Our approach allows us to produce credence intervals to quantify the uncertainty in our predictions. In this comparison, we cannot compare the credence intervals produced from the Trfyos MMSE estimator approach with our approach since they were not stated alongside their predictions.
We emphasize that even though the Tryfos MMSE estimator approach can produce credence intervals, they express uncertainty only in sampling variability and do not capture parametric uncertainty. Our approach also captures parametric uncertainty in the fit of our model, which provides a possible explanation for why the posterior mean estimator for the Marathon event performs better than the Tryfos MMSE.

Comparison of different attempt distributions

Our approach extends seamlessly to other attempt distributions. In this section, we repeat the same exercise on the Tryfos dataset but instead consider the effect of varying the form of the attempt distribution. Specifically, we compare the performance of a Gaussian attempt distribution with that of a Gumbel and of a Weibull attempt distribution. For this experiment, we again choose uninformative priors for each of the parameters of the underlying attempt distributions.