Forecasting future records

Given the likelihood, we can use a Bayesian posterior sampling method like the No-U-Turn Sampler (NUTS)  \citep{andrew2014} to sample the posterior distribution of the model parameters \(\theta\). We draw samples from the conditional distribution of the records given the parameters (the posterior predictive distribution), and compare simulated data generated from these samples to the actual data for a sanity check of our model.