Moralized graph factorization from Bayesian network - Cross Validated most recent 30 from stats.stackexchange.com 2019-07-20T11:46:12Z https://stats.stackexchange.com/feeds/question/298377 http://www.creativecommons.org/licenses/by-sa/3.0/rdf https://stats.stackexchange.com/q/298377 2 Moralized graph factorization from Bayesian network Yi Yang https://stats.stackexchange.com/users/156208 2017-08-17T09:36:18Z 2018-03-19T08:35:11Z <p>Given the Bayesian network on the left hand side in the following figure, it shows that the random variable $B$ is dependent on $A$ and $C$, and the Bayesian network $G$ can be factorized as: $P(G) = p(A) \times p(C) \times p(B|A,C)$. The Bayesian network $G$ can be moralized to a Markov network $M$ for junction tree algorithm and it is shown on the right hand side of the figure. In $M$, all the existing edges in $G$ are changed to undirected ones and it adds a new undirected edge between the parents of $B$. Is it correct to use the same probability $P(G) = p(A) \times p(C) \times p(B|A,C)$ to factorize $M$ (assuming the factors over $A$, $B$, and $C$ are probabilities)? I understand that a new edge is added between $A$ and $C$, but I think the edge is added to capture the dependencies in the Markov network, is it compulsory to introduce an edge factor/potential in the factorization of $M$? <a href="https://i.stack.imgur.com/ARXR8.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/ARXR8.png" alt="enter image description here"></a></p>