论文标题
空间均匀性的贝叶斯非参数估计：NBA射击位置的空间分析
Bayesian Nonparametric Estimation for Point Processes with Spatial Homogeneity: A Spatial Analysis of NBA Shot Locations
论文作者
论文摘要
篮球投篮位置数据提供了有关球员，体育分析师，球迷，统计学家以及球员本身的宝贵摘要信息。以空间点为代表，使用空间点过程模型自然分析了此类数据。我们提出了一种新型的非参数贝叶斯方法，用于学习在Dirichlet过程和Markov随机场的结合上构建的潜在强度表面。我们的方法具有在估计全球异质强度表面时有效鼓励局部空间均匀性的优点。使用有效的Markov链蒙特卡洛（MCMC）算法进行后推断。模拟研究表明，与竞争方法相比，这些推论是准确的，该方法优越。在2017-2018常规赛中，适用于$ 20 $代表性NBA球员的Shot Location数据提供了有关这些玩家的射击模式的有趣见解。与竞争方法的比较表明，所提出的方法可以有效地将空间连续性纳入强度表面的估计中。
Basketball shot location data provide valuable summary information regarding players to coaches, sports analysts, fans, statisticians, as well as players themselves. Represented by spatial points, such data are naturally analyzed with spatial point process models. We present a novel nonparametric Bayesian method for learning the underlying intensity surface built upon a combination of Dirichlet process and Markov random field. Our method has the advantage of effectively encouraging local spatial homogeneity when estimating a globally heterogeneous intensity surface. Posterior inferences are performed with an efficient Markov chain Monte Carlo (MCMC) algorithm. Simulation studies show that the inferences are accurate and that the method is superior compared to the competing methods. Application to the shot location data of $20$ representative NBA players in the 2017-2018 regular season offers interesting insights about the shooting patterns of these players. A comparison against the competing method shows that the proposed method can effectively incorporate spatial contiguity into the estimation of intensity surfaces.
