Modeling uncertainty in trends

You may have noticed in different component plots throughout this book that the trend shows uncertainty bounds, while the seasonality curves do not. By default, Prophet only estimates uncertainty in the trend, plus uncertainty due to random noise in the data. The noise is modeled as a normal distribution around the trend and trend uncertainty is modeled with maximum a posteriori (MAP) estimation.

MAP estimation is an optimization problem that is solved with Monte Carlo simulations. Named after the famous casino in Monaco, the Monte Carlo method uses repeated random sampling to estimate an unknown value, usually used when closed-form equations are either non-existent or computationally difficult.

In Chapter 5, Holidays, we talked about prior distributions, or the probability distribution of an estimate prior to receiving additional information about it. In MAP estimation, you are estimating the central tendency of a posterior distribution, or a probability...