Statistics, Causality, and Graphs

  • J. Pearl
Chapter

Abstract

Some of the main users of statistical methods – economists, social scientists, and epidemiologists – are discovering that their fields rest not on statistical but on causal foundations. The blurring of these foundations over the years follows from the lack of mathematical notation capable of distinguishing causal from equational relationships. By providing formal and natural explication of such relations, graphical methods have the potential to revolutionize how statistics is used in knowledge-rich applications. Statisticians, in response, are beginning to realize that causality is not a metaphysical deadend but a meaningful concept with clear mathematical underpinning. The paper surveys these developments and outlines future challenges.

Keywords

Mathematical Notation Covariate Selection Causal Assumption Causal Foundation Causal Meaning 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.1
    Aldrich, J. (1993): Cowles' exogeneity and core exogeneity. Technical Report Discussion Paper 9308, Department of Economics, University of Southampton, UKGoogle Scholar
  2. 1.2
    Balke, A. and Pearl, J. (1994): Counterfactual probabilities: Computational methods, bounds, and applications. In: R. Lopez de Mantaras and D. Poole (eds.), Uncertainty in Artificial Intelligence 10, 46–54. Morgan Kaufmann, San Mateo, CAGoogle Scholar
  3. 1.3
    Balke, A. and Pearl, J. (1995): Counterfactuals and policy analysis in structural models. In: P. Besnard and S. Hanks (eds.), Uncertainty in Artificial Intelligence 11, 11–18. Morgan Kaufmann, San FranciscoGoogle Scholar
  4. 1.4
    Balke, A. and Pearl, J. (1997): Nonparametric bounds on causal effects from partial compliance data. J. Am. Statistical Assoc. 92(439), 1–6CrossRefGoogle Scholar
  5. 1.5
    Bickel, P. J. Hammel, E. A. and O'Cornell. J. W. (1975): Sex bias in graduate admissions: Data from Berkeley. Science, 187, 398–404CrossRefGoogle Scholar
  6. 1.6
    Bollen, K. A. (1989): Structural Equations with Latent Variables. John Wiley & Sons, New YorkMATHGoogle Scholar
  7. 1.7
    Bullock, H. E., Harlow, L. L. and Mulaik, S. A. (1994): Causation issues in structural equation modeling research. Structural Equation Modeling 1(3), 253–267CrossRefGoogle Scholar
  8. 1.8
    Cartwright, N. (1995): Causal structures in econometrics. In: D. Little (ed.), On the Reliability of Economic Models, 63–74. Kluwer Academic, Boston, MAGoogle Scholar
  9. 1.9
    Cartwright, N. (1995): Probabilities and experiments. J. Econometrics, 67, 47–59MATHCrossRefGoogle Scholar
  10. 1.10
    Chickering, D. M. and Pearl, J. (1996): A clinician's apprentice for analyzing non-compliance. Proceedings of the National Conference on Artificial Intelligence (AAAI-96), 1269–1276. PortlandGoogle Scholar
  11. 1.11
    Cox, D. R. and Wermuth, N. (1996): Multivariate Dependencies-Models, Analysis and Interpretation. Chapman & Hall, LondonGoogle Scholar
  12. 1.12
    Dawid, A. P. (1979): Conditional independence in statistical theory. J. Roy. Statistical Soc. Series A, 41, 1–31MathSciNetMATHGoogle Scholar
  13. 1.13
    de Morgan, A. (1864): On the syllogism. Trans. Cambridge Philosophical Soc. 10, 173–230 (Read 8 Feb 1958)Google Scholar
  14. 1.14
    Dhrymes, P. J. (1970): Econometrics. Springer-Verlag, New YorkGoogle Scholar
  15. 1.15
    Engle, R. F., Hendry, D. F. and Richard, J. F. (1983): Exogeneity. Econometrica, 51, 277–304MathSciNetMATHCrossRefGoogle Scholar
  16. 1.16
    Epstein, R. J. (1987): A History of Econometrics. Elsevier, New YorkMATHGoogle Scholar
  17. 1.17
    Freedman, D. (1987): As others see us: A case study in path analysis (with discussion). J. Educational Statistics, 12, 101–223Google Scholar
  18. 1.18
    Galles, D. and Pearl, J. (1995): Testing identifiability of causal effects. In: P. Besnard and S. Hanks (eds.), Uncertainty in Artificial Intelligence 11, 185–195. Morgan Kaufmann, San FranciscoGoogle Scholar
  19. 1.19
    Galles, D. and Pearl, J. (1997): Axioms of causal relevance. Artif. Intell. 97(1-2), 9–43MathSciNetMATHCrossRefGoogle Scholar
  20. 1.20
    Galles, D. and Pearl, J. (1998): An axiomatic characterization of causal coun terfactuals. Foundations of Science, 3, 151–182MathSciNetCrossRefGoogle Scholar
  21. 1.21
    Galton, F. (1888): Co-relations and their measurement, chiefly from anthro-pological data. Proc. Roy. Soc. Lond. 45, 135–145CrossRefGoogle Scholar
  22. 1.22
    Goldberger, A. S. (1991): A Course of Econometrics. Harvard University Press, Cambridge, MAGoogle Scholar
  23. 1.23
