Modelling with Non-stratified Chain Event Graphs

  • Aditi ShenviEmail author
  • Jim Q. Smith
  • Robert Walton
  • Sandra Eldridge
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 296)


Chain Event Graphs (CEGs) are recent probabilistic graphical modelling tools that have proved successful in modelling scenarios with context-specific independencies. Although the theory underlying CEGs supports appropriate representation of structural zeroes, the literature so far does not provide an adaptation of the vanilla CEG methods for a real-world application presenting structural zeroes also known as the non-stratified CEG class. To illustrate these methods, we present a non-stratified CEG representing a public health intervention designed to reduce the risk and rate of falling in the elderly. We then compare the CEG model to the more conventional Bayesian Network model when applied to this setting.


Bayesian networks Bayesian statistics Chain event graphs Event tree Public health intervention 



Jim Q. Smith was supported by the Alan Turing Institute and funded by the EPSRC [grant number EP/K03 9628/1].


  1. 1.
    Barclay, L.M., Collazo, R.A., Smith, J.Q., Thwaites, P.A., Nicholson, A.E.: The dynamic chain event graph. Electron. J. Stat. 9(2), 2130–2169 (2015)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Barclay, L.M., Hutton, J.L., Smith, J.Q.: Refining a Bayesian network using a chain event graph. Int. J. Approx. Reason. 54(9), 1300–1309 (2013)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Boutilier, C., Friedman, N., Goldszmidt, M., Koller, D.: Context-specific independence in Bayesian networks. In: Proceedings of the Twelfth international conference on uncertainty in artificial intelligence, pp. 115–123. Morgan Kaufmann Publishers Inc. (1996)Google Scholar
  4. 4.
    Buntine, W.: Theory refinement on Bayesian networks. In: Proceedings of the seventh conference on uncertainty in artificial intelligence, pp. 52–60. Morgan Kaufmann Publishers Inc. (1991)Google Scholar
  5. 5.
    Collazo, R.A.: The dynamic chain event graph. Ph.D. Thesis, University of Warwick (2017)Google Scholar
  6. 6.
    Collazo, R.A., Görgen, C., Smith, J.Q.: Chain Event Graphs. Chapman & Hall/CRC, Boca Raton (2017)zbMATHGoogle Scholar
  7. 7.
    Collazo, R.A., Smith, J.Q.: An N time-slice dynamic chain event graph. arXiv:1808.05726 (2018)
  8. 8.
    Cowell, R.G., Smith, J.Q.: Causal discovery through MAP selection of stratified chain event graphs. Electron. J. Stat. 8(1), 965–997 (2014)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Eldridge, S., Spencer, A., Cryer, C., Parsons, S., Underwood, M., Feder, G.: Why modelling a complex intervention is an important precursor to trial design: lessons from studying an intervention to reduce falls-related injuries in older people. J. Health Serv. Res. Policy 10(3), 133–142 (2005)CrossRefGoogle Scholar
  10. 10.
    Falls in older people: assessing risk and prevention. In: Guidance and Guidelines — NICE. (2013)
  11. 11.
    Freeman, G., Smith, J.Q.: Bayesian MAP model selection of chain event graphs. J. Multivar. Anal. 102(7), 1152–1165 (2011)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Friedman, N., Goldszmidt, M.: Learning Bayesian networks with local structure. In: Learning in Graphical Models, pp. 421–459. Springer, Dordrecht (1998)Google Scholar
  13. 13.
    Kass, R.E., Raftery, A.E.: Bayes factors. J. Am. Stat. Assoc. 90(430), 773–795 (1995)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Korb, K.B., Nicholson, A.E.: Bayesian Artificial Intelligence. CRC Press, Boca Raton (2010)zbMATHGoogle Scholar
  15. 15.
    Nandy, S., Parsons, S., Cryer, C., Underwood, M., Rashbrook, E., Carter, Y., Eldridge, S., Close, J., Skelton, D., Taylor, S.: Development and preliminary examination of the predictive validity of the Falls Risk Assessment Tool (FRAT) for use in primary care. J. Public Health 26(2), 138–143 (2004)CrossRefGoogle Scholar
  16. 16.
    Nurmi, I., Lüthje, P.: Incidence and costs of falls and fall injuries among elderly in institutional care. Scand. J. Prim. Health Care 20(2), 118–122 (2002)CrossRefGoogle Scholar
  17. 17.
    Pearl, J.: Causality. Cambridge University Press, Cambridge (2009)CrossRefGoogle Scholar
  18. 18.
    Poole, D., Zhang, N.L.: Exploiting contextual independence in probabilistic inference. J. Artif. Intell. Res. 18, 263–313 (2003)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Shafer, G.: The Art of Causal Conjecture. MIT press, Cambridge (1996)CrossRefGoogle Scholar
  20. 20.
    Shenvi, A., Smith, J.Q.: The reduced dynamic chain event graph. arXiv:1811.08872 (2018)
  21. 21.
    Silander, T., Tze-Yun L.: A dynamic programming algorithm for learning chain event graphs. In: International Conference on Discovery Science, pp. 201–216. Springer, Berlin (2013)Google Scholar
  22. 22.
    Smith, J.Q., Anderson, P.E.: Conditional independence and chain event graphs. Artif. Intell. 172(1), 42–68 (2008)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Smith, J.Q., Shenvi, A.: Assault crime dynamic chain event graphs. University of Warwick repository. (2018)
  24. 24.
    Thwaites, P.: Causal identifiability via chain event graphs. Artif. Intell. 195, 291–315 (2013)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Thwaites, P., Smith, J.Q.: A separation theorem for chain event graphs. arXiv:1501.05215 (2015)
  26. 26.
    Thwaites, P., Smith, J.Q., Riccomagno, E.: Causal analysis with chain event graphs. Artif. Intell. 174(12–13), 889–909 (2010)MathSciNetCrossRefGoogle Scholar
  27. 27.
    Verma, T., Pearl, J.: Causal networks: semantics and expressiveness. In: Machine Intelligence and Pattern Recognition, vol. 9, pp. 69–76. North-Holland (1990)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Aditi Shenvi
    • 1
    Email author
  • Jim Q. Smith
    • 2
    • 3
  • Robert Walton
    • 4
  • Sandra Eldridge
    • 4
  1. 1.Centre for Complexity Science, University of WarwickCoventryUK
  2. 2.Department of StatisticsUniversity of WarwickCoventryUK
  3. 3.The Alan Turing InstituteLondonUK
  4. 4.Centre for Primary Care and Public Health, Barts and The London School of Medicine and DentistryQueen Mary University of LondonLondonUK

Personalised recommendations