The success rate of a basketball shot may be higher at locations where a player makes more shots. For a marked spatial point process, this means that the mark and the intensity are associated. We propose a Bayesian joint model for the mark and the intensity of marked point processes, where the intensity is incorporated in the mark model as a covariate. Inferences are done with a Markov chain Monte Carlo algorithm. Two Bayesian model comparison criteria, the Deviance Information Criterion and the Logarithm of the Pseudo-Marginal Likelihood, were used to assess the model. The performances of the proposed methods were examined in extensive simulation studies. The proposed methods were applied to the shot charts of four players (Curry, Harden, Durant, and James) in the 2017–2018 regular season of the National Basketball Association to analyze their shot intensity in the field and the field goal percentage in detail. Application to the top 50 most frequent shooters in the season suggests that the field goal percentage and the shot intensity are positively associated for a majority of the players. The fitted parameters were used as inputs in a secondary analysis to cluster the players into different groups.

中文翻译：

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篮球投篮图的贝叶斯标记空间点过程模型

在球员进行更多投篮的地方，篮球投篮的成功率可能更高。对于标记的空间点过程，这意味着标记和强度相关联。我们为标记和标记点过程的强度提出了贝叶斯联合模型，其中强度作为协变量并入标记模型。推论是用马尔可夫链蒙特卡罗算法完成的。使用两个贝叶斯模型比较标准（偏差信息准则和伪边际可能性的对数）来评估模型。在广泛的模拟研究中检查了所提出方法的性能。拟议的方法已应用于四名球员（库里，哈登，杜兰特，和詹姆斯（James）在美国国家篮球协会（National Basketball Association）2017-2018常规赛中分析他们的投篮强度和射门命中率的详细信息。在本赛季前50名最频繁的射手中的应用表明，大多数球员的投篮命中率和射门强度成正相关。拟合的参数在辅助分析中用作输入，以将玩家分为不同的组。