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Probabilities of causation: Bounds and identification
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“It can also be shown (Tian and Pearl, 2000) that the expression in (54) provides a lower bound for PN in the general, nonmonotonic case.”
From Causal inference in statistics: An overview (2009) · cites this paper as Tian and Pearl, 2000
In the citing paper
“In particular, the tight upper and lower bounds on PN are given by:”
From Causal inference in statistics: An overview (2009) · cites this paper as Tian and Pearl, 2000
In the citing paper
“the algebraic machinery offered by the counterfactual notation, Y x (u), once a problem is properly formalized, can be extremely powerful in refining assumptions (Angrist et al., 1996, Heckman andVytlacil, 2005), deriving consistent estimands (Robins, 1986), bounding probabilities of necessary and sufficient causation (Tian and Pearl, 2000), and combining data from experimental and nonexperimental”
From An Introduction to Causal Inference (2010) · cites this paper as Tian and Pearl, 2000
In the citing paper
“In particular, the tight upper and lower bounds on PN are given by: max 0, P(y)-P(y|do(x )) P(x,y) ≤PN ≤min 1, P(y |do(x ))-P(x ,y ) P(x,y)”
From An Introduction to Causal Inference (2010) · cites this paper as Tian and Pearl, 2000
In the citing paper
“It can also be shown (Tian and Pearl, 2000) that the expression in (61) provides a lower bound for PN in the general, nonmonotonic case.”
From An Introduction to Causal Inference (2010) · cites this paper as Tian and Pearl, 2000
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Cited by
Sorted by citations
Causal inference in statistics: An overview
Pearl, J. (2009) · Statistics Surveys · doi:10.1214/09-ss057 · Cited by 2,336
“…powerful in refining assumptions (Angrist et al., 1996; Heckman and Vytlacil, 2005), deriving consistent estimands (Robins, 1986), bounding probabilities of necessary and sufficient causation (Tian and Pearl, 2000), and combining data from experimental and nonexperimental studies (Pearl, 2000a).”
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Metadata
- Authors
- Tian, J., & Pearl, J.
- Affiliations
- University of California, Los Angeles (US)
- ORCID
- Tian, Jin
- Venue
- Annals of Mathematics and Artificial Intelligence
- Published
- 2000-10
- Volume
- 28
- Issue
- 1-4
- Pages
- 287-313
- ISSN
- 1012-2443 (ISSN-L)
- 1573-7470
- OpenAlex
- W1498383682
- Cited by
- 179
- References
- 50
- Citations by year
- 2026: 12 · 2025: 18 · 2024: 18 · 2023: 18 · 2022: 18 · 2021: 15 · 2020: 6 · 2019: 10 · 2018: 4 · 2017: 4 · 2016: 8 · 2015: 3 · 2014: 8 · 2013: 7 · 2012: 3
- FWCI
- 1.66
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- Annals of Mathematics and Artificial Intelligence (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- eScholarship (California Digital Library) (submittedVersion)
- arXiv (Cornell University)
- Department of Statistics, UCLA
- Funders
- National Science Foundation
- Office of Naval Research
- Air Force Office of Scientific Research
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
- Physical Sciences › Computer Science › Artificial Intelligence › Bayesian Modeling and Causal Inference
- Social Sciences › Arts and Humanities › History and Philosophy of Science › Philosophy of Biology and Scientific Explanation
- Keywords
- probability of causation, sharp bounds, causal inference, exogeneity, monotonicity, attribution, structural causal models
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