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What Is a Causal Graph?

Philip Dawid

TL;DR

This article surveys the variety of ways in which a directed acyclic graph (DAG) can be used to represent a problem of probabilistic causality and suggests that the cleanest such representation is that embodied in an augmented DAG, which contains nodes for non-stochastic intervention indicators in addition to the usual nodes for domain variables.

Abstract

This article surveys the variety of ways in which a directed acyclic graph (DAG) can be used to represent a problem of probabilistic causality. For each of these we describe the relevant formal or informal semantics governing that representation. It is suggested that the cleanest such representation is that embodied in an augmented DAG, which contains nodes for non-stochastic intervention indicators in addition to the usual nodes for domain variables.

What Is a Causal Graph?

TL;DR

This article surveys the variety of ways in which a directed acyclic graph (DAG) can be used to represent a problem of probabilistic causality and suggests that the cleanest such representation is that embodied in an augmented DAG, which contains nodes for non-stochastic intervention indicators in addition to the usual nodes for domain variables.

Abstract

This article surveys the variety of ways in which a directed acyclic graph (DAG) can be used to represent a problem of probabilistic causality. For each of these we describe the relevant formal or informal semantics governing that representation. It is suggested that the cleanest such representation is that embodied in an augmented DAG, which contains nodes for non-stochastic intervention indicators in addition to the usual nodes for domain variables.
Paper Structure (17 sections, 8 equations, 9 figures)

This paper contains 17 sections, 8 equations, 9 figures.

Table of Contents

  1. Introduction
  2. Probabilistic DAG
  3. Instrumental variable
  4. Markov equivalence
  5. Bayesian network
  6. Structural probabilistic model
  7. Reification?
  8. Informal causal semantics
  9. Probabilistic Causality
  10. A problem
  11. Interventional causality and extended conditional independence
  12. Augmented DAG
  13. Pearlian DAG
  14. Structural Causal Model
  15. Causes of Effects
  16. ...and 2 more sections

Figures (9)

  • Figure 1: Directed acyclic graph ${\cal D}$
  • Figure 4: Instrumental variable
  • Figure 5: SPM representation of instrumental variable model
  • Figure 6: Instrumental variable: Augmented DAG
  • Figure 7: Instrumental variable: Augmented DAG with error variables
  • ...and 4 more figures

Theorems & Definitions (3)

  • Example 1
  • Example 2
  • Example 3