Index: Bareinboim Pearl 2016 - Causal Inference and Data Fusion

Bareinboim Pearl 2016 - Causal Inference and Data Fusion

Routing Summary

This folder fully captures Bareinboim and Pearl (2016), Causal inference and the data-fusion problem (PNAS 113(27): 7345-7352): the four generalization tasks, the two principles of causal inference, backdoor/front-door/z-identification, the selection-backdoor criterion for sampling bias, clinical-trial generalization with post-treatment variables, transport formulas (Eqs. 15-17) and multi-source data fusion. 4 notes plus this index.

• Need the paper on one page or the section-to-note map? → Bareinboim Pearl 2016 - Causal Inference and Data Fusion - Overview
• Need the SCM, counterfactual semantics, d-separation, do-calculus, backdoor, front-door or z-identification? → Bareinboim 2016 - SCM Principles and Confounding Bias
• Need selection bias, S-backdoor (Definition 4, Theorem 1) or the clinical-trial Eq. 14? → Bareinboim 2016 - Sample Selection Bias and Recoverability
• Need transport formulas 15-17, the transportability criterion or data fusion (Summary Result 3)? → Bareinboim 2016 - Transportability and Data Fusion

Concept Map

Concept	Note	Type	Depends On	Key Result
Four tasks / designs (Fig. 1)	Bareinboim 2016 - SCM Principles and Confounding Bias	concept	-	design = (population, regime, sampling)
Two principles of causal inference	Bareinboim 2016 - SCM Principles and Confounding Bias	theorem	SCM	structural counterfactuals; structural independences
Backdoor criterion and adjustment	Bareinboim 2016 - SCM Principles and Confounding Bias	definition	d-separation	${\sum }_{z}P(y\mid x,z)P(z)$
Front-door adjustment	Bareinboim 2016 - SCM Principles and Confounding Bias	theorem	do-calculus	Eq. 10
z-identification	Bareinboim 2016 - SCM Principles and Confounding Bias	theorem	do-calculus	iff $X$ intercepts $Z\to Y$ paths and Q identifiable in $G_{\overline{Z}}$
Selection backdoor criterion	Bareinboim 2016 - Sample Selection Bias and Recoverability	definition	backdoor	Def. 4
Recovery under S-backdoor	Bareinboim 2016 - Sample Selection Bias and Recoverability	theorem	Def. 4	${\sum }_{z}P(y\mid x,z,S=1)P(z)$
Clinical trial generalization	Bareinboim 2016 - Sample Selection Bias and Recoverability	theorem	S-admissibility	Eq. 14 with $P(z\mid x)$
Transport formulas	Bareinboim 2016 - Transportability and Data Fusion	theorem	selection diagrams	Eqs. 15-17
Transportability iff criterion	Bareinboim 2016 - Transportability and Data Fusion	theorem	do-calculus	rule sequence separating $do$ from $S$
Data fusion	Bareinboim 2016 - Transportability and Data Fusion	concept	transportability	consistent estimator from limited sources (Summary Result 3)

Notes

• Bareinboim Pearl 2016 - Causal Inference and Data Fusion - Overview — CONTAINS: abstract; thesis; contributions; Source Map; key results table.
• Bareinboim 2016 - SCM Principles and Confounding Bias — CONTAINS: Fig. 1 task table; SCM; Eq. 1; two principles; Definitions 1-3; Rules 1-3; Eqs. 8-12; Fig. 3; Summary Result 1; numeric backdoor example.
• Bareinboim 2016 - Sample Selection Bias and Recoverability — CONTAINS: Fig. 4A-F; Definition 4; Eq. 13; Theorem 1; Eq. 14; S-ignorability critique; Summary Result 2; simulation.
• Bareinboim 2016 - Transportability and Data Fusion — CONTAINS: selection diagram; Fig. 5A-D; Eqs. 15-17; transportability criterion; data fusion; Summary Result 3; conclusion; marketing fusion illustration.

Sources

• Bareinboim 2016 - Causal Inference and the Data-Fusion Problem — Bareinboim E and Pearl J (2016), PNAS 113(27): 7345-7352 (UCLA TR R-450 reprint, 8 pp.), the sole source.

See Also

• Pearl Bareinboim 2014 - External Validity and Transportability - Overview — full single-source theory.
• Degtiar Rose 2023 - Generalizability and Transportability Review - Overview — estimators.
• Directed Acyclic Graphs, DAGs and Causal Identification, Do-Calculus in Summary Causal DAGs, Instrumental Variables.