# Should causal models always be Markovian? The case of multi-causal forks in medicine

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## Abstract

The development of causal modelling since the 1950s has been accompanied by a number of controversies, the most striking of which concerns the Markov condition. Reichenbach's conjunctive forks did satisfy the Markov condition, while Salmon's interactive forks did not. Subsequently some experts in the field have argued that adequate causal models should always satisfy the Markov condition, while others have claimed that non-Markovian causal models are needed in some cases. This paper argues for the second position by considering the multi-causal forks, which are widespread in contemporary medicine (Section 2). A non-Markovian causal model for such forks is introduced and shown to be mathematically tractable (Sections 6, 7, and 8). The paper also gives a general discussion of the controversy about the Markov condition (Section 1), and of the related controversy about probabilistic causality (Sections 3, 4, and 5).

## Keywords

Probabilistic causality Conjunctive forks Interactive forks Multi-causal forks Markov condition Bayesian networks Causal factors Heart disease## Notes

### Acknowledgments

Earlier drafts of this paper were read at the *International Workshop on Causal Inference in the Health Sciences*, which Maria Carla Galavotti and Raffaella Campaner organised in Bologna on 27-28 May 2011, and at a meeting of the Kent-UCL Causality group, held in UCL on 11 August 2011. Many comments were received at these meetings – some favourable, and some highly critical, indicating the controversial nature of the material. Later we received further comments, again some favourable and some highly critical, on subsequent drafts of the paper. We have tried to take into account both types of comment in revising the paper, and would like to thank those who made comments, particularly Carlo Berzuini, Raffaella Campaner, Nancy Cartwright, Brendan Clarke, David Corfield, Philip Dawid, Maria Carla Galavotti, Phyllis McKay Illari, Judea Pearl, Federica Russo, Jon Williamson, and several anonymous referees.

