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Theories of Probability

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Bayes Theory

Part of the book series: Springer Series in Statistics ((SSS))

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Abstract

A theory of probability will be taken to be an axiom system that probabilities must satisfy, together with rules for constructing and interpreting probabilities. A person using the theory will construct some probabilities according to the rules, compute other probabilities according to the axioms, and then interpret these probabilities according to the rules; if the interpretation is unreasonable perhaps the original construction will be adjusted.

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References

  • Bayes, T. (1763), An essay towards solving a problem in the doctrine of chances, Phil. Trans. Roy. Soc. 53, 370–418

    Article  Google Scholar 

  • Bayes, T. (1763), An essay towards solving a problem in the doctrine of chances, Phil. Trans. Roy. Soc. 54, 296–325, reprinted in Biometrika 45 (1958), 293–315.

    Google Scholar 

  • Bernoulli, James (1713), Ars Conjectandi.

    Google Scholar 

  • Borel, E. (1924), Apropos of a treatise on probability, Revue philosophique, reprinted in H. E. Kyburg and H. E. Smokier (eds.), Studies in Subjective Probability. London: John Wiley, 1964, pp. 47–60.

    Google Scholar 

  • Church, A. (1940), On the concept of a random sequence, Bull. Am. Math. Soc. 46, 130–135.

    Article  MathSciNet  Google Scholar 

  • Cox, D. R. and Hinkley, D. V. (1974), Theoretical Statistics. London: Chapman and Hall.

    MATH  Google Scholar 

  • De Finetti, B. (1937), Foresight: Its logical laws, in subjective sources, reprinted in H. E. Kyburg and H. E. Smokier (eds.), Studies in Subjective Probability. London: John Wiley, 1964, pp. 93–158.

    Google Scholar 

  • Good, I. J. (1950), Probability and the Weighing of Evidence. London: Griffin.

    MATH  Google Scholar 

  • Good, I. J. (1976), The Bayesian influence, or how to sweep subjectivism under the carpet, in Harper and Hooker (eds.), Foundations of Probability Theory, Statistical Inference, and Statistical Theory of Science. Dordrecht: Reidel.

    Google Scholar 

  • Jeffreys, H. (1939), Theory of Probability. London: Oxford University Press.

    Google Scholar 

  • Keynes, J. M. (1921), A Treatise on Probability. London: MacMillan.

    Google Scholar 

  • Kolmogorov, A. N. (1950). Foundations of the Theory of Probability. New York: Chelsea. (The German original appeared in 1933.)

    Google Scholar 

  • Kolmogorov, A. N. (1965), Three approaches to the quantitative definition of information, Problemy Peredaci Informacii 1, 4–7.

    MathSciNet  Google Scholar 

  • Laplace, P. S. (1814), Essai philosophique sur les probabilités, English translation. New York: Dover.

    Google Scholar 

  • Martin-Löf, M. (1966), The definition of random sequences, Information and Control 9, 602–619.

    Article  MathSciNet  Google Scholar 

  • Ramsey, F. (1926), Truth and probability, reprinted in H. E. Kyburg and H. E. Smokier (eds.), Studies in Subjective Probability. New York: John Wiley, 1964, pp. 61–92.

    Google Scholar 

  • Savage, L. J. (1954), The Foundations of Statistics. New York: John Wiley.

    MATH  Google Scholar 

  • Smith, C. A. B. (1961). Consistency in statistical inference and decision, J. Roy. Statist. Soc. B 23, 1–25.

    MATH  Google Scholar 

  • von Mises, R. and Geiringer, H. (1964), The Mathematical Theory of Probability and Statistics. New York: Academic Press.

    Google Scholar 

  • Wallsten, Thomas S. (1974), The psychological concept of subjective probability: a measurement theoretic view: in C. S. Staël von Holstein (ed.), The Concept of Probability in Psychological Experiments. Boston: Reidel, p. 49–72.

    Chapter  Google Scholar 

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© 1983 Springer-Verlag New York Inc.

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Hartigan, J.A. (1983). Theories of Probability. In: Bayes Theory. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8242-3_1

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  • DOI: https://doi.org/10.1007/978-1-4613-8242-3_1

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-8244-7

  • Online ISBN: 978-1-4613-8242-3

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