论文标题
一个基于Copula的多元隐藏Markov模型，用于建模足球中的动量
A copula-based multivariate hidden Markov model for modelling momentum in football
论文作者
论文摘要
我们研究了足球比赛动态中的变化点的可能发生的可能发生的可能性（通常称为“动量变化”）。为此，我们使用隐藏的Markov模型（HMM）对德甲联赛匹配的逐分钟统计量进行建模。为了允许所考虑的变量的状态内相关性，我们使用Copulas制定了多元状态依赖性分布。对于所考虑的德甲数据，我们发现拟合的HMMS包括可以将其解释为显示对匹配的不同控制水平的团队。我们的建模框架可以推断与动量转变和团队战术的原因有关，这对经理，庄家和体育迷来说引起了人们的关注。
We investigate the potential occurrence of change points - commonly referred to as "momentum shifts" - in the dynamics of football matches. For that purpose, we model minute-by-minute in-game statistics of Bundesliga matches using hidden Markov models (HMMs). To allow for within-state correlation of the variables considered, we formulate multivariate state-dependent distributions using copulas. For the Bundesliga data considered, we find that the fitted HMMs comprise states which can be interpreted as a team showing different levels of control over a match. Our modelling framework enables inference related to causes of momentum shifts and team tactics, which is of much interest to managers, bookmakers, and sports fans.
