, Volume 191, Issue 8, pp 1651–1681 | Cite as

Modelling mechanisms with causal cycles

  • Brendan Clarke
  • Bert Leuridan
  • Jon Williamson


Mechanistic philosophy of science views a large part of scientific activity as engaged in modelling mechanisms. While science textbooks tend to offer qualitative models of mechanisms, there is increasing demand for models from which one can draw quantitative predictions and explanations. Casini et al. (Theoria 26(1):5–33, 2011) put forward the Recursive Bayesian Networks (RBN) formalism as well suited to this end. The RBN formalism is an extension of the standard Bayesian net formalism, an extension that allows for modelling the hierarchical nature of mechanisms. Like the standard Bayesian net formalism, it models causal relationships using directed acyclic graphs. Given this appeal to acyclicity, causal cycles pose a prima facie problem for the RBN approach. This paper argues that the problem is a significant one given the ubiquity of causal cycles in mechanisms, but that the problem can be solved by combining two sorts of solution strategy in a judicious way.


Bayesian nets Recursive Bayesian nets Cyclic causality Mechanisms Feedback Causal models Causation Mechanistic modelling 



We would like to thank Lorenzo Casini, George Darby, Phyllis Illari, Mike Joffe, Federica Russo, and Michael Wilde for their helpful comments on this paper. Jon Williamson’s research is supported by the UK Arts and Humanities Research Council. Bert Leuridan is Postdoctoral Fellow of the Research Foundation—Flanders (FWO).


