Skip to main content
SpringerLink
Log in
Book cover

Quantified Representation of Uncertainty and Imprecision pp 111–134Cite as

The Bayesian Approach

  • Chapter

  • 354 Accesses

Part of the book series: Handbook of Defeasible Reasoning and Uncertainty Management Systems ((HAND,volume 1))

Abstract

We live in an uncertain world in which decisions have to be taken. From the point of view of the decision-maker, it is obviously desirable to have some reasonably reliable notion of which possible outcomes of their decisions are more or less likely. This seems to be the province of a theory of probability, and the groundwork of one was duly developed in that century we now recognise to inaugurate the era of modern science, the seventeenth century.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   259.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   329.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. Allais. Le comportement de l’homme rationnel devant le risque: critique des postulats et axiomes de l’école americaine. Econometrica, 21, 503–546, 1953.

    Article  Google Scholar 

  2. B. Armendt. Is there a Dutch Book Argument for probability kinematics? Philosophy of Science, 47, 365–383, 1980.

    Article  Google Scholar 

  3. T. Bayes. An essay towards solving a problem in the doctrine of chances. Philosophical Transactions of the Royal Society, 53, 370–418, 1763.

    Article  Google Scholar 

  4. D. Blackwell and L. Dubins. Merging of opinions with increasing information. annals of Mathematical Statistics, 33, 882–887, 1962.

    Article  Google Scholar 

  5. G. E. P. Box and G. C. Tiao. Bayesian Inference in Statistical Analysis. Addison-Wesley, Reading, MA, 1973.

    Google Scholar 

  6. R. T. Cox. The Algebra of Probable Inference. Johns Hopkins Press, Baltimore, 1961.

    Google Scholar 

  7. A. P. Dawid. The well-calibrated Bayesian. Journal of the American Statistical Association, 77, 605–610, 1982.

    Article  Google Scholar 

  8. A. P. Dawid. Invariant Prior distributions. In Encyclopaedia of Statistical Sciences, S. Kotz and N. L. Johnson, eds. pp. 228–236. Wiley, NY, 1983.

    Google Scholar 

  9. A. P. Dawid, M. Stone and J. V. Zidek. Marginalisation paradoxes in Bayesian and structural inference. Journal of the Royal Statistical Society,B, 189–223, 1973.

    Google Scholar 

  10. B. de Finetti. Foresight, its logical laws, its subjective sources. In Studies in Subjective Probability, H. E. Kyburg and H. Smolker, eds. John Wiley, NY, 1937.

    Google Scholar 

  11. B. de Finetti. Theory of Probability, Vol. 1. John Wiley, NY, 1974.

    Google Scholar 

  12. de Finetti, 1989] B. de Finetti. Recent progress on de Finetti’s notions of exchangability. BayesianStatistics 3,J. M. Bernardo et al.,eds. pp. 111–125. Oxford University Press, Oxford, 1989.

    Google Scholar 

  13. P. Diaconis and D. Freedman. De Finetti’s generalisations of exchangability. Studies in Inductive Logic and Probability, Vol. 2. R. C. Jeffrey, ed. pp. 233–249. University of California Press, Berkeley, 1980.

    Google Scholar 

  14. P. Diaconis and S. Zabell. Updating subjective probability. Journal of the American Statistical Association, 77, 822–830, 1982.

    Article  Google Scholar 

  15. J. Earman. Bayes or Bust? A Critical Examination of Bayesian Confirmation Theory. MIT Press, Cambridge, MA, 1992.

    Google Scholar 

  16. Bayesian statistical inference for psychological research. Psychological Review,70, 193, 1963.

    Google Scholar 

  17. Eells, 19821 E. Eells. Rational Decision and Causality. Cambridge University Press, Cambridge, 1982.

    Google Scholar 

  18. D. Ellsberg. Risk, ambiguity and the Savage axioms. The Quarterly Journal of Economics, 75, 643–669, 1961.

    Article  Google Scholar 

  19. P. Gärdenfors and N-E. Sahlin. Decision, Probability and Utility. Cambridge University Press, 1988.

    Google Scholar 

  20. Counterfactuals and two kinds of expected utility. In Foundations and Applicatioqs of Decision Theory, Vol. 1, C. A. Hooker et al. eds. pp. 125–162, Reidel, Dordrecht, 1978.

    Google Scholar 

  21. D. A. Gillies. An Objective Theory of Probability. Methuen, London, 1971.

    Google Scholar 

  22. D. A. Gillies. Confirmation theory. In Handbook for Practical Reasoning,Vol. 4.

    Google Scholar 

  23. I. J. Good. Good Thinking. University of Minnesota Press, Minneapolis, 1983.

    Google Scholar 

  24. P. Halmos. Measure Theory. van Nostrand-Reinhold, NY, 1950.

    Google Scholar 

  25. C. Howson. On the consistency of Jeffrey’s simplicity postulate and its role in Bayesian inference. The Philosophical Quarterly, 38, 68–83, 1988.

