Bayesian inference of the impulse-response model of athlete training and performance

ABSTRACTThe Banister impulse-response (IR) model was designed to predict an athlete’s performance ability from their past training. Despite its long history, the model’s usefulness remains limited due to difficulties in obtaining precise parameter estimates and performance predictions. To help address these challenges, we developed a Bayesian implementation of the IR model, which formalises the combined use of prior knowledge and data. We report the following methodological contributions: 1) we reformulated the model to facilitate the specification of informative priors, 2) we derived the IR model in Bayesian terms, and 3) we developed a method that enabled the JAGS software to be used while enforcing parameter constraints. To demonstrate proof-of-principle, we applied the model to the data of a national-class middle-distance runner. We specified the priors from published values of IR model parameters, followed by estimating the posterior distributions from the priors and the athlete’s data. The Bayesian approach led to more precise and plausible parameter estimates than nonlinear least squares. We conclude that the Bayesian implementation of the IR model shows promise in addressing a primary challenge to its usefulness for athlete monitoring.KEYWORDS: Athletic performancemathematical modellingBayes theoremcomputer simulation AcknowledgementsThe authors thank Dr. Marc D. Klimstra of the Canadian Sport Institute Pacific and University of Victoria for his support and guidance.Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis study was funded by an Own The Podium-Mitacs Accelerate Fellowship to RTB and DCC and by a Canadian Statistical Sciences Institute Collaborative Research Team grant in sports analytics. TBS and DCC are supported by grants from the Natural Sciences and Engineering Research Council of Canada.