Inference on a bivariate binomial distribution with zero-inflation applicable to baseball data.

This article focuses on developing a zero-inflated bivariate binomial (ZIBVB) distribution model for analyzing nested binary data with excessive zeros, motivated by Major League Baseball (MLB) data involving extra-base hits and home runs. The proposed model extends traditional zero-inflated binomial (ZIB) models to handle two correlated success probabilities simultaneously, incorporating Bayesian inference with objective Jeffreys priors and Bayesian model selection via Bayes factors. The methodology includes deriving predictive distributions for future observations and is illustrated through real MLB player data, demonstrating zero-inflation patterns in both batters' and pitchers' performances. Simulation studies support the model's estimation accuracy and predictive capability, while the authors discuss potential extensions and limitations, such as assuming a common zero-inflation parameter for both components and the complexity of regression model adaptations.