Bradley-Terry-Zermelo模型在大学曲棍球运动中的预测与评价
Prediction and Evaluation in College Hockey using the Bradley-Terry-Zermelo Model
摘要：
我们描述的应用程序的布拉德利-特里模型NCAA司I男子冰球。贝叶斯构造给出了对数强度参数的联合后验概率分布，给出了一组博弈结果和先验分布的选择。对于几个合适的先验选择，可以直接找到最大后验点（MAP）和Hessian矩阵，从而可以构建高斯近似。后验预测概率可通过以下方式估计：1）将对数强度设置为其MAP值，2）使用高斯近似进行分析或蒙特卡罗积分，或3）应用重要性抽样对蒙特卡罗模拟的结果重新加权。我们定义了一种方法来评估任何模型，生成预测的概率为未来的结果，使用贝叶斯因子给定的实际结果，并将其应用到NCAA锦标赛的结果。最后，我们描述了一个在线工具，目前估计未来的结果，使用MAP评估的概率，并描述了如何可以使用高斯近似或重要性抽样来完善。
英文摘要：
We describe the application of the Bradley-Terry model to NCAA Division I Men's Ice Hockey. A Bayesian construction gives a joint posterior probability distribution for the log-strength parameters, given a set of game results and a choice of prior distribution. For several suitable choices of prior, it is straightforward to find the maximum a posteriori point (MAP) and a Hessian matrix, allowing a Gaussian approximation to be constructed. Posterior predictive probabilities can be estimated by 1) setting the log-strengths to their MAP values, 2) using the Gaussian approximation for analytical or Monte Carlo integration, or 3) applying importance sampling to re-weight the results of a Monte Carlo simulation. We define a method to evaluate any models which generate predicted probabilities for future outcomes, using the Bayes factor given the actual outcomes, and apply it to NCAA tournament results. Finally, we describe an on-line tool which currently estimates probabilities of future results using MAP evaluation and describe how it can be refined using the Gaussian approximation or importance sampling.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
