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Bayesian statistics and biased procedures

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Abstract

A comparison of Neyman's theory of interval estimation with the corresponding subjective Bayesian theory of ‘credible intervals’ shows that the Bayesian approach to the estimation of statistical parameters allows experimental procedures which, from the orthodox objective viewpoint, are clearly biased and clearly inadmissible. This demonstrated methodological difference focuses attention on the key difference in the two general theories, namely, that the orthodox theory is supposed to provide a known average frequency of successful estimates, whereas the Bayesian account provides only a coherent ordering of degrees of belief and a subsequent maximization of subjective expected utilities. To rebut the charge of allowing biased procedures, the Bayesian must attack the foundations of orthodox, objectivist methods. Two apparently popular avenues of attack are briefly considered and found wanting. The first is that orthodox methods fail to apply to the single case. The second is that orthodox methods are subject to a typical Humean regress. The conclusion is that orthodox objectivist methods remain viable in the face of the subjective Bayesian alternative — at least with respect to the problem of statistical estimation.

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Bibliography

  1. Anscombe, F. J.: 1957, ‘Dependence of the Fiducial Argument on the Sampling Rule’, Biometrika 44, 464–9.

    Google Scholar 

  2. Carnap, Rudolf: 1962, ‘The Aim of Inductive Logic’, in Logic, Methodology and Philosophy of Science (ed. by E. Nagel, P. Suppes, and A. Tarski), Stanford University Press, Stanford, pp. 303–18.

    Google Scholar 

  3. Clooper, C. J. and Pearson, E. S.: 1934, ‘The Use of Confidence or Fiducial Limits Illustrated in the Case of the Binomial’, Biometrika 26, 404–13.

    Google Scholar 

  4. De Finetti, Bruno: 1964, ‘Forsight: its Logical Laws, its Subjective Sources’, in Studies in Subjective Probability (ed. and tr. by H. E. Kyburg, Jr., and H. E. Smokler), Wiley, New York.

    Google Scholar 

  5. Edwards, Ward, Lindman, H., and Savage, L. J.: 1963, ‘Bayesian Statistical Inference for Psychological Research’, Psychological Review 70, 193–242.

    Google Scholar 

  6. Freeman, Harold: 1963, Introduction to Statistical Inference, Addison-Wesley, Reading, Mass.

    Google Scholar 

  7. Giere, Ronald N.: 1969, ‘Classical Interval Estimation as a Fundamental Inductive Method’, in Minnesota Studies in the Philosophy of Science: Inductive Logic and Probability (ed. by G. Maxwell), University of Minnesota Press, Minneapolis (forthcoming).

    Google Scholar 

  8. Hacking, Ian: 1965, Logic of Statistical Inference, Cambridge University Press, Cambridge.

    Google Scholar 

  9. Hacking, Ian: 1967, ‘Slightly More Realistic Personal Probability’, Philosophy of Science 34, 311–25.

    Google Scholar 

  10. Jeffrey, R. C.: 1965, The Logic of Decision, McGraw-Hill, New York.

    Google Scholar 

  11. Kemeny, John G.: 1955, ‘Fair Bets and Inductive Probabilities’, Journal of Symbolic Logic 20, 263–73.

    Google Scholar 

  12. Kendall, M. G. and Stuart, A.: 1958–61, The Advanced Theory of Statistics, Vols. 1 and 2, Charles Griffin & Co., London.

    Google Scholar 

  13. Levi, Isaac: 1967, Gambling with Truth, Knopf, New York.

    Google Scholar 

  14. Mellor, D. H.: 1969, ‘Chance’, Proceedings of the Aristotelian Society Supplementary Volume (forthcoming).

  15. Neyman, Jerzy: 1937, ‘Outline of a Theory of Statistical Estimation Based on the Classical Theory of Probability’, Philosophical Transactions of the Royal Society of London, Series A 136, 338–80.

    Google Scholar 

  16. Neyman, Jerzy: 1952, Lectures and Conferences on Mathematical Statistics and Probability, 2nd rev. ed., The Graduate School, U.S.D.A., Washington, D.C.

    Google Scholar 

  17. Peirce, C. S.: 1934–58, Collected Papers of Charles Sanders Peirce, 8 vols., Harvard University Press, Cambridge, Mass.

    Google Scholar 

  18. Popper, Karl R.: 1959, ‘The Propensity Interpretation of Probability’, British Journal for the Philosophy of Science 10, 25–42.

    Google Scholar 

  19. Reichenbach, Hans: 1949, The Theory of Probability, University of California Press, Berkeley.

    Google Scholar 

  20. Salmon, Wesley C.: 1966, The Foundations of Scientific Inference, University of Pittsburgh Press, Pittsburgh.

    Google Scholar 

  21. Savage, Leonard J.: 1954, The Foundations of Statistics, Wiley, New York.

    Google Scholar 

  22. Savage, Leonard J.: 1961, ‘The Foundations of Statistics Reconsidered’, in Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability (ed. by J. Neyman), Vol. I, University of California Press, Berkeley, pp. 575–8.

    Google Scholar 

  23. Savage, Leonard J.: 1962, ‘Bayesian Statistics’, in Recent Developments in Decision and Information Processes (ed. by Robert E. Machol and Paul Gray), Macmillan, New York.

    Google Scholar 

  24. Savage, Leonard J.: 1962, ‘Subjective Probability and Statistical Practice’, in The Foundations of Statistical Inference (ed. by D. R. Cox), Methuen, London.

    Google Scholar 

  25. Schlaifer, R.: 1959, Probability and Statistics for Business Decisions, McGraw-Hill, New York.

    Google Scholar 

  26. Shimony, Abner: 1967, ‘Amplifying Personal Probability’, Philosophy of Science 34, 326–32.

    Google Scholar 

  27. Suppes, Patrick: 1956, ‘The Role of Subjective Probability and Utility in Decision-Making’, in Third Berkeley Symposium on Mathematical Statistics and Probability (ed. by J. Neyman), University of California Press, Berkeley, Vol. 5, pp. 61–73.

    Google Scholar 

  28. Suppes, Patrick: 1966, ‘A Bayesian Approach to the Paradoxes of Confirmation’, in Aspects of Inductive Logic (ed. by Jaakko Hintikka and Patrick Suppes), North-Holland Publ. Co., Amsterdam, pp. 198–207.

    Google Scholar 

  29. Venn, John: 1866, The Logic of Chance, London. Paperback reprint of the 4th ed. (1888): Chelsea, New York, 1962.

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Giere, R.N. Bayesian statistics and biased procedures. Synthese 20, 371–387 (1969). https://doi.org/10.1007/BF00413734

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