# Bayesian Notation

Below is a fairly standard notation for dealing with Bayesian formulae and Bayesian networks, which you may need to look at to decipher some of our posts.

• $A \subset B$ : $A$ is a proper subset of $B$
• $A \subseteq B$ : $A$ is a proper subset of $B$ or equal to $B$
• $A \backslash B$ : set $A$ with all elements of $B$ removed
• $\emptyset$ : the empty set
• $A \cup B$ : the union of $A$ and $B$
• $A \cap B$ : the intersection of $A$ and $B$
• $x \in A$ : $x$ is a member of set $A$
• $|A|$ : the number of objects in set $A$
• $x \in [y,z]$ : $y \le x \le z$
• $\{ A_i \}$ : a set of sets indexed by $i$
• $\bigcup_i A_i$ : the union of all $A_i \in \{ A_i \}$
• $A \vee B$ : $A$ or $B$
• $A \wedge B$ : $A$ and $B$
• $A \equiv B$ : $A$ is equivalent to $B$
• $\neg A$ : not $A$
• $\forall x$ : for all $x$
• N! : $N$ factorial
• $X_i$ : A variable
• $X_i=x_i$ : The variable $X_i$ takes value $x_i$
• $\overline{X}$ : $\sum_{i=1}^{n} \frac{x_i}{n}$
• $P(X)$ : (prior, marginal) probability of $X$
• $p(X)$ : (prior, marginal) probability of $X$
• $P(X=x)$ : probability that $X$ takes value $x$
• $P(X|E)$ : probability of $X$ given evidence $E$
• $X \independent Y | Z$ : $X$ is independent of $Y$ given $Z$
• $X \perp Y | Z$ : $X$ is d-separated from $Y$ by $Z$
• $Bel(X)$ : posterior distribution over $X$
• $\pi(X)$ : set of parent nodes of $X$
• $A - B$ : an undirected link
• $A \rightarrow B$ : a directed link
• $i \leftarrow i+1$ : assignment
• $E[X]$ : the expected value of $X$
• $E[f(X)]$ : the expected value of $f(X)$
• $EU(A|E)$ : the expected utility of action $A$, given evidence $E$
• $U(O|A)$ : the utility of outcome $O$, given action $A$
• $\int_a^b f(x) dx$ : the integral of $f(x)$ from $a$ to $b$
• $\sum_i f(x_i)$ : the sum of $f(x_i)$ indexed by $i$
• $\prod_i f(x_i)$ : the product of $f(x_i)$ indexed by $i$
• $C^n_j = \left( \begin{array}{c} n \\ j \end{array} \right)$ : The number of ways of taking a subset of j objects from a set of size n