Bayesian Binary Segmentation Procedure for Detecting Streakiness in Sports
提出一种贝叶斯二元分割程序，通过贝叶斯因子或贝叶斯信息准则进行嵌套假设检验，同时定位运动员或球队的变点及其成功率，避免未知变点数带来的计算复杂性，并应用于篮球、高尔夫和棒球数据。
Summary When an individual player or team enjoys periods of good form, and when these occur, is a widely observed phenomenon typically called ‘streakiness’. It is interesting to assess which team is a streaky team, or who is a streaky player in sports. Such competitors might have a large number of successes during some periods and few or no successes during other periods. Thus, their success rate is not constant over time. We provide a Bayesian binary segmentation procedure for locating changepoints and the associated success rates simultaneously for these competitors. The procedure is based on a series of nested hypothesis tests each using the Bayes factor or the Bayesian information criterion. At each stage, we only need to compare a model with one changepoint with a model based on a constant success rate. Thus, the method circumvents the computational complexity that we would normally face in problems with an unknown number of changepoints. We apply the procedure to data corresponding to sports teams and players from basketball, golf and baseball.