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Foundations of Bayesianism pp 75–115Cite as

Foundations for Bayesian Networks

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Part of the book series: Applied Logic Series ((APLS,volume 24))

Abstract

Bayesian networks are normally given one of two types of foundations: they are either treated purely formally as an abstract way of representing probability functions, or they are interpreted, with some causal interpretation given to the graph in a network and some standard interpretation of probability given to the probabilities specified in the network. In this chapter I argue that current foundations are problematic, and put forward new foundations which involve aspects of both the interpreted and the formal approaches.

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Bibliography

  1. S. Andersson, D. Madigan & M. Perlman: ‘An alternative Markov property for chain graphs’, Proceedings of the 12th Conference on Uncertainty in Artificial Intelligence, Portland OR: Morgan Kaufmann, pages 40–48.

    Google Scholar 

  2. Frank Amtzenius: ‘The common cause principle’, Philosophy of Science Association 1992 (2), pages 227–237.

    Google Scholar 

  3. John Binder, Daphne Koller, Stuart Russell & Keiji Kanazawa: ‘Adaptive probabilistic networks with hidden variables’, Machine Learning 29, pages 213–244.

    Google Scholar 

  4. Wray Buntine: ‘A guide to the literature on learning probabilistic networks from data’, IEEE Transactions on Knowledge and Data Engineering 8(2), pages 195–210.

    Google Scholar 

  5. Jeremy Butterfield: ‘Bell’s theorem: what it takes’, British Journal for the Philosophy of Science 43, pages 41–83.

    Google Scholar 

  6. Nancy Cartwright: ‘Nature’s capacities and their measurement’, Oxford: Clarendon Press.

    Google Scholar 

  7. C.K. Chow & C.N. Liu: ‘Approximating discrete probability distributions with dependence trees’, IEEE Transactions on Information Theory IT-14, pages 462–467.

    Google Scholar 

  8. Ronald Fisher: ‘The design of experiments’, Edinburgh: Oliver & Boyd.

    Google Scholar 

  9. Bas C. van Fraassen: ‘The scientific image’, Clarendon Press, Oxford.

    Google Scholar 

  10. M. Frydenberg: ‘The chain graph Markov property’, Scandanavian Journal of Statistics 17, pages 333–353.

    Google Scholar 

  11. Clark Glymour: ‘A review of recent work on the foundations of causal inference’

    Google Scholar 

  12. ], pages 201–248.

    Google Scholar 

  13. Clark Glymour & Gregory F. Cooper(eds.): ‘Computation, causation, and discovery’, Cambridge, Massachusetts: The M.I.T. Press.

    Google Scholar 

  14. Peter Grünwald: ‘Maximum entropy and the glasses you are looking through’, Proceedings of the 16th conference of Uncertainty in Artificial Intelligence, Stanford University, Morgan Kaufmann, pages 238–246.

    Google Scholar 

  15. Daniel M. Hausman: ‘Causal asymmteries’, Cambridge: Cambridge University Press.

    Google Scholar 

  16. Daniel M. Hausman: ‘The mathematical theory of causation’, review of [McKim & Turner 1997], British Journal for the Philosophy of Science 50, pages 151–162.

    Google Scholar 

  17. Richard Healey: ‘Review of Paul Horwich’s “Asymmetries in time”’, The Philosophical Review 100, pages 125–130.

    Google Scholar 

  18. David Heckerman, Christopher Meek & Gregory Cooper: ‘A Bayesian approach to causal discovery’, in [Glymour & Cooper 1999], pages 141–165.

    Google Scholar 

  19. Edward Herskovitz: ‘Computer-based probabilistic-network construction’, PhD Thesis, Stanford University.

    Google Scholar 

  20. Paul Humphreys: ‘A critical appraisal of causal discovery algorithms’, in [McKim & Turner 1997], pages 249–263.

    Google Scholar 

  21. Paul Humphreys & David Freedman: ‘The grand leap’, British Journal for the Philosophy of Science 47, pages 113–123.

    Google Scholar 

  22. Nathalie Jitnah: ‘Using mutual information for approximate evaluation of Bayesian networks’, PhD Thesis, School of Computer Science and Software Engineering, Monash University.

