Bayesian Networks and Hidden Markov Models

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