Understanding statistical paradoxes using causal graphical models

At the root of scientific explanations, causal inference plays a significant role in many fields such as social studies, economics, and artificial intelligence. However, making causal conclusions in many cases can be very challenging as in general causation is not the same as association and making decisions solely based on statistical methods can be counterintuitive and misleading. This project focuses a few famous statistical paradoxes and discusses how causal inference techniques can be used to explain those. Among the many causal inference frameworks, the project focuses on the causal graphical model which is widely used in econometrics and artificial intelligence. Both the backdoor and frontdoor adjustment formulas are discussed as how they can be applied to resolve the paradoxes through simulated observational data examples.

Bayesian Network Concepts

• Factorization of a Bayesian Network
• Local Markov Property
• Fundamental structures in a Bayesian network
• Markov equivalence
• Conditional independence and d-separation

Causal Bayesian networks

• Causal assumption and invariance assumption
• Do-calculus and the do-operator
• Confounding bias
• Backdoor adjustment formula
• Conditional independence and d-separation

Understanding Simpson’s paradox, birth-weight paradox, and Berkson’s paradox

• Making the right decision in Simpson’s paradox
• Understanding Simpson’s paradox in Example 3 using causal graphical models
• Explain the paradox using expert knowledge or educated guess

Frontdoor adjustment and unobserved variables

• Unobserved variables and confounding effects
• Frontdoor criterion and frontdoor adjustment formula

Last updated on Jan 1, 2019