Bayesian inference of the impulse-response model of athlete training and performance
Bibliographic record
Abstract
The 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.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.011 | 0.035 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".