Skip to main content

Also called Probabilistic Graphical Model, used for statistical models expressed via graphs, causal or not. (Nb, "graph" as in graph theory, *not* as in figure or plot).

A graphical model is a probabilistic model which expresses the relationship among random variables using a graph (in the sense of graph theory). The nodes of the graph represent the random variables, while the edges of the graph encode the relationships between them.

Two broad categories of probabilistic graphical models are:

  1. Directed Acyclic Graphs (DAG) also known as Bayesian Networks.
    • DAGs are used to express the factorization of the joint probability distribution.
    • The direction of an edge indicates the conditional independence of random variables in a graph.
  2. Undirected Graphical Model (UGM) also known as Markov Random Fields.
    • UGMs, by definition, allow for cycles, therefore cannot express the induced dependence structure that a DAG can.
    • However, since the dependence structure of certain phenomena is difficult to establish, people use UGMs to express certain types of relationships that are more flexible. Notably, UGMs are used in spatial statistics and image analysis.