Inference & Intelligence Lab
No Overlap, No Answer: The Positivity Assumption A causal effect can only be estimated where a comparison is actually possible. Imagine evaluating a loyalty program where every enterprise customer is already enrolled—leaving you with no unenrolled counterparts to compare against. This is a violation of Positivity. While exchangeability requires that groups are comparable, positivity requires that the comparison actually exists. In this episode, we discuss: * Structural vs. Random Violations: Why business-logic "zeros" cannot be fixed with more data. * The Propensity Score Plot: How to visually verify if your treated and untreated groups cover the same territory. * The Trimming Trade-off: Why discarding extreme observations to force overlap changes the population your results apply to. The Positivity Audit (Key Takeaways): * Verify Overlap: Use propensity scores to ensure groups share common support. * Identify Structural Zeros: Recognize when policy or logic makes receiving a treatment impossible for certain subgroups. * Watch External Validity: Always report dropped observations to clarify the narrowed scope of your findings. 🚀 Support the Craft If you found this episode valuable, please consider: * Following the Podcast: Tap the "+" or "Follow" button on Spotify to never miss a deep dive into causal inference and GenAI. * Sharing the Episode: Know a Data Scientist or Product Leader struggling with "No Overlap"? Send this their way. * Joining the Conversation: Share your thoughts on today’s topic on LinkedIn—let’s raise the standard of the DS craft together. 📖 Read the companion deep dive (with illustrations and takeaways): https://open.substack.com/pub/inferenceintel/p/no-overlap-no-answer-the-positivity?r=7bs4uy&utm_campaign=post&utm_medium=web&showWelcomeOnShare=true [https://open.substack.com/pub/inferenceintel/p/no-overlap-no-answer-the-positivity?r=7bs4uy&utm_campaign=post&utm_medium=web&showWelcomeOnShare=true] 🤝 Connect with me on LinkedIn: https://www.linkedin.com/in/linjia/ [https://www.linkedin.com/in/linjia/] About the Host Lin Jia is a Senior Data Scientist and Craft Lead at Booking.com with over 9 years of experience. Operating at the intersection of statistical inference, causal machine learning, and GenAI evaluation, she specializes in building the frameworks that enable trustworthy, decision-ready insights under real-world constraints. A recognized expert in the field, Lin has authored research on sensitivity analysis presented at KDD 2024 and leads the development of organization-wide standards for experimentation and observational causal inference.
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