The DOI matches its Crossref record; 47 of the 51 references it cites were found in a registry or an index, and 4 are not checked yet.
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
Citations
Cites
The central role of the propensity score in observational studies for causal effects
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Causality: Models, Reasoning, and Inference
Pearl, J. (2009) · doi:10.1017/cbo9780511803161 · Cited by 11,653
Self-citationCAUSALITY: MODELS, REASONING AND INFERENCE
Hitchcock, C., & Pearl, J. (2001) · The Philosophical Review · doi:10.2307/3182612 · Cited by 4,827
Self-citationCausation, Prediction, and Search
Spirtes, P., Glymour, C., & Scheines, R. (1993) · Lecture Notes in Statistics · doi:10.1007/978-1-4612-2748-9 · Cited by 4,617
The Central Role of the Propensity Score in Observational Studies for Causal Effects
Rosenbaum, P. R., & Rubin, D. B. (1983) · Biometrika · doi:10.2307/2335942 · Cited by 3,495
Robins, J. (1986) · Mathematical Modelling · doi:10.1016/0270-0255(86)90088-6 · Cited by 2,451
Case-Control Studies: Design, Conduct, Analysis.
Youkeles, L., & Schlesselman, J. J. (1983) · Journal of the American Statistical Association · doi:10.2307/2288156 · Cited by 2,358
Causal diagrams for empirical research
PEARL, J. (1995) · Biometrika · doi:10.1093/biomet/82.4.669 · Cited by 2,355
Self-citationHennekens, C. H., Buring, J. E., & Mayrent, S. L. (1987) · Medical Entomology and Zoology · Cited by 2,319
Engle, R. F., Hendry, D. F., & Richard, J.-F. (1983) · Econometrica · doi:10.2307/1911990 · Cited by 1,346
Research works printed but not linked: 8
- A. Balke, Probabilistic counterfactuals: Semantics, computation, and applications, Ph.D. thesis, Computer Science Department, University of California, Los Angeles, CA (November 1995).
- P. Cole, Causality in epidemiology, health policy, and law, Journal of Marketing Research 27 (1997) 10279-10285.
- P.J. Dhrymes, Econometrics (Springer, New York, 1970).
- N. Hall, Two concepts of causation (1998) in press.
- D. Lewis, Philosophical Papers (Oxford University Press, New York, 1986).
- J. Marschak, Statistical inference in economics, in: Statistical Inference in Dynamic Economic Models, ed. T. Koopmans (Wiley, New York, 1950) pp. 1-50. Cowles Commission for Research in Economics, Monograph 10.
- J.S. Mill, System of Logic, Vol. 1 (John W. Parker, London, 1843).
- D.W. Robertson, The common sense of cause in fact, Texas Law Review 75(7) (1997) 1765-1800.
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).”
BackgroundSelf-citationCausal Inference in Statistics
Pearl, J., Glymour, M., & Jewell, N. P. (2016) · Cited by 1,436
Self-citationCauses and Explanations: A Structural-Model Approach. Part I: Causes
Halpern, J. Y., & Pearl, J. (2005) · The British Journal for the Philosophy of Science · doi:10.1093/bjps/axi147 · Cited by 829
Self-citationAn Introduction to Causal Inference
Pearl, J. (2010) · The International Journal of Biostatistics · doi:10.2202/1557-4679.1203 · Cited by 755
Self-citationDatta, A., Sen, S., & Zick, Y. (2016) · 2016 IEEE Symposium on Security and Privacy (SP) · doi:10.1109/sp.2016.42 · Cited by 728
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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