Introduction to High-Dimensional Statistics, 2nd Edition

Chapter 9

Graphical Models

DOI: 10.1201/9781003158745-9

Graphical modeling is a convenient theory for encoding the conditional dependencies between p random variables X₁,...,X_p by a graph g. Graphical models are used in many different frameworks (image analysis, physics, economics, etc.), and they have been proposed for investigating biological regulation networks, brain connections, etc.

The concept of conditional dependence is more suited than the concept of dependence in order to catch “direct links” between variables, as explained in Figure 9.1 below.

Figure 9.1 Difference between dependence and conditional dependence.

When there ...