Modeling uncertainty in seasonality

MAP estimation is very fast, which is why it is Prophet's default mode, but it will not work with seasonalities, so a different method is needed. To model seasonality uncertainty, Prophet needs to use an MCMC method. A Markov chain is a model that describes a sequence of events, with the probability of each event depending upon the state in the previous event. Prophet models seasonal uncertainty with this chained sequence and uses the Monte Carlo method, which was described at the beginning of the previous section, to repeat the sequence many times.

The downside is that MCMC sampling is slow; on a macOS or Linux machine, you should expect fitting times of several minutes instead of several seconds. On a Windows machine, unfortunately, the PyStan API, which interfaces with Prophet's model in the Stan language, has upstream issues, meaning MCMC sampling is extremely slow. Depending upon the number of data points, fitting a model on a...