## References

- Bandyoapdhyay, P. S., Nelson, D., Greenwood, M., Brittan, G., & Berwald, J. (2011). The logic of Simpson’s paradox.
*Synthese, 181*, 185–208.CrossRefGoogle Scholar - Campaner, R., & Galavotti, M.C. (2007). Plurality in causality. In P. Machamer & G. Wolters (eds.),
*Thinking about causes from Greek philosophy to modern physics*. University of Pittsburgh Press, Ch. 10, pp. 178–199Google Scholar - Cartwright, N. (1979). Causal laws and effective strategies. Reprinted in
*How the laws of physics lie*. Oxford: Oxford University Press, 1983, pp. 21–43.Google Scholar - Cartwright, N. (1989).
*Nature’s capacities and their measurement*. Oxford: Oxford University Press.Google Scholar - Cartwright, N. (1995). False idealisation: a philosophical threat to scientific method.
*Philosophical Studies, 77*, 339–352.CrossRefGoogle Scholar - Cartwright, N. (2001). What is wrong with Bayes nets?
*The Monist, 84*, 242–264.CrossRefGoogle Scholar - Codell Carter, K. (2003). The rise of causal concepts of disease. Case Histories. Ashgate.Google Scholar
- Doll, R., & Peto, R. (1976). Mortality in relation to smoking: 20 years’ observations on male British doctors.
*British Medical Journal, 2*, 1525–1536.CrossRefGoogle Scholar - Eells, E. (1991).
*Probabilistic causality*. Cambridge: Cambridge University Press.CrossRefGoogle Scholar - Galavotti, M. C. (2010). Probabilistic causality, observation and experimentation. In W. J. Gonzalez (Ed.),
*New methodological perspectives on observation and experimentation in science*(pp. 139–155). A. Coruña: Netbiblo.Google Scholar - Gillies, D. (2004). An action-related theory of causality.
*The British Journal for the Philosophy of Science, 56*, 823–842.CrossRefGoogle Scholar - Gillies, D. (2011). The Russo-Williamson thesis and the question of whether smoking causes heart disease. In Illari, Russo, and Williamson, 2011, pp. 110–125.Google Scholar
- Good, I.J. (1961). A causal calculus I.
*British Journal for the Philosophy of Science*, 11, 305–318. Reprinted in I.J.Good,*Good thinking*.*The foundations of probability and its applications*. Minneapolis: University of Minnesota Press, pp. 197–217.Google Scholar - Good, I.J. (1962). A causal calculus II.
*British Journal for the Philosophy of Science*, 12, 43–51. Reprinted in I.J.Good,*Good thinking*.*The foundations of probability and its applications*. Minneapolis: University of Minnesota Press, pp. 197–217.Google Scholar - Haavelmo, T. (1943). The statistical implications of a system of simultaneous equations, 11, pp. 1–12. Reprinted in D.F. Hendry & M.S. Morgan (eds.),
*The foundations of econometric analysis*. Cambridge University Press, 1995, pp. 477–490.Google Scholar - Hennig, C. (2010). Mathematical models and reality – a constructivist view.
*Foundations of Science, 15*, 29–48.CrossRefGoogle Scholar - Hesslow, G. (1976). Discussion: two notes on the probabilistic approach to causality.
*Philosophy of Science, 43*, 290–292.CrossRefGoogle Scholar - Hitchcock, C. (2001). A tale of two effects.
*Philosophical Review, 110*(3), 361–396.Google Scholar - Hitchcock, C. (2010). Probabilistic causality.
*Stanford encyclopedia of philosophy*(http://plato.stanford.edu). - Illari, Phyllis, McKay, Russo, Federica, Williamson, J. (eds) (2011).
*Causality in the sciences*. Oxford University Press.Google Scholar - Kim, J.H. & Pearl, J. (1983). A computational model for combined causal and diagnostic reasoning in inference systems.
*Proceedings of the 8*^{th}*International Joint Conference on AI*(*IJCAI*-*85*), pp. 190–193.Google Scholar - Korb, K.B., Hope, L.R., Nicholson, A.E., Annick, K. (2004). Varieties of causal intervention.
*Pacific Rim International Conference on AI*’*04*, pp. 322–331.Google Scholar - Lauritzen, S. L., & Spiegelhalter, D. J. (1988). Local computations with probabilities on graphical structures and their application to expert systems (with discussion).
*Journal of the Royal Statistical Society B, 50*, 157–224.Google Scholar - Levy, D., & Brink, S. (2005).
*A change of heart. Unraveling the mysteries of cardiosvacular disease*. New York: Vintage Books.Google Scholar - Neapolitan, R. E. (1990).
*Probabilistic reasoning in expert systems. Theory and algorithms*. New York: John Wiley.Google Scholar - Pearl, J. (1982). Reverend Bayes on inference engines: a distributed hierarchical approach.
*Proceedings of the National conference on AI, ASSI-82*, 133–136.Google Scholar - Pearl, J. (1985a). How to do with probabilities what people say you can’t.
*Proceedings of the Second IEEE Conference on AI Applications*. Miami, Fl., pp. 6–12.Google Scholar - Pearl, J. (1985b). Bayesian networks: a model of self-activated memory for evidential reasoning.
*Proceedings of the Cognitive Science Society*, Ablex, pp. 329–34.Google Scholar - Pearl, J. (1986). Fusion, propagation and structuring in belief networks.
*Artificial Intelligence, 29*, 241–288.CrossRefGoogle Scholar - Pearl, J. (1988).
*Probabilistic reasoning in intelligent systems. Networks of plausible inference*. San Mateo, California: Morgan Kaufmann.Google Scholar - Pearl, J. (2000).
*Causality. models, reasoning, and inference*. Cambridge: Cambridge University Press.Google Scholar - Pearl, J. (2011). The structural theory of causation. In Illari, Russo, and Williamson, 2011, pp. 697–727.Google Scholar
- Popper, K. R. (1963).
*Conjectures and refutations. the growth of scientific knowledge*. London: Routledge & Kegan Paul.Google Scholar - Reichenbach, H. (1956). In M. Reichenbach (Ed.),
*The direction of time*. Berkeley: University of California Press. 1971.Google Scholar - Russo, F. (2009).
*Causality and causal modelling in the social sciences*. New York: Springer.CrossRefGoogle Scholar - Russo, F., & Williamson, J. (2007). Interpreting causality in the health sciences.
*International Studies in the Philosophy of Science, 21*(2), 157–170.CrossRefGoogle Scholar - Russo, F., & Williamson, J. (2011). Generic versus single-case causality: the case of autopsy.
*European Journal for Philosophy of Science, 1*, 47–69.CrossRefGoogle Scholar - Salmon, W. (1978). Why Ask, : “Why?”? An inquiry concerning scientific explanation. Reprinted in Salmon, 1998, pp. 125–141.Google Scholar
- Salmon, W. (1980). Probabilistic causality. Reprinted in Salmon, 1998, pp. 208–232.Google Scholar
- Salmon, W. (1998).
*Causality and explanation*. Oxford: Oxford University Press.CrossRefGoogle Scholar - Spirtes, P., Glymour, C., & Scheines, R. (1993).
*Causation, prediction and search*. New York: Springer Verlag.CrossRefGoogle Scholar - Sucar, L. E., Gillies, D. F., & Gillies, D. A. (1993). Objective probabilities in expert systems.
*Artificial Intelligence, 61*, 187–203.CrossRefGoogle Scholar - Suppes, P. (1970).
*A probabilistic theory of causality*. Amsterdam: North-Holland.Google Scholar - Suppes, P. (1986). Non-Markovian causality in the social sciences with some theorems on transitivity.
*Synthese, 68*(1), 129–140.Google Scholar - Twardy, C. R., & Korb, K. B. (2004). A criterion of probabilistic causality.
*Philosophy of Science, 71*, 241–262.CrossRefGoogle Scholar - Williamson, J. (2005).
*Bayesian nets and causality*. Oxford: Oxford University Press.Google Scholar - Williamson, J. (2010).
*In defence of objective Bayesianism*. Oxford: Oxford University Press.CrossRefGoogle Scholar