We use this data to:
  1. Compare the results of the Bayesian posterior with a Gaussian attempt distribution to the reported results of the MMSE estimator.
  2. Study the effects of modeling the problem using different attempt distributions and parameter priors.
  3. Produce forecasts for the record progressions for each event over the course of the next decade.  

Comparison with the Tryfos MMSE approach

\citep{tryfos_forecasting_1985} provided forecasts for future records of the six men categories between 1983 and 1997, for their model fit to the records in the previous years 1968 to 1982. Their approach is to derive the Minimum Mean Square Error (MMSE) estimator assuming an underlying Gumbel distribution of attempts. Here we compare the results from their approach to an analogous Bayesian model using our approach with a Gumbel attempt distribution. Note that the MMSE estimator of \citep{tryfos_forecasting_1985} is a maximum likelihood estimate that does not incorporate a prior for the solution. To make an accurate comparison, we opt to use highly uninformative priors for the parameters of the underlying Gumbel attempt distribution used in our approach.
Consider the mile run event. In Figures 2, 3, and 4, we present the results of the Bayesian model on the mile run in comparison to the MMSE estimator. Here we have used the No-U-Turn Sampler (NUTS) implementation of PyMC3 to compute 10 independent chains of 25,000 samples each, with posterior statistics calculated using samples from all chains.