  1. Bechtel, W. (2011). Mechanism and biological explanation. Philosophy of Science, 78(4), 533–557.CrossRefGoogle Scholar
  2. Bechtel, W., & Abrahamsen, A. (2005). Explanation: A mechanist alternative. Studies in History and Philosophy of Biological and Biomedical Sciences, 36(2), 421–441.Google Scholar
  3. Bernard, A., & Hartemink, A. (2005). Informative structure priors: Joint learning of dynamic regulatory networks from multiple types of data. In R. Altman, A. K. Dunker, L. Hunter, T. Jung, & T. Klein (Eds.), Proceedings of the Pacific symposium on biocomputing (PSB05) (pp. 459–470). Hackensack, NJ: World Scientific.Google Scholar
  4. Boon, N. A., Colledge, N. R., Walker, B. R., & Hunter, J. A. (Eds.). (2006). Davidson’s principles & practice of medicine (20th ed.). Edinburgh: Churchill Livingstone.Google Scholar
  5. Bouchaffra, D. (2010). Topological dynamic Bayesian networks. In Proceedings of the twentieth IEEE international conference on pattern recognition (pp. 898–901).Google Scholar
  6. Cartwright, N. (2001). What is wrong with Bayes nets? The Monist, 84(2), 242–264.CrossRefGoogle Scholar
  7. Cartwright, N. (2002). Against modularity, the causal Markov condition, and any link between the two: Comments on Hausman and Woodward. The British Journal for the Philosophy of Science, 53(3), 411–453.Google Scholar
  8. Casini, L., Illari, P. M., Russo, F., & Williamson, J. (2011). Models for prediction, explanation and control: Recursive Bayesian networks. Theoria, 26(1), 5–33.Google Scholar
  9. Cowell, R. G., Dawid, A. P., Lauritzen, S. L., & Spiegelhalter, D. J. (1999). Probabilistic networks and expert systems. Berlin: Springer.Google Scholar
  10. Craver, C. F. (2006). When mechanistic models explain. Synthese, 153(3), 355–376.CrossRefGoogle Scholar
  11. Craver, C. F. (2007). Explaining the brain: Mechanisms and the mosaic unity of neuroscience. Oxford: Clarendon Press.CrossRefGoogle Scholar
  12. Crunelli, V., & Hughes, S. W. (2010). The slow (\({<}\) 1 Hz) rhythm of non-REM sleep: A dialogue between three cardinal oscillators. Nature Neurosciences, 13(1), 9–17.CrossRefGoogle Scholar
  13. Dean, T., & Kanazawa, K. (1989). A model for reasoning about persistence and causation. Computational Intelligence, 5(3), 142–150.CrossRefGoogle Scholar
  14. Doshi-Velez, F., Wingate, D., Tenenbaum, J., & Roy, N. (2011). Infinite dynamic bayesian networks. In L. Getoor & T. Scheffer (Eds.), Proceedings of the 28th international conference on machine learning (ICML) (pp. 913–920). Montreal: Omnipress.Google Scholar
  15. Friedman, N., Murphy, K. P., & Russell, S. J. (1998). Learning the structure of dynamic probabilistic networks. In G. F. Cooper & S. Moral (Eds.), Proceedings of the fourteenth conference on uncertainty in artificial intelligence (UAI) (pp. 139–147), San Mateo, CA. Morgan Kaufmann.Google Scholar
  16. Gebharter, A., & Kaiser, M. I. (2012). Causal graphs and mechanisms. In A. Hüttemann, M. I. Kaiser, & O. Scholz (Eds.), Explanation in the special sciences. The case of biology and history. Synthese Library. Dordrecht: Springer.Google Scholar
  17. Ghahramani, Z. (1998). Learning dynamic bayesian networks. In C. Giles & M. Gori (Eds.), Adaptive processing of sequences and data structures. Lecture notes in computer science (Vol. 1387, pp. 168–197). Berlin: Springer. doi: 10.1007/BFb0053999.
  18. Glennan, S. S. (1996). Mechanisms and the nature of causation. Erkenntnis, 44(1), 49–71.CrossRefGoogle Scholar
  19. Glennan, S. S. (2002). Rethinking mechanistic explanation. Philosophy of Science, 69(3), S342–S353.CrossRefGoogle Scholar
  20. Glennan, S. S. (2005). Modeling mechanisms. Studies in History and Philosophy of Biological and Biomedical Sciences, 36(2), 443–464.Google Scholar
  21. Gottlieb, D. J., Yenokyan, G., Newman, A. B., O’Connor, G. T., Punjabi, N. M., Quan, S. F., et al. (2010). Prospective study of obstructive sleep apnea and incident coronary heart disease and heart failure. Circulation, 122(4), 352–360.CrossRefGoogle Scholar
  22. Grandner, M., Hale, L., Moore, M., & Patel, N. V. (2010). Mortality associated with short sleep duration: The evidence, the possible mechanisms, and the future. Sleep Medicine Reviews, 14(3), 191–203.CrossRefGoogle Scholar
  23. Hausman, D. M., & Woodward, J. (1999). Independence, invariance and the causal Markov condition. The British Journal for the Philosophy of Science, 50(4), 521–583.CrossRefGoogle Scholar
  24. Hausman, D. M., & Woodward, J. (2004a). Manipulation and the causal Markov condition. Philosophy of Science, 55(5), 147–161.Google Scholar
  25. Hausman, D. M., & Woodward, J. (2004b). Modularity and the causal Markov condition: A restatement. The British Journal for the Philosophy of Science, 55(1), 147–161.CrossRefGoogle Scholar
  26. Koster, J. T. A. (1996). Markov properties of nonrecursive causal models. Annals of Statistics, 24(5), 2148–2177.Google Scholar
  27. Lauritzen, S., Dawid, A., Larsen, B., & Leimer, H.-G. (1990). Independence properties of directed Markov fields. Networks, 20(5), 491–505.CrossRefGoogle Scholar