    Google Scholar 

  23. Michae] I. Jordan(ed.): ‘Learning in Graphical Models’, Cambridge, Massachusetts: The M.I.T. Press 1999.

    Google Scholar 

  24. Chee-Keong Kwoh & Duncan F. Gillies: ‘Using hidden nodes in Bayesian networks’, Artificial Intelligence 88, pages 1–38.

    Google Scholar 

  25. Frank Lad: ‘Assessing the foundation for Bayesian networks: a challenge to the principles and the practice’, Soft Computing 3(3), pages 174–180.

    Google Scholar 

  26. John F. Lemmer: ‘Causal modeling’, in Proceedings of the 9th Conference on Uncertainty in Artificial Intelligence, San Mateo: Morgan Kaufmann, pages 143–151.

    Google Scholar 

  27. John F. Lemmer: ‘The causal Markov condition, fact or artifact?’, SIGART 7(3).

    Google Scholar 

  28. Vaughn R. McKim & Stephen Turner: ‘Causality in crisis? Statistical methods and the search for causal knowledge in the social sciences’, University of Notre Dame Press.

    Google Scholar 

  29. John Stuart Mill: ‘A system of logic, ratiocinative and inductive: being a connected view of the principles of evidence and the methods of scientific investigation’, New York: Harper & Brothers, eighth edition, 1874.

    Google Scholar 

  30. Richard E. Neapolitan: ‘Probabilistic reasoning in expert systems: theory and algorithms’, New York: Wiley.

    Google Scholar 

  31. R.M. Oliver & J.Q. Smith: ‘Influence diagrams, belief nets and decision analysis’, Chichester: Wiley.

    Google Scholar 

  32. David Papineau: ‘Can we reduce causal direction to probabilities?’, Philosophy of Science Association 1992 (2), pages 238–252.

    Google Scholar 

  33. Jeff Paris: ‘The uncertain reasoner’s companion’, Cambridge: Cambridge University Press.

    Google Scholar 

  34. Jeff Paris: ‘Common sense and maximum entropy’, Synthese 117, pages 73–93.

    Google Scholar 

  35. Jeff Paris & Alena Vencovskâ: ‘In defense of the maximum entropy inference process’, International Journal of Automated Reasoning 17, pages 77–103.

    Google Scholar 

  36. J.B. Paris & A. Vencovskâ: ‘Common sense and stochastic independence’, this volume.

    Google Scholar 

  37. Judea Pearl: ‘Probabilistic reasoning in intelligent systems: networks of plausible inference’, San Mateo, California: Morgan Kaufmann.

    Google Scholar 

  38. Judea Pearl: ‘Causality: models, reasoning, and inference’, Cambridge University Press.

    Google Scholar 

  39. J. Pearl & R. Dechter: ‘Identifying independencies in causal graphs with feedback’, Proceedings of the 12th Conference of Uncertainty in Artificial Intelligence, Portland OR: Morgan Kaufmann.

    Google Scholar 

  40. Judea Pearl, Dan Geiger & Thomas Verma: ‘The logic of influence diagrams’, in [Oliver & Smith 1990], pages 67–87.

    Google Scholar 

  41. Huw Price: ‘The direction of causation: Ramsey’s ultimate contingency’, Philosophy of Science Association 1992 (2), pages 253–267.

    Google Scholar 

  42. Hans Reichenbach: ‘The direction of time’, Berkeley & Los Angeles, University of California Press, reprinted 1971.

    Google Scholar 

  43. T. Richardson: ‘A discovery algorithm for directed cyclic graphs’, Proceedings of the 12th Conference of Uncertainty in Artificial Intelligence, Portland OR: Morgan Kaufmann, pages 454–461.

    Google Scholar 

  44. James M. Robins & Larry Wasserman: ‘On the impossibility of inferring causation from association without background knowledge’, in

    Google Scholar 

  45. pages 305–321.

