In this chapter, we're going to introduce the basic concepts of Bayesian models, which allow working with several scenarios where it's necessary to consider uncertainty as a structural part of the system. The discussion will focus on static (time-invariant) and dynamic methods that can be employed where necessary to model time sequences.

In particular, the chapter covers the following topics:

• Bayes' theorem and its applications
• Bayesian networks
• Sampling from a Bayesian network using direct methods and Markov chain Monte Carlo (MCMC) ones (Gibbs and Metropolis-Hastings samplers)
• Modeling a Bayesian network with PyMC3
• Hidden Markov Models (HMMs)
• Examples with hmmlearn