  28. Lazebnik, Y. (2002). Can a biologist fix a radio?—Or, what I learned while studying apoptosis. Cancer Cell, 2, 179–182.CrossRefGoogle Scholar
  29. Leuridan, B. (2010). Can mechanisms really replace laws of nature? Philosophy of Science, 77(3), 317–340.CrossRefGoogle Scholar
  30. Leuridan, B. (2012). Three problems for the mutual manipulability account of constitutive relevance in mechanisms. The British Journal for the Philosophy of Science, 63(2), 399–427.CrossRefGoogle Scholar
  31. Leuridan, B. (2014). The structure of scientific theories, explanation, and unification. A causal-structural account. The British Journal for the Philosophy of Science doi: 10.1093/bjps/axt015.
  32. Machamer, P., Darden, L., & Craver, C. F. (2000). Thinking about mechanisms. Philosophy of Science, 67(1), 1–25.CrossRefGoogle Scholar
  33. Marshall, L., Helgadóttir, H., Mölle, M., & Born, J. (2006). Boosting slow oscilllations during sleep potentiates memory. Nature, 444(7119), 610–613.CrossRefGoogle Scholar
  34. McNicholas, W., & Bonsignore, M. (2007). Sleep apnoea as an independent risk factor for cardiovascular disease: Current evidence, basic mechanisms and research priorities. European Respiratory Journal, 29(1), 156–178.CrossRefGoogle Scholar
  35. Mitchell, S. (2009). Unsimple truths: Science, complexity, and policy. Chicago, IL: University of Chicago Press.CrossRefGoogle Scholar
  36. Murphy, K. P. (2002). Dynamic Bayesian networks: Representation, inference and learning. PhD thesis, Computer Science, University of California, Berkeley.Google Scholar
  37. Neal, R. (2000).On deducing conditional independence from \(d\)-separation in causal graphs with feedback: The uniqueness condition is not suffient. Journal of Artificial Intelligence Research, 12, 87–91.Google Scholar
  38. Neapolitan, R. E. (1990). Probabilistic reasoning in expert systems: Theory and algorithms. New York: Wiley.Google Scholar
  39. Nervi, M. (2010). Mechanisms, malfunctions and explanation in medicine. Biology and Philosophy, 25(2), 215–228.CrossRefGoogle Scholar
  40. Pearl, J. (1988). Probabilistic reasoning in intelligent systems: Networks of plausible inference. San Mateo, CA: Morgan Kaufmann.Google Scholar
  41. Pearl, J. (2000). Causality: Models, reasoning, and inference. Cambridge: Cambridge University Press.Google Scholar
  42. Pearl, J., & Dechter, R. (1996). Identifying independencies in causal graphs with feedback. In Uncertainty in artificial intelligence: Proceedings of the twelfth conference (pp. 420–426). San Mateo, CA. Morgan Kaufmann.Google Scholar
  43. Perini, L. (2005a). Explanation in two dimensions: Diagrams and biological explanation. Biology and Philosophy, 20(2–3), 257–269.CrossRefGoogle Scholar
  44. Perini, L. (2005b). The truth in pictures. Philosophy of Science, 72(1), 262–285.CrossRefGoogle Scholar
  45. Perini, L. (2005c). Visual representations and confirmation. Philosophy of Science, 72(5), 913–926.CrossRefGoogle Scholar
  46. Seidenfeld, T. (1987). Entropy and uncertainty. In I. B. MacNeill & G. J. Umphrey (Eds.), Foundations of statistical inference (pp. 259–287). Dordrecht: Reidel.Google Scholar
  47. Spirtes, P. (1995). Directed cyclic graphical representation of feedback models. In P. Besnard & S. Hanks (Eds.), Proceedings of the eleventh conference on uncertainty in artificial intelligence (pp. 491–498). San Mateo, CA: Morgan Kaufmann.Google Scholar
  48. Spirtes, P., Glymour, C., & Scheines, R. (2000). Causation, prediction, and search. Cambridge, MA: MIT Press.Google Scholar
  49. Spirtes, P., Glymour, C., Scheines, R., & Tillman, R. (2010). Automated search for causal relations—Theory and practice. In R. Dechter, H. Geffner, & J. Y. Halpern (Eds.), Heuristics, probability and causality: A tribute to Judea Pearl (pp. 467–506). London: College Publications.Google Scholar
  50. Steel, D. (2006). Comment on Hausman & Woodward on the causal Markov condition. British Journal for the Philosophy of Science, 57(1), 219–231.CrossRefGoogle Scholar
  51. Williamson, J. (2005). Bayesian nets and causality: Philosophical and computational foundations. Oxford: Oxford University Press.Google Scholar
  52. Williamson, J. (2010). In defence of objective Bayesianism. Oxford: Oxford University Press.CrossRefGoogle Scholar
  53. Woodward, J. (2002). What is a mechanism? A counterfactual account. Philosophy of Science, 69(3), S366–S377.CrossRefGoogle Scholar
  54. Woodward, J. (2003). Making things happen. A theory of causal explanation. New York: Oxford University Press.Google Scholar
  55. Yumino, D., Redolfi, S., Ruttanaumpawan, P., Su, M., Smith, S., Newton, G. E., et al. (2010). Nocturnal rostral fluid shift. Circulation, 121(14), 1598–1605.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of Science and Technology StudiesUniversity College LondonLondonUK
  2. 2.Centre for Logic and Philosophy of Science, Department of Philosophy and Moral ScienceGhent UniversityGentBelgium
  3. 3.Philosophy DepartmentUniversity of KentCanterburyUK

Personalised recommendations