Matching Items (7)
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- All Subjects: NBA
- All Subjects: Bayesian Parameter Estimation
- Creators: Armbruster, Dieter
- Creators: Marburger, Daniel
Description
Pre-Exposure Prophylaxis (PrEP) is any medical or public health procedure used before exposure to the disease causing agent, its purpose is to prevent, rather than treat or cure a disease. Most commonly, PrEP refers to an experimental HIV-prevention strategy that would use antiretrovirals to protect HIV-negative people from HIV infection. A deterministic mathematical model of HIV transmission is developed to evaluate the public-health impact of oral PrEP interventions, and to compare PrEP effectiveness with respect to different evaluation methods. The effects of demographic, behavioral, and epidemic parameters on the PrEP impact are studied in a multivariate sensitivity analysis. Most of the published models on HIV intervention impact assume that the number of individuals joining the sexually active population per year is constant or proportional to the total population. In the second part of this study, three models are presented and analyzed to study the PrEP intervention, with constant, linear, and logistic recruitment rates. How different demographic assumptions can affect the evaluation of PrEP is studied. When provided with data, often least square fitting or similar approaches can be used to determine a single set of approximated parameter values that make the model fit the data best. However, least square fitting only provides point estimates and does not provide information on how strongly the data supports these particular estimates. Therefore, in the third part of this study, Bayesian parameter estimation is applied on fitting ODE model to the related HIV data. Starting with a set of prior distributions for the parameters as initial guess, Bayes' formula can be applied to obtain a set of posterior distributions for the parameters which makes the model fit the observed data best. Evaluating the posterior distribution often requires the integration of high-dimensional functions, which is usually difficult to calculate numerically. Therefore, the Markov chain Monte Carlo (MCMC) method is used to approximate the posterior distribution.
ContributorsZhao, Yuqin (Author) / Kuang, Yang (Thesis advisor) / Taylor, Jesse (Committee member) / Armbruster, Dieter (Committee member) / Tang, Wenbo (Committee member) / Kang, Yun (Committee member) / Arizona State University (Publisher)
Created2014
Description
Modern measurement schemes for linear dynamical systems are typically designed so that different sensors can be scheduled to be used at each time step. To determine which sensors to use, various metrics have been suggested. One possible such metric is the observability of the system. Observability is a binary condition determining whether a finite number of measurements suffice to recover the initial state. However to employ observability for sensor scheduling, the binary definition needs to be expanded so that one can measure how observable a system is with a particular measurement scheme, i.e. one needs a metric of observability. Most methods utilizing an observability metric are about sensor selection and not for sensor scheduling. In this dissertation we present a new approach to utilize the observability for sensor scheduling by employing the condition number of the observability matrix as the metric and using column subset selection to create an algorithm to choose which sensors to use at each time step. To this end we use a rank revealing QR factorization algorithm to select sensors. Several numerical experiments are used to demonstrate the performance of the proposed scheme.
ContributorsIlkturk, Utku (Author) / Gelb, Anne (Thesis advisor) / Platte, Rodrigo (Thesis advisor) / Cochran, Douglas (Committee member) / Renaut, Rosemary (Committee member) / Armbruster, Dieter (Committee member) / Arizona State University (Publisher)
Created2015
Description
This paper intends to analyze the Phoenix Suns' shooting patterns in real NBA games, and compare them to the "NBA 2k16" Suns' shooting patterns. Data was collected from the first five Suns' games of the 2015-2016 season and the same games played in "NBA 2k16". The findings of this paper indicate that "NBA 2k16" utilizes statistical findings to model their gameplay. It was also determined that "NBA 2k16" modeled the shooting patterns of the Suns in the first five games of the 2015-2016 season very closely. Both, the real Suns' games and the "NBA 2k16" Suns' games, showed a higher probability of success for shots taken in the first eight seconds of the shot clock than the last eight seconds of the shot clock. Similarly, both game types illustrated a trend that the probability of success for a shot increases as a player holds onto a ball longer. This result was not expected for either game type, however, "NBA 2k16" modeled the findings consistent with real Suns' games. The video game modeled the Suns with significantly more passes per possession than the real Suns' games, while they also showed a trend that more passes per possession has a significant effect on the outcome of the shot. This trend was not present in the real Suns' games, however literature supports this finding. Also, "NBA 2k16" did not correctly model the allocation of team shots for each player, however, the differences were found only in bench players. Lastly, "NBA 2k16" did not correctly allocate shots across the seven regions for Eric Bledsoe, however, there was no evidence indicating that the game did not correctly model the allocation of shots for the other starters, as well as the probability of success across the regions.
