Graphical Models: D-Separation

$$\newcommand{\bigci}{\perp\mkern-10mu\perp}$$ This article is a brief overview of conditional independence in graphical models, and the related d-separation. Let us begin with a definition. For three random variables $X$, $Y$ and $Z$, we say $X$ is conditionally independent of $Y$ given $Z$ iff $$p(X, Y | Z) = p(X | Z) p(Y | Z).$$ We can use a shorthand notation $$X \bigci Y | Z$$