How are MRFs better than Bayesian networks?
They can model range of problems where there are no natural dependencies between random variables
Undirected graphs can better express certain dependencies that Bayesian network cannot easily describe
What are the drawbacks of MRFs?
Computing normalisation constant Z requires summing over all the assignments, which could grow exponentially. This will be an NP-hard problem and so many undirected models are actually intractable and approximation techniques are required
Undirected models may be difficult to interpret as they don’t necessarily model causality
It is much easier to generate data from a Bayesian network
What is moralisation?
Moralisation is the process of converting a Bayesian network to an MRF. Bayesian networks are a special case of MRFs with a specific type of clique factor and a normalisation constant of one. See below the figure of moralisation:
Overall, MRFs have more flexibility and power than Bayesian network but they might be intractable and so are more difficult to deal with. A rule of thumb is to use Bayesian network whenever possible and only switch to MRFs if there’s no natural way to model problem with a directed graph.