Common Cause Graphs in Python

Introduction

Bayesian networks are probabilistic graphical models that facilitate the representation of complex, uncertain relationships among variables compactly and intuitively. Understanding the fundamental graph patterns that emerge in Bayesian networks is crucial for accurate modeling and interpretation of the underlying relationships within data.

In this lesson, we will delve into the theory behind common cause patterns, as well as their practical implications in real-world scenarios.

A common cause graph is a type of causal graph in which a single variable, the common cause, influences two or more other variables. In other words, the common cause is a shared or confounding variable that affects multiple variables in the graph. This shared variable can create an association between the influenced variables, even if there is no direct causal relationship between them.

In a common cause graph, the structure typically involves an arrow pointing from the common cause variable to each of the affected variables. When analyzing such a graph, it is crucial to consider the potential confounding effects of the common cause variable on the relationships between the other variables. Accounting for these confounding effects can help improve the accuracy of causal inferences drawn from the graph.

For example, suppose we have a graph with variables A, B, and C, where A is the common cause affecting both B and C. In this scenario, the common cause graph would be structured as follows: