Causal Inference: Foundations and the Fundamental Problem

Introduction

What this guide covers

A rigorous and comprehensive breakdown of the mathematical and statistical frameworks of Rubin (Potential Results) and Pearl (Structural Causal Models). We address identification, estimation and theoretical application.

Overview

Topics covered

• Introduction
• Causal Inference vs. Statistical Association
• The Potential Outcomes Model (Roy-Rubin Causal Model)
• The Fundamental Problem of Causal Inference
• Causal Parameters of Interest
• 4.1 Average Causal Effect (Average Treatment Effect - ATE)

Related concepts

Main connections

• Causal inference & potential outcomes
• Mean & expected value
• Confounding & selection bias
• Directed acyclic graphs (DAGs)
• Conditional probability & independence
• Residual analysis & diagnostics

Compatible notation

Mathematical sample in LaTeX

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