Browsing by Subject "Hierarchical"
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Item Bayesian hierarchical linear modeling of NFL quarterback rating(2015-05) Hernandez, Steven V.; Walker, Stephen G., 1945-; Mahometa, Michael JWith endless amounts of statistics in American football, there are numerous ways to evaluate quarterback performance in the National Football League. Owners, general managers, and coaches are always looking for ways to improve quarterback play to increase overall team performance. In doing so, one may ask: Does the performance in the first quarter have any effect on the fourth quarter performance? This paper will investigate the linear dependence of the first quarter NFL QB rating on the fourth quarter NFL QB rating for 17 NFL starting quarterbacks from the 2014-2015 season. The aim is to use Bayesian hierarchical linear modeling to attain slope and intercept estimates for each quarterback in the study and attempt to determine what is causing the dependence, if any. Then, if a linear dependence is detected, investigating whether or not the statistic used is a viable measure of performance.Item Bayesian hierarchical parametric survival analysis for NBA career longevity(2012-05) Lakin, Richard Thomas; Scott, James Gordon; Powers, DanielIn evaluating a prospective NBA player, one might consider past performance in the player’s previous years of competition. In doing so, a general manager may ask the following questions: Do certain characteristics of a player’s past statistics play a role in how long a player will last in the NBA? In this study, we examine the data from players who entered in the NBA in a five-‐year period (1997-‐1998 through 2001-‐2002 season) by looking at their attributes from their collegiate career to see if they have any effect on their career longevity. We will look at basic statistics take for each of these players, such as field goal percentage, points per game, rebounds per game and assists per game. We aim to use Bayesian survival methods to model these event times, while exploiting the hierarchical nature of the data. We will look at two types of models and perform model diagnostics to determine which of the two we prefer.Item Flux: for brass quintet with analysis(2010-12) Devet, Robert; Fischer, Peter; Berry, Michael F.; Decker, James T.This paper will examine the piece Flux: for Brass Quintet, completed in the spring of 2010 by Robert DeVet. It will first examine the system of quartal harmony employed in the piece and define a concise system of analysis. It will then present a several examples of quartal harmony in the music of other composers and briefly inspect a similarly rigorous system based on perfect intervals. Each movement will then be analyzed formally, harmonically, and motivically. The piece consists of three individual movements, “Waiting to Win,” “Strides Forward,” and “Ostinato.”Item Statistical clustering of data(2015-05) Zhang, Lihao; Sager, Thomas W.; Hersh, MatthewCluster analysis aims at segmenting objects into groups with similar members and, therefore helps to discover distribution of properties and correlations in large datasets. Data clustering has been widely studied as it arises in many domains in marketing, engineering, and social sciences. Especially, the occurrence of transactional and experimental datasets in large scale in recent years significantly increased the necessity of clustering techniques to reduce the size of the existing objects, to achieve a better knowledge of the data. This report introduced fundamental concepts related to cluster analysis, addressed the similarity and dissimilarity measurements for cluster definition, and clarified three major clustering algorithms-hierarchical clustering, K-means clustering and Gaussian mixture model fitted by Expectation-Maximization (EM) algorithm-theoretically and experimentally to illustrate the process of clustering. Finally, methods of determining the number of clusters and validating the clustering were presented as for clustering evaluation.