Mathematics / advanced
Mathematical causal inference
Separate causal questions from association using interventions, identification, experimental design, and sensitivity analysis.
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Module 01 advanced
Mathematical causal inference
Separate causal questions from association using interventions, identification, experimental design, and sensitivity analysis.
- 01
Potential outcomes and causal estimands
Define the intervention, population, and contrast before asking whether observed data identify an effect.
30 min - 02
Randomization and finite-population inference
Hold potential outcomes fixed and derive uncertainty from the known assignment mechanism.
30 min - 03
Causal graphs and d-separation
Read conditional-independence implications while tracking collider selection and intervention semantics.
30 min - 04
Backdoor identification and adjustment
Identify intervention means by averaging comparable conditional outcomes over one target population.
30 min - 05
Propensity scores and overlap
Use a balancing score without confusing good treatment prediction with credible causal comparison.
30 min - 06
Inverse probability weighting
Reconstruct intervention means with inverse assignment probabilities and distinguish exact identities from fitted estimators.
30 min - 07
Doubly robust estimation and cross-fitting
Combine outcome regression and assignment weighting while stating what robustness and rate conditions actually guarantee.
30 min - 08
Instrumental variables and local effects
Identify the effect among compliers only under explicit randomization, exclusion, monotonicity, and relevance assumptions.
30 min - 09
Difference in differences and parallel trends
Identify a post-treatment effect from changes only when untreated counterfactual trends are comparable.
30 min - 10
Sensitivity analysis and partial identification
Report what observed data determine under bounded outcomes and show how explicit extra assumptions narrow the answer.
30 min