Until now, we have discussed two different models for representing graphical models. Each of these can represent independence constraints that the other cannot. In this section, we will look at the relationship between these two models.
Both Bayesian models and Markov models parameterize a probability distribution using a graphical model. Further, these structures also encode the independencies among the random variable. So, when converting a Bayesian model into a Markov one, we have to look from the following two perspectives:
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From the perspective of parameterization, that is, representing the probability distribution of the Bayesian model
using a fully parameterized Markov model
From the perspective of independencies, that is, representing the independence constraints encoded by the Bayesian model using the Markov model
From the first perspective, conversion of the Bayesian model into the Markov model is fairly simple...