The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Subjective Probability

  • I. J. Good
Reference work entry
DOI: https://doi.org/10.1057/978-1-349-95189-5_1625

Abstract

The usual meaning of ‘probable’ in ordinary conversation is closely related to its derivation from a Latin word meaning provable or capable of being made convincing. The concept is even clearer in the derivation of the German word Wahrscheinlichkeit, ‘having the appearance of truth’. In fact, when we say an event is probable we usually mean that we would not be surprised (or we ought not to be) if it occurred, or that we would be somewhat surprised (or ought to be) if did not occur. Since ‘surprise’ refers to a personal or subjective experience it seems clear that the ordinary concept of probability is subjectivistic (or else in some sense logical). Also a probability, in this subjective or logical sense, can be more or less large so it can be interpreted as a degree of belief or a rational degree of belief or intensity of conviction. A subjective probability is usually regarded as somewhat more than just a degree of belief – it is a degree of belief that belongs to a body of beliefs from which the worst inconsistencies have been removed by means of detached judgements. In short, the degree of belief should be more or less rational.

This is a preview of subscription content, log in to check access

Bibliography

  1. For an article covering somewhat similar ground to the present one see Good (1982a). On some points it says more and on some less.Google Scholar
  2. For books giving applications of subjective or logical probability in statistics see, for example, Jeffreys (1939–1961), Lindley (1965), Zellner (1971, 1980), De Groot (1970), Box and Tiao (1973), Rosenkratz (1977), Good (1965, 1983a), and Berger (1985).Google Scholar
  3. Bayes, T. 1763. An essay toward solving a problem in the doctrine of chances (with discussion and a foreword by Richard Price). Philosophical Transactions of the Royal Society 53: 370–418; 54: 295–325. Reprinted by the Graduate School, US Department of Agriculture, Washington, DC (1940); and in Biometrika 45 (1958), 293–315.CrossRefGoogle Scholar
  4. Berger, J.O. 1984. The robust Bayesian viewpoint. In Robustness of Bayesian analysis, ed. J.B. Kadane, 64–144. Amsterdam: North-Holland.Google Scholar
  5. Berger, J.O. 1985. Statistical decision theory and Bayesian analysis, 2nd ed. New York: Springer.CrossRefGoogle Scholar
  6. Bernardo, J.M., M.H. De Groot, D.V. Lindley, and A.F.M. Smith (eds.). 1983–1985. Bayesian Statistics 2: Proceedings of the second Valencia international meeting. September 6–10, 1983. Amsterdam: North-Holland.Google Scholar
  7. Box, G.E.P., and G.C. Tiao. 1973. Bayesian inference in statistical analysis. Reading, MA: Addison-Wesley.Google Scholar
  8. Carnap, R. 1952. The continuum of inductive methods. Chicago: University of Chicago Press.Google Scholar
  9. Cox, R.T. 1946. Probability, frequency and reasonable expectation. American Journal of Physics 14: 1–13.CrossRefGoogle Scholar
  10. Cox, R.T. 1961. The algebra of probable inference. Baltimore: Johns Hopkins University Press.Google Scholar
  11. de Finetti, B. 1937. La prévision: ses lois logiques, ses sources subjectives. Annales de l’Institut Henri Poincaré 7: 1–68. Translated in Kyburg and Smokler (1980).Google Scholar
  12. de Finetti, B. 1968–1970. Initial probabilities: A prerequisite for any valid induction. Synthese 20, 1969, 2–24 (with discussion). In Induction, physics and ethics: Proceedings and discussions of the 1968 Salzburg Colloquium in the Philosophy of Science, ed. P. Weingartner and G. Zechs. Dordrecht: D. Reidel, 1970.Google Scholar
  13. De Groot, M.H. 1970. Optimal statistical decisions. New York: McGraw-Hill.Google Scholar
  14. Geisser, S. 1983–1985. On the prediction of observables: A selective update, in Bernardo et al. (1983–1985), 203–229 (with discussion).Google Scholar