    Article  Google Scholar 

  26. C. Howson. Bayesian updating. In Proceedings of the 1996 Luino Conference,Springer-Verlag, forthcoming.

    Google Scholar 

  27. C. Howson and P. Urbach. Scientific Reasoning: the Bayesian Approach, second edition. Open Court, Chicago, 1993.

    Google Scholar 

  28. E. T. Jaynes. The well-posed problem. Foundations of Physics, 3, 477–493, 1973.

    Article  Google Scholar 

  29. E. T. Jaynes. Prior probabilities. IEEE Transactions on Systems Science and Cybernetics, SSC-4, 227–241, 1968.

    Google Scholar 

  30. R. C. Jeffrey. The Logic of Decision, first edition. McGraw-Hill, NY, 1965.

    Google Scholar 

  31. R. C. Jeffrey. Probability and the Art of Judgement. Cambridge University Press, Cambridge, 1992.

    Book  Google Scholar 

  32. H. Jeffreys. Theory of Probability, third edition. Oxford University Press, Oxford, 1961.

    Google Scholar 

  33. B. O. Koopman. The bases of probability. Bulletin of the American Mathematical Society, 46, 763–774, 1940.

    Article  Google Scholar 

  34. D. Lewis. Probabilities of conditionals and the conditional probabilities. The Philosophical Review, LXXXV, 297–315, 1973.

    Google Scholar 

  35. D. Lewis. A subjectivist’s guide to objective chance. In Studies in Inductive Logic and Probability, Vol. 2. R. C. Jeffrey, ed. pp. 263–293. University of California Press, Berkeley, 1980.

    Google Scholar 

  36. M. Li and P. M. B. Vitanyi. Inductive reasoning and Kolmogorov complexity. Journal of Computer and System Sciences, 44, 343–384, 1992.

    Article  Google Scholar 

  37. D. V. Lindley. Introduction to Probability and Statistics from a Bayesian Viewpoint, part 2. Cambridge University Press, Cambridge, 1965.

    Google Scholar 

  38. D. V. Lindley. Scoring rules and the inevitability of probability. International Statistical Review, 50, 1–26, 1982.

    Article  Google Scholar 

  39. D. V. Lindley The probability approach to the treatment of uncertainty in artificial intelligence and expert systems. Statistical Science, 2, 17–24, 1987.

    Article  Google Scholar 

  40. Luce and Suppes, 1965] R. D. Luce and P. Suppes. Preference, utility and subjective probability. In handbookofMathematical Psychology,Vol. 3, R. D. Luce et al.,eds. pp. 249–410, Wiley, NY, 1965.

    Google Scholar 

  41. J. Pearl. Probabilistic Reasoning in Intelligent Systems, Morgan Kaufmann, San Mateo, 1988.

    Google Scholar 

  42. K. R. Popper. The Logic of Scientific Discovery, Hutchinson, London, 1959.

    Google Scholar 

  43. E. P. Ramsey. Truth and probability Reprinted in Studies in Subjective Probability, H. Kyburg and H. Smolker, eds. pp. 61–93. Wiley, NY, 1926.

    Google Scholar 

  44. H. Reichenbach. The Theory of Probability. University of California Press, Berkeley, 1949.

    Google Scholar 

  45. R. Rosenkrantz. Inference, Method and Decision. Reidel, Dordrecht, 1977.

    Google Scholar 

  46. L. J. Savage. The Foundations of Statistics. Wiley, NY, 1954.

    Google Scholar 

  47. F. Schick. Dutch bookies and money pumps. Journal ofPhilosophy, 83, 112–119, 1986.

    Article  Google Scholar 

  48. M. Schervish and T. Seidenfeld. An approach to consensus and certainty with increasing evidence. Journal of Statistical Planning and Inference, 25, 401–414, 1990.

    Article  Google Scholar 

  49. Skyrms, 1991] B. Skyrms. Stability and chance. In Existence and Explanation,W. Spohn et al.,eds. pp. 149–163,1991.

    Google Scholar 

  50. C. A. B. Smith. Consistency in statistical inference and decision. Journal of the Royal Statistical Society, B, 23, 1–25, 1961.

    Google Scholar 

  51. S. Spielman. Exchangeability and the certainty of objective randomness. Journal of Philosophical Logic, 5, 399–406, 1976.

    Google Scholar 

  52. R. Teller. Conditionalisation and observation. Synthese, 26, 218–258, 1973.

    Article  Google Scholar 

  53. B. C. van Fraassen. The Scientific Image. Oxford University Press, Oxford, 1980.

    Book  Google Scholar 

  54. B. C. van Fraassen. Belief and the will. Journal of Philosophy, 81, 235–256, 1984.

    Article  Google Scholar 

  55. B. C. van Fraassen. Laws and Symmetry. Oxford University Press, Oxford, 1989.

    Book  Google Scholar 

  56. R. von Mises. Probability, Statistics and Truth. George Allen and Unwin, 1939.

    Google Scholar 

  57. J. von Plato. Creating Modern Probability. Cambridge University Press, Cambridge, 1994.

    Book  Google Scholar 

  58. P. Walley. Statistical Reasoning with Imprecise Probabilities. Chapman and Hall, London, 1991.

    Book  Google Scholar 

  59. E M. Williams. Bayesian conditionalisation and the principle of minimum information. British Journal for the Philosophy of Science, 31, 131–144, 1980.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Philosophy, Logic and Scientific Method, The London School of Economics and Political Science, London, UK

    Colin Howson

Authors
  1. Colin Howson
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. IRIDIA, Université Libre de Bruxelles, Belgium

    Philippe Smets

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Howson, C. (1998). The Bayesian Approach. In: Smets, P. (eds) Quantified Representation of Uncertainty and Imprecision. Handbook of Defeasible Reasoning and Uncertainty Management Systems, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1735-9_4

Download citation

  • DOI: https://doi.org/10.1007/978-94-017-1735-9_4

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-5038-0

  • Online ISBN: 978-94-017-1735-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation