A Bayesian Joint Model for Spatial Point Processes with Application to Basketball Shot Chart
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The success rate of a basketball shot may be higher at locations where a player makes more shots. In a marked spatial point process model, this means that the marks are dependent on the intensity of the process. We develop a Bayesian joint model of the mark and the intensity of marked spatial point process, where the intensity is incorporated in the model for the mark as a covariate. Further, we allow variable selection through the spike-slab prior. Inferences are developed with a Markov chain Monte Carlo algorithm to sample from the posterior distribution. Two Bayesian model comparison criteria, the modified Deviance Information Criterion and the modified Logarithm of the Pseudo-Marginal Likelihood, are developed to assess the fitness of different models focusing on the mark. The empirical performances of the proposed methods are examined in extensive simulation studies. We apply the proposed methods to the shot charts of four players in the NBA's 2017–2018 regular season to analyze the shot intensity in the field and the field goal percentage. The results suggest that the field goal percentages of three players are significantly positively dependent on their shot intensities, and that different players have different predictors for their field goal percentages.
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