Author:
Glickman Mark E.,Hennessy Jonathan
Abstract
AbstractMany games and sports, including races, involve outcomes in which competitors are rank ordered. In some sports, competitors may play in multiple events over long periods of time, and it is natural to assume that their abilities change over time. We propose a Bayesian state-space framework for rank ordered logit models to rate competitor abilities over time from the results of multi-competitor games. Our approach assumes competitors’ performances follow independent extreme value distributions, with each competitor’s ability evolving over time as a Gaussian random walk. The model accounts for the possibility of ties, an occurrence that is not atypical in races in which some of the competitors may not finish and therefore tie for last place. Inference can be performed through Markov chain Monte Carlo (MCMC) simulation from the posterior distribution. We also develop a filtering algorithm that is an approximation to the full Bayesian computations. The approximate Bayesian filter can be used for updating competitor abilities on an ongoing basis. We demonstrate our approach to measuring abilities of 268 women from the results of women’s Alpine downhill skiing competitions recorded over the period 2002–2013.
Subject
Decision Sciences (miscellaneous),Social Sciences (miscellaneous)
Reference88 articles.
1. Individual Choice Behavior a Theoretical;Luce;Analysis,1959
2. Foundation for Statistical Environment for Statistical Foundation for Statistical;Vienna;Computing Language Computing Austria Computing,2012
3. Maximum Likelihood Estimates of Linear Dynamic Systems;Rauch;AIAA Journal,1965
4. Parameter Estimation in Large Dynamic Paired Comparison Experiments of the;Glickman;Journal Royal Statistical Society Series Applied Statistics,1999
5. Models for Paired Comparison Data with Emphasis on Dependent Data;Cattelan;Review Statistical Science,2012
Cited by
11 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献