First encounter with the term, I'd like some help understanding it. I know there are several approaches, but this one is important to me because I'm trying to understand an article that uses it throughout its text.(adsbygoogle = window.adsbygoogle || []).push({});

Definition:Let G=(V,E) be a finite (connected) graph and let S be a finite set. A random element X taking values in [tex]S^V[/tex] is said to be a Markov random field if for each [tex]W\subset V[/tex], the conditional distribution of X(W) given X(V\W) depends on X(V\W) only through its values on [tex]\partial W[/tex].

It goes on to write this mathematically, which I will write down here if you ask me to. My problem is with the phrase "A random element X taking values in...".

I just want to know from where to where X is. Obviously X takes values in [tex]S^V[/tex], so this is the range of X. What is its domain?

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# Markov Random Field - Understanding the Definition

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