    Google Scholar 

  46. William B. Rolnick: ‘Causality and physical theories’, New York: American Institute of Physics.

    Google Scholar 

  47. Wesley C. Salmon: ‘Probabilistic causality’, in [Salmon 1998], pages 208–232.

    Google Scholar 

  48. Wesley C. Salmon: ‘Scientific explanation and the causal structure of the world’, Princeton: Princeton University Press.

    Google Scholar 

  49. Steven F. Savitt: ‘The direction of time’, British Journal for the Philosophy of Science 47, pages 347–370.

    Google Scholar 

  50. Richard Schemes: ‘An introduction to causal inference’, in

    Google Scholar 

  51. pages 185–199.

    Google Scholar 

  52. Richard Schlegel: ‘Historic views of causality’, in [Rolnick 1974], pages 3–21. [Smith 1990] J.Q. Smith: ‘Statistical principles on graphs’, in

    Google Scholar 

  53. ], pages 89–120.

    Google Scholar 

  54. Elliott Sober: ‘The principle of the common cause’, in James H. Fetzer (ed.): ‘Probability and causality: essays in honour of Wesley C. Salmon’, pages 211–228.

    Google Scholar 

  55. P. Spirtes: ‘Directed cyclic graphical representation of feedback models’, Proceedings of the 11th Conference on Uncertainty in Artificial Intelligence, Montreal QU: Morgan Kaufmann, pages 491–498.

    Google Scholar 

  56. Peter Spirtes, Clark Glymour & and Richard Schemes: ‘Causation, Prediction, and Search’, Lecture Notes in Statistics 81, Springer-Verlag.

    Google Scholar 

  57. Peter Spirtes, Clark Glymour & Richard Schemes: ‘Reply to Humphreys and Freedman’s review of ‘Causation, prediction, and search“, British Journal for the Philosophy of Science 48, pages 555–568.

    Google Scholar 

  58. L.E. Sucar, D.F. Gillies & D.A. Gillies: ‘Objective probabilities in expert systems’, Artificial Intelligence 61, pages 187–208.

    Google Scholar 

  59. Sundaram 1996] Rangarajan K Sundaram: ‘A first course in optimisation theory’, Cambridge: Cambridge University Press.

    Google Scholar 

  60. Verma & Pearl 1991] T. Verma & J. Pearl: ‘Equivalence and synthesis of causal models’, Los Angeles, Cognitive Systems Laboratory, University of California.

    Google Scholar 

  61. N. Wermuth, D. Cox & J. Pearl: ‘Explanations for multivariate structures derived from univariate recursive regressions’, Center of Survey Research and Methodology, ZUMA, Mannheim, FRG, revised 1998.

    Google Scholar 

  62. Williamson 1999] Jon Williamson. ‘Does a cause increase the probability of its effects?’, philosophy.ai report pai jw_99_d, http://www.kcl.ac.uk/philosophy.ai

    Google Scholar 

  63. Jon Williamson: ‘A probabilistic approach to diagnosis’, Proceedings of the Eleventh International Workshop on Principles of Diagnosis (DX-00), Morelia, Michoacen, Mexico, June 811 2000.

    Google Scholar 

  64. Williamson 2000b] Jon Williamson: ‘Approximating discrete probability distributions with Bayesian networks’, in Proceedings of the International Conference on Artificial Intelligence in Science and Technology, Hobart Tasmania, 16–20 December 2000, pages 106–114.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Philosophy, King’s College, London, UK

    Jon Williamson

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  1. Jon Williamson
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Editors and Affiliations

  1. Department of Philosophy, King’s College, London, UK

    David Corfield  & Jon Williamson  & 

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© 2001 Springer Science+Business Media Dordrecht

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Williamson, J. (2001). Foundations for Bayesian Networks. In: Corfield, D., Williamson, J. (eds) Foundations of Bayesianism. Applied Logic Series, vol 24. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1586-7_4

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  • DOI: https://doi.org/10.1007/978-94-017-1586-7_4

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-5920-8

  • Online ISBN: 978-94-017-1586-7

  • eBook Packages: Springer Book Archive

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