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Mathematical and statistical insights in evaluating state dependent effectiveness of HIV prevention interventions

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.…

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

Observability methods in sensor scheduling

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…

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

Are NBA Video Games Representing the Real Game? A Statistical Comparison of Phoenix Suns' Shooting Patterns and their Video Game Counterpart

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…

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

Home Advantage in Sports: The Value it Holds with COVID Restrictions

Description

Home advantage affects the game in almost all team sports across the world. Due to<br/>COVID and all of the precautions being taken to keep games played, more extensive research is able to be conducted about what factors truly go into creating a home advantage. Some common factors of home advantage…

Home advantage affects the game in almost all team sports across the world. Due to<br/>COVID and all of the precautions being taken to keep games played, more extensive research is able to be conducted about what factors truly go into creating a home advantage. Some common factors of home advantage include the crowd, facility familiarity, and travel. In the English Premier League, there are no fans allowed at any of the games; furthermore, in the NBA, a bubble was created at one neutral venue with no fans in attendance. Even with the NBA being at a neutral site, there was still a “home team” at every game. The sports betting industry struggled due to failing to shift betting lines in accordance with this decreased home advantage. With these leagues removing some of the factors that are frequently associated with home advantage, analysts are able to better see what the results would be of removing these variables. The purpose of this research is to determine if these adjustments made due to COVID had an impact on the home advantage in different leagues around the world, and if they did, to what extent. Individual game data from the past 10 seasons were used for analysis of both the NBA and the Premier League. The results show that there is a significant difference in win percentage between prior seasons and seasons behind closed doors. In addition to win percentage, many other game statistics see a significant shift as well. Overall, the significance of being the home team disappears in games following the COVID-19 break.

ContributorsOsborne, Ashley A (Author) / Sopha, Matthew (Thesis director) / McIntosh, Daniel (Committee member) / Department of Information Systems (Contributor) / Department of Marketing (Contributor) / WPC Graduate Programs (Contributor) / Barrett, The Honors College (Contributor)

Created2021-05

Fatigue and Free Throw Shooting Ability in the NBA

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…

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

NBA Player Clustering: Exploring Player Archetypes in a Changing NBA

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,…

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

Bienvenidos a México: Breaking Down Borders of the NBA

Description

While basketball has been traditionally regarded as an American sport, the National Basketball Association (NBA) has gained substantial traction outside the United States over the past decade. In order to further encourage attention from international fans and increase league profit, I propose that the league adds an expansion team to…

While basketball has been traditionally regarded as an American sport, the National Basketball Association (NBA) has gained substantial traction outside the United States over the past decade. In order to further encourage attention from international fans and increase league profit, I propose that the league adds an expansion team to Mexico City. I believe that through thorough market research and conscientious brand development, the team be successfully integrated into both the local community as well as the league’s current fan base. Local infrastructure, player safety, border customs, and financials were all taken into consideration into this proposal. The purpose of this project is twofold: first, to advocate for league expansion of the NBA into Mexico City through discussion and exploration of both the anticipated opportunities and obstacles, and second, to design three brand concepts and then propose a final brand concept based off of qualitative and quantitative feedback systematically collected via a survey.

ContributorsArd, Dalin Max (Author) / Montoya, Detra (Thesis director) / McIntosh, Daniel (Committee member) / Department of Marketing (Contributor) / Department of Information Systems (Contributor) / Barrett, The Honors College (Contributor)

Created2019-05

The Winning Losers: Combatting the Economic and Competitive Balance Effects of Tanking in the National Basketball Association

Description

In order to establish sustainable parity in competition year over year, all four major professional sports organizations in the United States have established a first-year draft with an order decided or influenced by their Win-Loss record the previous year. The assumption is that this draft structure should keep all teams…

In order to establish sustainable parity in competition year over year, all four major professional sports organizations in the United States have established a first-year draft with an order decided or influenced by their Win-Loss record the previous year. The assumption is that this draft structure should keep all teams competitive. Rather, there is an overwhelming shift to analytical problem-solving that suggests building a winning team requires a period of losing and collecting young talent. The separation has become so apparent that it has been referred to as, “Twelve teams a-tanking.” (Boras, 2018) The trend was so pronounced this last season that the seven worst teams that held their own pick all lost by more than 15 points in the span of two days.(Sheinin, 2018) This leaves the ratio of games with a 15 point or more point differential to that of less than 15 points was 8:9 on the date described by Sheinin, as opposed to the usual ratio of 2:5 for the rest of the season. This stretch of games occurred during a pivotal time in the season and should have garnered high interest for entertainment as teams grapple for playoff position heading into the post season. Instead, viewers were treated to seven blow-out games. In this thesis, the effects of tanking will be studied as it pertains to the NBA, as a whole, losing attendance in multiple aspects. This applies directly to the value of sponsorships in the NBA. In short, this thesis will answer three of questions; (1) How does expected point spread, which is highly affected by tanking, affect NBA attendance, of all teams, down the stretch of games? (2) How can the NBA protect its sponsors from the effects of tanking? (3) How can NBA sponsors protect themselves from the effects of tanking?

ContributorsThomas, Isaiah (Author) / McIntosh, Daniel (Thesis director) / Eaton, John (Committee member) / Department of Information Systems (Contributor) / Department of Marketing (Contributor) / Barrett, The Honors College (Contributor)

Created2020-05

Contract Year's Effects on NBA Salary Caps and What Statistics Can Identify These Players

Description

The National Basketball Association is one of the most popular and most profitable sports leagues in the entire world, and with stars like Giannis Antetokounmpo, Nikola Jokić, and Luka Dončić, it continues to expand its international reach. In the past decade this has meant that the salary cap has continued…

The National Basketball Association is one of the most popular and most profitable sports leagues in the entire world, and with stars like Giannis Antetokounmpo, Nikola Jokić, and Luka Dončić, it continues to expand its international reach. In the past decade this has meant that the salary cap has continued to increase considerably. From 2013 to 2017 the salary cap increased by about $40.5 million from around $58.5 million to $99 million meaning there was an extra $1.2 billion worth of cap space to fill. All this new cap space created a perfect storm for numerous players to be overpaid. Many saw the performance of these overpaid players as a part of the contract year phenomenon where a player performs better before a new contract and then after receiving their new contract, their performance deteriorates. The purpose of this research is twofold. First, it looks at whether the contract year phenomenon has been present in the NBA since 2015. After that it looks to find what statistics are the best predictors for performance based on their positions. This was done through various statistical analysis techniques such as T-tests and piecewise regression. Box score statistics like point, rebounds, and assists as well as advanced metrics like player efficiency rating, usage percentage, and true shooting percentage were utilized in this study. The results indicated that the concept of the contract year phenomenon was present in the players sampled. However, rather than contract year only being for players who increased their performance in the previous year, it is a more general phenomenon. Also, there was major differences in the statistics that predicted performance. The biggest of these was the importance of usage percentage rather than points and that centers had the least predictors, most likely due to the evolution in the play of centers.

ContributorsUmland, Matthew (Author) / Eaton, John (Thesis director) / McIntosh, Daniel (Committee member) / Barrett, The Honors College (Contributor) / School of Accountancy (Contributor) / WPC Graduate Programs (Contributor)

Created2022-05

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