In this chapter, we have introduced Bayesian networks, describing their structure and relations. We have seen how it's possible to build a network to model a probabilistic scenario where some elements can influence the probability of others. We have also described how to obtain the full joint probability using the most common sampling methods, which allow reducing the computational complexity through an approximation.
The most common sampling methods belong to the family of MCMC algorithms, which model the transition probability from a sample to another one as a first-order Markov chain. In particular, the Gibbs sampler is based on the assumption that it's easier to sample from conditional distribution than work directly with the full joint probability. The method is very easy to implement, but it has some performance drawbacks that can be avoided by adopting more complex strategies. The Metropolis-Hastings sampler, instead, works with a candidate-generating distribution and a criterion...