    Greenland, S. and Robins, J. (1986): Identifiability, exchangeability, and epi-demiological confounding. Int. J. Epidemiology, 15, 413–419Google Scholar
  24. 1.24
    Haavelmo, T. (1943): The statistical implications of a system of simultaneous equations. Econometrica, 11, 1–12MathSciNetMATHCrossRefGoogle Scholar
  25. 1.25
    Holland, P. W. and Rubin, D. B. (1983): On Lord's paradox. In: H. Wainer and S. Messick (eds.), Principals of Modern Psychological Measurement, 3–25. Lawrence Earlbaum, Hillsdale, NJGoogle Scholar
  26. 1.26
    Holland, P. W. (1995): Some reflections on Freedman's critiques. Foundations of Science, 1, 50–57Google Scholar
  27. 1.27
    Hoover, K. (1995): Comments on Cartwright and Woodward: Causation, estimation, and statistics. In: D. Little (ed.), On the Reliability of Economic Models, 75–89. Kluwer Academic, Boston, MAGoogle Scholar
  28. 1.28
    Kotz, S. and Johnson, N. L. (eds.) (1982): Encyclopedia of Statistical Sciences. John Wiley & Sons, New YorkMATHGoogle Scholar
  29. 1.29
    Lauritzen, S. L., Dawid, A. P., Larsen, B. N. and Leimer, H. G. (1990): Independence properties of directed Markov fields. Networks, 20, 491–505MathSciNetMATHCrossRefGoogle Scholar
  30. 1.30
    Learner, E. E. (1985): Vector autoregressions for causal inference? Carnegie-Rochester Conference Series on Public Policy, 22, 255–304CrossRefGoogle Scholar
  31. 1.31
    LeRoy, S. F. (1995): Causal orderings. In: K. D. Hoover (ed.), Macroeconometrics: Developments, Tensions, Prospects, 211–228. Kluwer Academic, Boston, MAGoogle Scholar
  32. 1.32
    Muthen, B. (1987): Response to Freedman's “As others see us: A case study in path analysis”. J. Educational Statistics, 12, 168–175Google Scholar
  33. 1.33
    Pearl, J. and Robins, J. M. (1995): Probabilistic evaluation of sequential plans from causal models with hidden variables. In: P. Besnard and S. Hanks (eds.), Uncertainty in Artificial Intelligence 11, 444–453. Morgan Kaufmann, San FranciscoGoogle Scholar
  34. 1.34
    Pearl, J. (1988): Probabilistic Reasoning in Intelligence Systems. Morgan Kaufmann, San Mateo, CAGoogle Scholar
  35. 1.35
    Pearl, J. (1993): Comment: Graphical models, causality and intervention. Statistical Science, 8, 266–269CrossRefGoogle Scholar
  36. 1.36
    Pearl, J. (1995): Causal diagrams for experimental research. Biometrika, 82, 669–710MathSciNetMATHCrossRefGoogle Scholar
  37. 1.37
    Pearl, J. (1995): Causal inference from indirect experiments. Artificial Intelligence in Medicine, 7, 561–582CrossRefGoogle Scholar
  38. 1.38
    Pearson, K. (1911): Grammar of Science. A. & C. Black, LondonMATHGoogle Scholar
  39. 1.39
    Richard, J. F. (1980): Models with several regimes and changes in exogeneity. Rev. Economic Studies, 47, 1–20MathSciNetMATHCrossRefGoogle Scholar
  40. 1.40
    Robins, J. M. (1986): A new approach to causal inference in mortality studies with a sustained exposure period-applications to control of the healthy workers survivor effect. Mathematical Modeling, 7, 1393–1512MathSciNetMATHCrossRefGoogle Scholar
  41. 1.41
    Rosenbaum, P. and Rubin, D. (1983): The central role of propensity score in observational studies for causal effects. Biometrica, 70, 41–55MathSciNetMATHCrossRefGoogle Scholar
  42. 1.42
    Shafer, G. (1996): The Art of Causal Conjecture. MIT Press, Cambridge, MAMATHGoogle Scholar
  43. 1.43
    Sims, C. (1972): Money, income, and causality. Am. Economic Rev. 62, 540–552Google Scholar
  44. 1.44
    Speed, T. P. (1990): Complexity calibration and causality in influence diagrams. In: R. M. Oliver and J. Q. Smith (eds.), Influence Diagrams, Belief Nets and Decision Analysis, 58. John Wiley & Sons, New YorkGoogle Scholar
  45. 1.45
    Spirtes, P., Glymour, C. and Schienes, R. (1993): Causation, Prediction, and Search. Springer-Verlag, New YorkMATHCrossRefGoogle Scholar
  46. 1.46
    Wainer, H. (1991): Adjusting for differential base-rates: Lord's paradox again. Psychological Bulletin, 109, 147-151CrossRefGoogle Scholar
  47. 1.47
    Weinberg, C. R. (1993): Toward a clearer definition of confounding. Am. J. Epidemiology, 137, 1–8Google Scholar
  48. 1.48
    Woodward, J. (1995): Causation and explanation in econometrics. In: D. Little (ed.), On the Reliability of Economic Models, 9–61. Kluwer Academic, Boston, MAGoogle Scholar
  49. 1.49
    Wright, S. (1921): Correlation and causation. J. Agricultural Res. 20, 557–585Google Scholar
  50. 1.50
    Wright, S. (1923): The theory of path coefficients: A reply to Niles' criticism. Genetics, 8, 239–255Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • J. Pearl
    • 1
  1. 1.Computer Science DepartmentUniversity of California, Los AngelesLos AngelesUSA

Personalised recommendations