Index: Pearl Bareinboim 2014 - External Validity and Transportability

Pearl Bareinboim 2014 - External Validity and Transportability

Routing Summary

This folder fully captures Pearl and Bareinboim (2014), External Validity: From Do-Calculus to Transportability Across Populations (Statistical Science 29(4): 579-595): selection diagrams, the formal definition of transportability, Theorem 1 (do-calculus criterion), Theorems 2-3 with S-admissibility, Corollaries 1-2, Examples 1-10, the transport formulas (3.1)-(3.4), (5.9), (5.10) and their appendix derivations. 8 notes plus this index, with a marketing reading and runnable checks.

• Need the paper on one page or the section-to-note map? → Pearl Bareinboim 2014 - External Validity and Transportability - Overview
• Need SEM, $do(x)$, identifiability, d-separation or the three do-calculus rules? → Pearl 2014 - Threats vs Licenses and SCM Preliminaries
• Need the LA-to-NYC examples and Eqs. 3.1-3.4? → Pearl 2014 - Motivating Examples and Transport Formulas
• Need Definition 4 (selection diagram), Definitions 5-7, Theorem 1? → Pearl 2014 - Selection Diagrams and Definition of Transportability
• Need S-admissibility, Theorems 2-3, Corollaries 1-2, Examples 7-10? → Pearl 2014 - S-Admissibility and the Graphical Criterion
• Need the step-by-step derivation of Eqs. 5.9 and 5.10? → Pearl 2014 - Appendix Derivations of Transport Formulas
• Need limits, meta-transportability, and the comparison with meta-analysis? → Pearl 2014 - Conclusions, Extensions and Limits
• Need to transport a geo or lift result to a new market (worked numbers)? → Pearl 2014 - Marketing Application Transporting Geo and Lift Results

Concept Map

Concept	Note	Type	Depends On	Key Result
Structural equation model	Pearl 2014 - Threats vs Licenses and SCM Preliminaries	definition	Directed Acyclic Graphs	$v_i=f_i(p{a}_i,u)$ with $P(u)$
Identifiability	Pearl 2014 - Threats vs Licenses and SCM Preliminaries	definition	SEM	$P(M_1)=P(M_2)\Rightarrow Q(M_1)=Q(M_2)$
d-separation	Pearl 2014 - Threats vs Licenses and SCM Preliminaries	definition	DAG	blocking of paths
Do-calculus Rules 1-3	Pearl 2014 - Threats vs Licenses and SCM Preliminaries	theorem	d-separation	complete for $P(y\mid do(x),z)$
Transport formula (3.1)	Pearl 2014 - Motivating Examples and Transport Formulas	example	Rules	${\sum }_{z}P(y\mid do(x),z)P^{\ast }(z)$
Transport formula (3.4), surrogate	Pearl 2014 - Motivating Examples and Transport Formulas	example	(3.1)	${\sum }_{z}P(y\mid do(x),z)P^{\ast }(z\mid x)$
Selection diagram (Def. 4)	Pearl 2014 - Selection Diagrams and Definition of Transportability	definition	SEM	$S_i\to V_i$ where mechanisms may differ
Transportability (Def. 5)	Pearl 2014 - Selection Diagrams and Definition of Transportability	definition	Def. 4, identifiability	$R({\Pi }^{\ast })$ computable from $P,P^{\ast },I$
Trivial / direct transportability (Defs. 6-7)	Pearl 2014 - Selection Diagrams and Definition of Transportability	definition	Def. 5	identifiable in target / $R({\Pi }^{\ast })=R(\Pi )$
Theorem 1	Pearl 2014 - Selection Diagrams and Definition of Transportability	theorem	Rules	$S$ only as conditioning in do-free terms
S-admissibility (Def. 8), Theorem 2, Corollaries 1-2	Pearl 2014 - S-Admissibility and the Graphical Criterion	theorem	Thm 1	$(Y\perp S\mid Z,X{)}_{D_{\overline{X}}}$ licenses reweighting
Theorem 3 (three conditions)	Pearl 2014 - S-Admissibility and the Graphical Criterion	theorem	Thm 2	recursive, sufficient, not complete
Derivations of (5.9), (5.10)	Pearl 2014 - Appendix Derivations of Transport Formulas	example	Thm 3	what to measure where
Meta-transportability, caveats	Pearl 2014 - Conclusions, Extensions and Limits	concept	all	worst-case nonparametric licenses

Notes

• Pearl Bareinboim 2014 - External Validity and Transportability - Overview — CONTAINS: research question, contributions, key result, full Source Map (every section, Definition, Theorem, Figure to note).
• Pearl 2014 - Threats vs Licenses and SCM Preliminaries — CONTAINS: Sec. 1 motivation; inference-engine inputs/outputs; Definitions 1-3; Rules 1-3; Manski footnote; Python d-separation test.
• Pearl 2014 - Motivating Examples and Transport Formulas — CONTAINS: Examples 1-3; Eqs. 3.1-3.4; proxy analysis; surrogate endpoint; numeric check and Python.
• Pearl 2014 - Selection Diagrams and Definition of Transportability — CONTAINS: Definition 4-7; Theorem 1 with proof; Examples 4-6; Manski remark; hierarchy of transport notions.
• Pearl 2014 - S-Admissibility and the Graphical Criterion — CONTAINS: Theorems 2-3 with proofs (Eqs. 5.1-5.7); Definition 8; Corollaries 1-2; Examples 7-10; limits; Python S-admissibility check.
• Pearl 2014 - Appendix Derivations of Transport Formulas — CONTAINS: line-by-line derivations of (5.9) and (5.10) with justifications; Monte Carlo verification.
• Pearl 2014 - Conclusions, Extensions and Limits — CONTAINS: worst-case character; statistical transportability; relation to meta-analysis; limited experiments and meta-transportability; caveats; checklist.
• Pearl 2014 - Marketing Application Transporting Geo and Lift Results — CONTAINS: mapping table; market-mix worked example (1.40 vs 0.96); mediator example (3.2 vs 2.3); checks before reporting.

Sources

• Pearl 2014 - External Validity From Do-Calculus to Transportability — Pearl J and Bareinboim E (2014), Statistical Science 29(4): 579-595 (arXiv 1503.01603), the sole source. The marketing note is interpretation.

See Also

• Bareinboim Pearl 2016 - Causal Inference and Data Fusion - Overview — PNAS survey placing this paper in a unified taxonomy.
• Degtiar Rose 2023 - Generalizability and Transportability Review - Overview — potential-outcomes review with estimators.
• Directed Acyclic Graphs, DAGs and Causal Identification, Do-Calculus in Summary Causal DAGs, Geo-Experiment Methodology - Overview.