用于英超联赛进球依存关系的贝叶斯双变量条件泊松回归模型
A Bayesian bivariate conditional Poisson regression for goal dependence in the English Premier League
AI总结：
针对传统足球得分模型的局限，本文提出贝叶斯双变量条件泊松回归模型，分析英超联赛主客场进球依存关系，发现二者负相关且上座率对主客场得分的影响不对称。
AI中文摘要：
理解足球比赛中主客场进球数的关系能为比赛层面的动态提供有价值的见解。虽然主场优势的影响已得到充分证实，历史记录显示约50%的比赛由主队获胜（而客队获胜约30%），但在考虑关键比赛因素的同时，正确确定联合进球分布的问题仍未得到充分探索。本文中，我们开发了贝叶斯双变量条件泊松（BCP）回归模型，以明确捕捉主客场进球数之间的依存关系，解决了传统足球得分模型假设独立性或仅允许正相关的核心局限。该BCP回归模型被应用于涵盖三个赛季的英格兰超级联赛（EPL）数据，纳入了体育场上座率和两队的犯规次数作为回归变量。在贝叶斯框架内进行推断，可通过后验预测检查实现可解释的不确定性量化和模型验证。我们的结果表明主客场进球数之间存在负相关，并强调了比赛上座率对主客场得分影响的不对称性。
英文摘要：
Understanding the relationship between home and away goal counts in football provides valuable insights into match-level dynamics. While the influence of home advantage is well-established, with historical records indicating roughly 50% of matches are won by home teams (versus about 30% by the away team), properly determining the joint goal distribution while accounting for key match factors remains under-explored. In this paper, we develop a Bayesian bivariate Conditional Poisson (BCP) regression model to explicitly capture the dependence between home and away goal counts, addressing a core limitation of traditional football scoring models that assume independence or only allow for positive correlation. The BCP regression is applied to the English Premier League (EPL) data spanning three seasons, incorporating stadium attendance and committed fouls by both teams as regressors. Inference is conducted within a Bayesian framework, enabling interpretable uncertainty quantification and model validation through posterior predictive checks. Our results reveal a negative correlation between home and away goal counts and highlight an asymmetry in how match attendance influences home versus away scoring.