ContributorsHarrington, John P. (Author) / Armbruster, Dieter (Thesis director) / Kamarianakis, Ioannis (Committee member) / Chemical Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
The NBA Draft has become one of the most exciting and unique events in sports. Draft decisions are so monumental; so crucial to be right, so disastrous to be wrong. The purpose of this project is to build a model that would help teams to predict which types of players perform at a high level upon entering the league. By using regression analysis to predict the rookie year PER (performance efficiency rating) as a dependent variable, teams would have some idea of whether their rookies were underperforming, excelling, or performing at a level they could expect. The independent variables and their statistical significance could help answer a host of questions that front offices have about players: If a player came from a worse conference, can we expect them to have a harder time adjusting? Will their shorter wingspan have a negative effect on their play in the NBA? Do guards or forwards tend to have higher PERs upon entering the league? To answer these questions, I've gathered data on every first round NBA draft pick from 2001-2014 who played at least one season of Division 1 NCAA basketball. The data consist of anthropometric measurements (height, wingspan, standing reach, etc.), NBA draft combine results (agility drills, sprint times, etc.) and their college statistics per 40 minutes in their final season of college basketball (points, rebounds, assist-to-turnover ratio, etc.). I then separated the data into seven different sets: aggregate, backcourt, frontcourt, guard, wing, forward, and big. For each of these data sets, I built a predictive model for rookie PER. In doing so, I aimed to gain both a broad understanding of what factors lead to translation of college basketball play to professional play, and also a precise understanding of how those factors change for each distinct position.
ContributorsMurphy, Benjamin Joseph (Author) / Goegan, Brian (Thesis director) / Marburger, Daniel (Committee member) / Economics Program in CLAS (Contributor) / School of Historical, Philosophical and Religious Studies (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
The NBA operates under a unique system with both forms of the salary cap. The league has a team salary cap that sets a limit that teams can spend on their entire roster. The NBA has a soft cap and a luxury tax system, meaning if teams spend over a determined amount, they are taxed for the salaries in excess. The league also has a player salary cap. The 1999 NBA collective bargaining agreement first introduced the individual player salary cap in the league. This cap sets a limit on what the best players can earn, otherwise known as the maximum contract. In an economic system with a soft team cap, the introduction of the player salary cap has important implications. The stated outcome of such a salary cap is to improve competitive balance and better distribute star players throughout the league. This study evaluated the 1990-2015 regular seasons to measure the impact of the player salary cap on competitive balance, the distribution of team payrolls, and the dispersion of star players. In accordance with the Rottenberg's invariance hypothesis, the player salary cap has hurt the players and benefited the owners by redistributing income from one party to the other, without impacting the distribution of talent in the league. The rule change has not affected competitive balance, while team payrolls have converged and star players have become more dispersed throughout the league. These changes hurt the league overall, preventing the maximization of revenues. Despite this inefficiency, the chance of the league moving to eliminate the player salary cap is low.
ContributorsWelu, Brian Andrew (Author) / Marburger, Daniel (Thesis director) / Goegan, Brian (Committee member) / Sandra Day O'Connor College of Law (Contributor) / Department of Economics (Contributor) / School of Historical, Philosophical and Religious Studies (Contributor) / W. P. Carey School of Business (Contributor) / Barrett, The Honors College (Contributor)
Created2016-12
Description
We attempt to analyze the effect of fatigue on free throw efficiency in the National Basketball Association (NBA) using play-by-play data from regular-season, regulation-length games in the 2016-2017, 2017-2018, and 2018-2019 seasons. Using both regression and tree-based statistical methods, we analyze the relationship between minutes played total and minutes played continuously at the time of free throw attempts on players' odds of making an attempt, while controlling for prior free throw shooting ability, longer-term fatigue, and other game factors. Our results offer strong evidence that short-term activity after periods of inactivity positively affects free throw efficiency, while longer-term fatigue has no effect.
ContributorsRisch, Oliver (Author) / Armbruster, Dieter (Thesis director) / Hahn, P. Richard (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
Description
The findings of this project show that through the use of principal component analysis and K-Means clustering, NBA players can be algorithmically classified in distinct clusters, representing a player archetype. Individual player data for the 2018-2019 regular season was collected for 150 players, and this included regular per game statistics, such as rebounds, assists, field goals, etc., and advanced statistics, such as usage percentage, win shares, and value over replacement players. The analysis was achieved using the statistical programming language R on the integrated development environment RStudio. The principal component analysis was computed first in order to produce a set of five principal components, which explain roughly 82.20% of the total variance within the player data. These five principal components were then used as the parameters the players were clustered against in the K-Means clustering algorithm implemented in R. It was determined that eight clusters would best represent the groupings of the players, and eight clusters were created with a unique set of players belonging to each one. Each cluster was analyzed based on the players making up the cluster and a player archetype was established to define each of the clusters. The reasoning behind the player archetypes given to each cluster was explained, providing details as to why the players were clustered together and the main data features that influenced the clustering results. Besides two of the clusters, the archetypes were proven to be independent of the player's position. The clustering results can be expanded on in the future to include a larger sample size of players, and it can be used to make inferences regarding NBA roster construction. The clustering can highlight key weaknesses in rosters and show which combinations of player archetypes lead to team success.
ContributorsElam, Mason Matthew (Author) / Armbruster, Dieter (Thesis director) / Gel, Esma (Committee member) / Computer Science and Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2019-05