A “simple” explanation of the concept of D-separation in a Bayesian Network?

Hello everyone.

I'm looking for a "simple" explanation of the concept of D-separation in a Bayesian Network.

As far as I know the definition is "two variables (nodes) in the network are D-Separated if the information is "blocked" between the two nodes by some evidence about the nodes in the middle.

But I can't pratically understand the concept.

I don't have enough rep to use images so these are the links to the images (just 25kbyte each one) from my dropbox folder.

What I would like to understand if in these three patterns:

1. When there is NO evidence What (and why) nodes are D-separated from the each others
2. In what cases EVIDENCE about a specific node cause two nodes to be separated

Thank you in advance for any help.

Regards

• The dropbox contents have expired. – Todd Trimble May 9 '16 at 19:59

Try this tutorial http://www.andrew.cmu.edu/user/scheines/tutor/d-sep.html

• thank you. I'll take a look later and of cource if it solves my doubts I'll accept your answer – Manuel Jun 20 '12 at 14:20

I found the following tutorial better. http://bayes.cs.ucla.edu/BOOK-2K/d-sep.html

• It's difficult to say whether this actually answers the question since the dropbox contents have expired. – Todd Trimble May 9 '16 at 19:58
• it's a question back to 4 years ago. I don't even know where the original images are now :) – Manuel May 9 '16 at 22:09
• :p well, I was looking for a good d-separation tutorial for myself, and this question was one of the top search. Just wanted to make it convenient for someone else in my shoes. I read through multiple tutorials (including the answer you accepted), and the link I left was what really helped me. – Jackson Wang May 10 '16 at 17:57

I can try to give you a simple way to think about the rules. Two nodes in a directed graph are dependent if, one is the ancestor of the other OR they both have a common ancestor.

Now observing a variable, changes the graph. All the ancestors of observed node, become descendants (descendants remain descendants), ie. information flows backwards. Now follow the same rules to find independence.

a -> b -> c -> d -> e -> f (Graph before observation) a <- b <- c <- d -> e -> f (Graph upon observing d)

Apply same rules on the graph to figure out independence.