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Probabilistic Token Causation: A Bayesian Perspective

  • Elja Arjas
Chapter
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 19)

Abstract

Many authors (e.g., Good [8, 9] and Eells [5, 6]) distinguish between two kinds of probabilistic causality: the tendency of C to cause E and the degree to which C actually caused E. The former, a generic form of causation, can be discussed by comparing two prediction probabilities, one conditional on the occurrence of C and the other on its “counterfactual” event, where C does not occur. The latter, a singular form, is often called token causality and corresponds to finding a causal explanation of the occurrence of an event after it has been observed to happen. The purpose of this chapter is to formulate token causality by using the mathematical framework of marked point processes (MPPs) and their associated prediction processes. The same framework was used by Arjas and Eerola [2] for considering predictive causality. Therefore, this chapter can also be seen as an attempt to bridge the gap between these two types of causality reasoning.

Keywords

Marked Point Latent Variable Model Prediction Probability Marked Point Process Bayesian Perspective 
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.

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References

  1. [1]
    Arjas, E. Survival models and martingale dynamics (with discussion). Scand. J. Stat. 16, 177–225, 1989.MathSciNetzbMATHGoogle Scholar
  2. [2]
    Arjas, E., and Eerola, M. On predictive causality in longitudinal studies. J. Stat. Planning Inference 34, 361–386, 1993.MathSciNetzbMATHCrossRefGoogle Scholar
  3. [3]
    Arjas, E., Haara, P., and Norros, I. Filtering the histories of a partially observed marked point process. Stock. Proc. Appl. 40, 225–250, 1992.MathSciNetzbMATHCrossRefGoogle Scholar
  4. [4]
    Cartwright, Nancy. Regular associations and singular causes. In: Skyrms, Brian, and Harper, William L. (eds), Causation, Chance, and Credence. Kluwer Academic Publishers, Dordrecht, 1988, pp. 79–97.CrossRefGoogle Scholar
  5. [5]
    Eells, Ellery. Probabilistic causal levels. In: Skyrms, Brian, and Harper, William L. (eds), Causation, Chance, and Credence. Kluwer Academic Publishers, Dordrecht, 1988, pp. 109–133.CrossRefGoogle Scholar
  6. [6]
    Eells, Ellery. Probabilistic Causality. Cambridge University Press, Cambridge, 1991.zbMATHCrossRefGoogle Scholar
  7. [7]
    Good, I. J. A causal calculus. Br. J. Phil Sci. 11, 305–318, 1961; 12, 43-51, 1961; 1b3, 88, 1962.MathSciNetCrossRefGoogle Scholar
  8. [8]
    Good, I. J. Causal propensity: a review. In: Asquith, P. D., and Kitcher, P. (eds), PSA 2, 829–850. Philosophy of Science Association, East Lansing MI, 1984.Google Scholar
  9. [9]
    Good, I. J. Causal tendency: a review. In: Skyrms, Brian, and Harper, William L. (eds), Causation, Chance, and Credence. Kluwer Academic Publishers, Dordrecht, 1988, pp. 23–50.CrossRefGoogle Scholar
  10. [10]
    Pearl, Judea. Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann Publishers, San Mateo, 1988.Google Scholar
  11. [11]
    Rosen, D. A. In defense of a probabilistic theory of causality. Phil. Sci. 45, 604–613, 1978.CrossRefGoogle Scholar
  12. [12]
    Suppes, Patrick. A Probabilistic Theory of Causality. North Holland, Amsterdam, 1970.Google Scholar

Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Elja Arjas

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