Bayesian Nonparametric Learning for Point Processes with Spatial Homogeneity: A Spatial Analysis of NBA Shot Locations

Basketball shot location data provide valuable summary information regardingplayers to coaches, sports analysts, fans, statisticians, as well as playersthemselves. Represented by spatial points, such data are naturally analyzed with spatial point process models. We present a novel nonparametric Bayesianmethod for learning the underlying intensity surface built upon acombination of Dirichlet process and Markov random field. Our method has theadvantage of effectively encouraging local spatial homogeneity when estimating a globally heterogeneous intensity surface. Posterior inferences are performedwith an efficient Markov chain Monte Carlo (MCMC) algorithm. Simulation studiesshow that the inferences are accurate and the method is superior comparedto a wide range of competing methods. Application to the shot location data of $20$ representative NBA players in the 2017-2018 regular season offers interestinginsights about the shooting patterns of these players. A comparison against thecompeting method shows that the proposed method can effectively incorporatespatial contiguity into the estimation of intensity surfaces.