  15. Good, I.J. 1950. Probability and the weighing of evidence. London/New York: Charles Griffin/Hafners.Google Scholar
  16. Good, I.J. 1952. Rational decisions. Journal of the Royal Statistical Society B 14: 107–114. Reprinted in Good (1983a).Google Scholar
  17. Good, I.J. 1953–1957. The appropriate mathematical tools for describing and measuring uncertainty. In Uncertainty and business decisions, ed. C.F. Carter, G.P. Meredith, and G.L.S. Shackle, 20–36. Liverpool: Liverpool University Press. Partly reprinted in Good (1983a).Google Scholar
  18. Good, I.J. 1960–1962. Subjective probability as the measure of a non-measurable set. In Logic, methodology, and philosophy of science, ed. E. Nagel, P. Suppes, and A. Tarski, 319–329. Stanford: Stanford University Press. Reprinted in Kyburg and Smokler (1980) and in Good (1983a).Google Scholar
  19. Good, I.J. 1965. The estimation of probabilities: An essay on modern Bayesian methods. Cambridge, MA: MIT Press.Google Scholar
  20. Good, I.J. 1966. How to estimate probabilities. Journal of the Institute of Mathematics and its Applications 2: 364–383.CrossRefGoogle Scholar
  21. Good, I.J. 1968. Corroboration, explanation, evolving probability, simplicity, and a sharpened razor. British Journal for the Philosophy of Science 19: 123–143.CrossRefGoogle Scholar
  22. Good, I.J. 1977. Dynamic probability, computer chess, and the measurement of knowledge. In Machine intelligence, vol. 8, ed. E.W. Elcock and D. Michie, 139–150. Chichester: Ellis Horwood. Reprinted in Good (1983a).Google Scholar
  23. Good, I.J. 1979–1981. Some history of the hierarchical Bayesian methodology. In Bayesian Statistics: Proceedings of the First International Meeting held in Valencia (Spain), May 28–June 2, 1979, ed. J.M. Bernardo, M.H. De Groot, D.V. Lindley, and A.F.M. Smith, University of Valencia, 1981, 489–510 and 512–519 (with discussion).Google Scholar
  24. Good, I.J. 1981–1983. The robustness of a hierarchical model for multinomials and contingency tables. In Scientific inference, data analysis, and robustness, ed. G.E.P. Box, Tom Leonard, and Chien-Fu Wu, New York: Academic Press.Google Scholar
  25. Good, I.J. 1982a. Degrees of belief. In Encyclopedia of statistical sciences, vol. 2, ed. S. Kotz and N.L. Johnson, 287–293. New York: Wiley.Google Scholar
  26. Good, I.J. 1982b. Standardized tail-area probabilities. Journal of Statistical Computation and Simulation 16: 65–66.CrossRefGoogle Scholar
  27. Good, I.J. 1983a. Good thinking: The foundations of probability and its applications. Minneapolis: University of Minnesota Press.Google Scholar
  28. Good, I.J. 1983b. The philosophy of exploratory data analysis. Philosophy of Science 50: 283–295.CrossRefGoogle Scholar
  29. Good, I.J. 1983c. A correction concerning my interpretation of Peirce, and the Bayesian interpretation of Neyman–Pearson ‘hypothesis determination. Journal of Statistical Computation and Simulation 18: 71–74.CrossRefGoogle Scholar
  30. Good, I.J. 1983d. The diminishing significance of a fixed P-value as the sample size increases: A discrete model. Journal of Statistical Computation and Simulation 16: 312–314.CrossRefGoogle Scholar
  31. Good, I.J. 1984. The best explicatum for weight of evidence. Journal of Statistical Computation and Simulation 19: 294–299.CrossRefGoogle Scholar
  32. Good, I.J. 1985a. Weight of evidence: A brief survey. In Bernardo et al. 1983–85, 249–269 (with discussion).Google Scholar
  33. Good, I.J. 1985b. A historical comment concerning novel confirmation. British Journal for the Philosophy of Science 36: 184–185.Google Scholar
  34. Good, I.J. 1986a. Statistical evidence. In Encyclopedia of statistical sciences, vol. 8, ed. S. Kotz, N.L. Johnson, and C. Read. New York: Wiley.Google Scholar
  35. Good, I.J. 1986b. Surprise index. In Encyclopedia of statistical sciences, vol. 9, ed. S. Kotz, N.L. Johnson, and C. Read. New York: Wiley.Google Scholar
