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


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