Given the distribution over the parameters, we can also generate \(n\) new samples of the attempt distribution \(X_{N+1},\dots, X_{N+n}\) and take the cumulative maximum to generate a distribution of records in future timesteps.
To help us and others with this process, we have developed and released
fmax, a Python library built on top of PyMC3
\citep{Salvatier2016ProbabilisticPI} to model and forecast future series. This expands on our previous article
\citep{lindbloom2021}.
Empirical results
With our theoretical framework established, we now study its applications with real-world data.
We will study the application of the framework to extrapolate the world record times for six athletic events (mile run, 1000 meters, 5000 meters, 10000 meters, 20000 meters, and marathon).
This is the same data discussed in \citep{tryfos_forecasting_1985}. We extend the dataset they used with data up until the present day, and also include data from the corresponding women's events. We gathered the data from the World Athletics sports federation. A snapshot of the data is available in Figure 1.