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Title: Applying Bayesian inference to the impulse-response model of athletic training and performance Authors:  Kangyi Peng - Simon Fraser University (Canada)
Ryan Brodie - Simon Fraser University (Canada)
Tim Swartz - Simon Fraser University (Canada)
David Clarke - Simon Fraser University (Canada) [presenting]
Abstract: The impulse-response (IR) model describes the relationship between athlete training history and performance. It takes as input daily training loads and fits them to past performance data. The model features five adjustable parameters and two derived parameters. Despite some past successes, IR models are often poorly estimated. We describe a novel Bayesian inference approach to estimate the IR model. We discuss the basis of informative priors and justify the assumption that performance conforms to a multivariate normal distribution. Markov chain Monte Carlo simulation (MCMC), via Gibbs sampling, was used to sample the posterior distributions. The method was applied to data from an international-class middle-distance runner, for which training was quantified as individualized training impulse and performance as IAAF points achieved in a sanctioned race. The inference procedure produced well-constrained estimates of the five adjustable parameters, but the posterior interval widths of the derived parameters were too wide to make reliable training optimization decisions. We conclude by discussing modifications to our approach that could further improve the Bayesian inference of the IR model.