  36. Haldane, J.B.S. 1931. A note on inverse probability. Proceedings of the Cambridge Philosophical Society 28: 55–61.CrossRefGoogle Scholar
  37. Hardy, G.F. 1889. In correspondence in Insurance Record, reprinted in Transactions of the Faculty of Actuaries 8, (1920), 174–182, esp. 181.Google Scholar
  38. Hogarth, R.M. 1975. Cognitive processes and the assessment of subjective probability distributions. Journal of the American Statistical Association 70: 271–294.CrossRefGoogle Scholar
  39. Jeffreys, H. 1926. Further significance tests. Proceedings of the Cambridge Philosophical Society 32: 416–445.CrossRefGoogle Scholar
  40. Jeffreys, H. 1957. Scientific inference, 2nd ed. Cambridge: Cambridge University Press.Google Scholar
  41. Jeffreys, H. 1961. Theory of probability. Oxford: Clarendon Press.Google Scholar
  42. Johnson, W.E. 1932. Appendix (ed. R.B. Braithwaite) to ‘Probability: Deductive and inductive problems’. Mind 41: 421–423.Google Scholar
  43. Keynes, J.M. 1921. A treatise on probability. London: Macmillan.Google Scholar
  44. Koopman, B.O. 1940a. The basis of probability. Bulletin of the American Mathematical Society 46: 763–774.CrossRefGoogle Scholar
  45. Koopman, B.O. 1940b. The axioms and algebra of intuitive probability. Annals of Mathematics 41: 269–292.CrossRefGoogle Scholar
  46. Kyburg, H.E., and H.E. Smokler (eds.). 1980. Studies in subjective probability, 2nd ed. Huntington/New York: Robert E. Krieger (1st ed, New York: Wiley, 1964).Google Scholar
  47. Lindley, D.V. 1965. Introduction to probability and statistics, vol. 2. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  48. Novick, M.R., and P.H. Jackson. 1974. Statistical methods for educational and psychological research. New York: McGraw-Hill.Google Scholar
  49. Pearson, K. 1892. The grammar of science. Reprinted, London: J.M. Dent & Sons, 1937.Google Scholar
  50. Pearson, K. 1899. Theory of genetic (reproductive) selection. Philosophical Transactions of the Royal Society of London (A) 192: 260–278, esp. 277–278, ‘On the spurious correlation produced by forming a mixture of heterogeneous but uncorrelated materials’.Google Scholar
  51. Peirce, C.S. 1878. The probability of induction. Popular Science Monthly. Reprinted in The world of mathematics, vol. 2, ed. James R. Newman. New York: Simon & Schuster, 1956, 1341–1354.Google Scholar
  52. Poisson, S.-D. 1837. Recherches sur la probabilité des jugements en matière criminelle et en matière civile. Paris: Bachelier.Google Scholar
  53. Ramsey, F.P. 1926. Truth and probability. In The foundations of mathematics and other logical essays. London/New York: Kegan Paul/Harcourt, Brace & Co. Reprinted in Kyburg and Smokler (1980).Google Scholar
  54. Rosenkrantz, R.D. 1977. Inference, method and decision. Dordrecht: Reidel.CrossRefGoogle Scholar
  55. Savage, L.J. 1954. The foundations of statistics. New York: Wiley.Google Scholar
  56. Schroedinger, E. 1947. The foundation of probability. Proceedings of the Royal Irish Academy 51A: 51–66 and 141–146.Google Scholar
  57. Shackle, G.L.S. 1949. Expectation in economics. Cambridge: Cambridge University Press.Google Scholar
  58. Smith, C.A.B.. 1961. Consistency in statistical inference and decision. Journal of the Royal Statistical Society, Series B 23: 1–37 (with discussion).Google Scholar
  59. Weaver, W. 1948. Probability, rarity, interest and surprise. Scientific Monthly 67: 390–392.Google Scholar
  60. Yule, G.U. 1903. Notes on the theory of association of attributes in statistics. Biometrika 2: 121–134. Reprinted in Statistical papers of George Udny Yule, ed. A. Stuart and M.G. Kendall. London: Griffin, 1971, 71–84.Google Scholar
  61. Zellner, A. 1971. An introduction to Bayesian inference in econometrics. New York: Wiley.Google Scholar
  62. Zellner, A. (ed.). 1980. Bayesian analysis in econometrics and statistics: Essays in honor of Harold Jeffreys. Amsterdam: North-Holland.Google Scholar

Copyright information

© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • I. J. Good
    • 1
  1. 1.