Athletic performance follows a typical pattern of improvement and decline during a career. This pattern is also often observed within-seasons as athlete aims for their performance to peak at key events such as the Olympic Games or World Championships. A Bayesian hierarchical model is developed to analyse the evolution of athletic sporting performance throughout an athlete's career and separate these effects whilst allowing for confounding factors such as environmental conditions. Our model works in continuous time and estimates both the average performance level of the population, $g(t)$, at age $t$ and how each $i$-th athlete differs from the average $f_i(t)$. We further decompose $f_i(t)$ into changes from season-to-season, termed the between-season performance trajectory, and within-season performance trajectories which are modelled by a constrained Bernstein polynomial. Hence, the specific focus of this project is to identify the differences in performance that exist both between and within-seasons for each athlete. For the implementation of the model an adaptive Metropolis-within-Gibbs algorithm is used. An illustration of algorithm's performance on 100 metres and 200 metres freestyle swimming in both female and male athletes is presented.

翻译：运动员的职业生涯中，其表现通常遵循提升与衰退的典型模式。这种模式在赛季内也常被观察到，因为运动员的目标是在奥运会或世锦赛等关键赛事中达到表现峰值。本研究开发了一个贝叶斯分层模型，用于分析运动员职业生涯中运动表现的演变过程，并在控制环境条件等混杂因素的同时分离这些效应。我们的模型在连续时间上工作，同时估计群体在年龄 $t$ 时的平均表现水平 $g(t)$，以及每位第 $i$ 名运动员与平均水平的差异 $f_i(t)$。我们进一步将 $f_i(t)$ 分解为赛季间的变化（称为赛季间表现轨迹）和由约束伯恩斯坦多项式建模的赛季内表现轨迹。因此，本项目的具体重点是识别每位运动员在赛季间和赛季内存在的表现差异。模型的实现采用了自适应吉布斯抽样框架内的Metropolis算法。本文展示了该算法在男、女运动员100米和200米自由泳项目上的应用效果。