论文标题
使用Bradley-Terry-Zermelo模型在大学曲棍球进行预测和评估
Prediction and Evaluation in College Hockey using the Bradley-Terry-Zermelo Model
论文作者
论文摘要
我们描述了Bradley-Terry模型在NCAA I级男子冰球上的应用。给定一组游戏结果和先前分布的选择，贝叶斯结构为对数 - 强度参数提供了联合后验概率分布。对于几种合适的先验选择，很容易找到最大的后验点（MAP）和HESSIAN矩阵，从而构建高斯近似值。可以通过1）将日志长度设置为其MAP值，2）使用高斯近似进行分析或蒙特卡洛整合，或3）应用重要性采样以重新进行蒙特卡洛模拟的结果。我们定义了一种评估任何模型的方法，这些模型使用贝叶斯因素为实际的结果，并将其应用于NCAA锦标赛结果。最后，我们描述了一个在线工具，该工具目前使用地图评估估算未来结果的概率，并描述如何使用高斯近似或重要性采样来对其进行完善。
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.
