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Probability theory and its models

Paul Humphreys

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Abstract

This paper argues for the status of formal probability theory as a mathematical, rather than a scientific, theory. David Freedman and Philip Stark’s concept of model based probabilities is examined and is used as a bridge between the formal theory and applications.

Chapter information

Source
Deborah Nolan and Terry Speed, eds., Probability and Statistics: Essays in Honor of David A. Freedman (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2008), 1-11

Dates
First available in Project Euclid: 7 April 2008

Permanent link to this document
https://projecteuclid.org/euclid.imsc/1207580074

Digital Object Identifier
doi:10.1214/193940307000000347

Mathematical Reviews number (MathSciNet)
MR2459945

Zentralblatt MATH identifier
1167.60302

Subjects
Primary: 62A01: Foundations and philosophical topics

Keywords
David Freedman Kolmogorov models Poisson process probability theory

Rights
Copyright © 2008, Institute of Mathematical Statistics

Citation

Humphreys, Paul. Probability theory and its models. Probability and Statistics: Essays in Honor of David A. Freedman, 1--11, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2008. doi:10.1214/193940307000000347. https://projecteuclid.org/euclid.imsc/1207580074


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References

  • [1] Anderson, M., Ensher, J., Matthews, M., Wieman, C. and Cornell, E. (1995). Observation of Bose–Einstein condensation in a dilute atomic vapor. Science 269 198.
  • [2] Bharucha-Reid, A. (1960). Elements of the Theory of Markov Processes and Their Applications. McGraw-Hill Book Company, New York.
  • [3] Clarke, R. (1946). An Application of the Poisson distribution. J. Institute of Actuaries 72 48.
  • [4] De Finetti, B. (1964). Foresight: Its logical laws, its subjective sources. In Studies in Subjective Probability (H. Kyburg and H. Smokler, eds.) 93–158. Wiley, New York.
  • [5] Diaconis, P., Holmes, S. and Montgomery, R. (2007). Dynamical bias in the coin toss. SIAM Rev. 49 211–235.
  • [6] Freedman, D. (1995). Some Issues in the foundations of statistics (with comments by James Berger, E. L. Lehmann, Paul Holland, Clifford Clogg and Neil Henry, with a rejoinder). Foundations of Science 1 19–83.
  • [7] Freedman, D. (1997). From association to causation via regression (with discussion). In Causality in Crisis? (V. McKim and S. Turner, eds.) 113–182. University of Notre Dame Press, South Bend.
  • [8] Freedman, D. (2005). Statistical Models: Theory and Practice. Cambridge Univ. Press.
  • [9] Freedman, D. and Stark, P. (2003). What is the probability of an earthquake? Earthquake Science and Seismic Risk Reduction 32 201–213.
  • [10] Hilbert, D. (1901). Mathematical Problems. Bull. American Math. Soc. 8 437–479.
  • [11] Hochkirchen, T. (1999). Die Axiomatisierung der Wahrscheinlichkeitsrechnung und ihre Kontext. In Von Hilberts sechstem Problem zu Kolmogoroffs Grundbegriffen. Vandenhoeck & Ruprecht, Göttingen.
  • [12] Humphreys, P. (2004). Extending Ourselves. Oxford Univ. Press, New York.
  • [13] Itô, K. (1984). Introduction to Probability Theory. Cambridge Univ. Press.
  • [14] Keller, J. B. (1986). The Probability of Heads. Amer. Math. Monthly 93 191–197.
  • [15] Kolmogorov, A. (1933/1956). Foundations of the Theory of Probability, 2nd English edition. Chelsea Publishing Company, New York. Translation of Grundbegriffe der Wahrscheinlichkeitsrechnung, Berlin, 1933.
  • [16] Laplace, P.-S. (1995). Philosophical Essay on Probabilities. Springer, New York.
  • [17] Montague, R. (1962). Deterministic theories. Decisions, Values and Groups 2 325–370. Reprinted as Chapter 11 of Formal Philosophy: Selected Papers of Richard Montague (R. Thomason, ed.) Yale Univ. Press, New Haven, 1974.
  • [18] Popper, K. (1959). The Logic of Scientific Discovery. Hutchinson, London.
  • [19] Quine, W. (1951). Two Dogmas of Empiricism. Philosophical Rev. 60 20–43.
  • [20] Reichenbach, H. (1949). The Theory of Probability. Univ. California Press, Berkeley.
  • [21] Renyi, A. (1970). Foundations of Probability. Holden-Day, San Francisco.
  • [22] Van Fraassen, B. (1980). The Scientific Image. Oxford Univ. Press.
  • [23] Von Mises, R. (1931). Wahrscheinlichkeitsrechnung und ihre Anwendung in der Statistik und theoretischen Physik. Deuticke, Leipzig.
  • [24] Von Mises, R. (1964). The Mathematical Theory of Probability and Statistics. Academic Press, New York.
  • [25] Von Plato, J. (1994). Creating Modern Probability. Cambridge Univ. Press.
  • [26] Walley, P. (1991). Statistical Reasoning with Imprecise Probabilities. Chapman and Hall, London.