis And Topic Modeling, Alexander A. Waggoner
CMC Senior Theses
Topic modeling refers to the process of algorithmically sorting documents into categories based on some common relationship between the documents. This common relationship between the documents is considered the “topic” of the documents. Sentiment analysis refers to the process of algorithmically sorting a document into a positive or negative category depending whether this document expresses a positive or negative opinion on its respective topic. In this paper, I consider the open problem of document classification into a topic category, as well as a sentiment category. This has a direct application to the retail industry where companies may want to scour …