Abstract
What do data tell us about hypotheses or claims? When do data provide good evidence for or a good test of a hypothesis? These are key questions for a philosophical account of evidence and inference, and in answering them, philosophers of science have often appealed to formal accounts of probabilistic and statistical inference. In so doing, it is obvious that the answer will depend on the principles of inference embodied in one or another statistical account. If inference is by way of Bayes’ theorem, then two data sets license different inferences only by registering differently in the Bayesian algorithm. If inference is by way of error statistical methods (e.g., Neyman and Pearson methods), as are commonly used in applications of statistics in science, then two data sets license different inferences or hypotheses if they register differences in the error probabilistic properties of the methods.
The likelihood principle emphasized in Bayesian statistics implies, among other things, that the rules governing when data collection stops are irrelevant to data interpretation. It is entirely appropriate to collect data until a point has been proved or disproven... [Edwards et al., 1963, p. 193].
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Bibliography
H. Akaike. On the fallacy of the likelihood principle. Statistics and Probability Letters 1, 75–78, 1982.
P. Armitage. Contribution to discussion in L. Savage, ed. 1962.
P. Armitage. Sequential Medical Trials. Oxford: Blackwell, 1975.
G. A. Barnard. Statistical inference. Journal of the Royal Statistical Society, Series B (Methodologial), 11, 115–149, 1949.
G. A. Barnard. Contribution to discussion in L. Savage, ed. 1962.
G. A. Barnard and V. P. Godambe. Memorial article: Allan Birnbaum 1923–1976. The Annals of Statistics 10, 1033–1039, 1982.
V. Barnett. Comparative Statistical Inference, 2nd edition. John Wiley, New York 1982.
J. O. Berger. Statistical Decision Theory and Bayesian Analysis. 2nd edition. Springer-Verlag, New York, 1985.
J. O. Berger and D. A. Berry. The relevance of stopping rules in statistical inference. In Statistical Decision Theory and Related Topics IV, vol. 1, S. S. Gupta and J. Berger, eds. Springer-Verlag, 1987.
J. O. Berger and R. L. Wolpert. The Likelihood Principle, 2nd edition. Institute of Mathematical Statistics, Hayward, CA, 1988.
J. M. Bernardo. Reference posterior distributions for Bayesian inference (with discussion). Journal of the Royal Statistical Society, series B: 41, 113–147, 1979.
J. M. Bernardo. Noninformative priors do not exist: A discussion with José M. Bernardo (with discussion). Journal of Statistical Planning and Inference 65, 159–189, 1997.
A. Birnbaum. On the foundations of statistical inference: binary experiments. Annals of Mathematical Statistics 32, 414–435, 1961.
A. Birnbaum. On the foundations of statistical inference. Journal of the American Statistical Association, 57, 269–306, 1962.
Birnbaum, 1969] A. Birnbaum. Concepts of statistical evidence. In Essays in Honor of Ernest Nagel
Sidney Morgenbesser, Patrick Suppes and Morton White, eds. St. Martin’s Press, 1969.
A. Birnbaum. More on concepts of statistical evidence. Journal of the American Statistical Association. 67, 858–861, 1972.
J. F. Bjomstad. Bimbaum (1962) on the foundations of statistical inference. In Breakthroughs in Statistics, vol. 1, 461–477. Samuel Kotz and Norman L. Johnson, eds. Springer-Verlag, New York, 1992.
G. Box and G. Tiao. Bayesian Inference in Statistical Analysis. Addison-Wesley, Reading, MA, 1973.
A. W. F. Edwards. Likelihood (2nd edition). Cambridge University Press, 1992.
W. Edwards, H. Lindman and L. J. Savage. Bayesian statistical inference for psychological research. Psychological Review 70, 450–499, 1963.
W. K. Feller. Statistical aspects of ESP. Journal of Parapsychology 4, 271–298, 1940.
R. N. Giere. Alan Bimbaum’s conception of statistical evidence. Synthese, 36, 5–13, 1977.
D. A. Gillies. Bayesianism versus falsificationism. Ratio, 3, 82–98, 1990.
I. J. Good. Good Thinking. University of Minnesota Press, Minneapolis, MN, 1983.
B. M. Hill. The validity of the likelihood principle. The American Statistician, 47, 95–100, 1987.
C. Howson and P. Urbach. Scientific Reasoning: The Bayesian Approach, second edition. Open Court, Chicago, 1993.
H. Jeffreys. Theory of Probability, 3rd edition. Clarendon Press, Oxford, 1961.
D. J. Johnstone, G. A. Barnard and D. V. Lindley. Tests of significance in theory and practice. The American Statistician,35, 491–504, 1986.
J. B. Kadane, M.J. Schervish and T. Seidenfeld. Rethinking the Foundations of Statistics. Cambridge University Press, Cambridge, 1999.
D. Kerridge. Bounds for the frequency of misleading Bayes’ inferences. Annals of Mathematical Statistics 34, 1109–1110, 1963.
D. V. Lindley. Bayesian Statistics — A Review. J. W. Arrowsmith, Bristol, 1972.
D. Mayo. Error and the Growth of Experimental Knowledge. University of Chicago Press, Chicago, 1996.
D. Mayo. experimental practice and an error statistical account of evidence. Philosophy of Science, 67, (Proceedings), S193–S207, 2000.
D. Mayo and A. Spanos. A Post-data Interpretation of Neyman-Pearson Methods Based on a Conception of Severe Testing. Measurements in Physics and Economics Discussion Paper Series, DP MEAS 8/00. Centre for Philosophy of Natural and Social Science, London School of Economics, 2000.
M. Oakes. Statistical Inference, Wiley, 1986.
E. S. Pearson and J. Neyman. On the problem of two samples. Bull. Acad. Pol. Sci., 73–96, 1930. Reprinted in J. Neyman and E. S. Pearson, Joint Statistical Papers. pp. 81–106 University of California Press, Berkeley, 1967.
J. W. Pratt, H. Raffia and R. Schlaifer. Introduction to Statistical Decision Theory. The MIT Press, Cambridge, MA, 1995.
H. V. Roberts. Informative stopping rules and inferences about population size. Journal of the American Statistical Association. 62, 763–775, 1967.
R. D. Rosenkrantz. Inference, Method, and Decision: Towards a Bayesian Philosophy of Science. Boston: Reidel, 1977.
R. Royall. The elusive concept of statistical evidence (with discussion). In Bayesian Statistics 4, J.M. Bernardo, J.O. Berger, A.P. Dawid and A.F.M. Smith, eds. pp. 405–418. Oxford University Press, Oxford, 1992.
R. Royall. Statistical Evidence: A Likelihood Paradigm. Chapman and Hall, London, 1997
L. J. Savage. The Foundations of Statistical Inference: A Discussion. Methuen, London, 1962.
L. J. Savage. The foundations of statistics reconsidered. In Studies in Subjective Probability, H. Kyberg and H. Smokier, eds. John Wiley, New York, 1964.
T. Seidenfeld. Why I am not an objective Bayesian. Theory and Decision 11, 413–440, 1979.
C. A. B. Smith. Consistency in statistical inference and decision (with discussion). Journal of the Royal Statistical Society, (B), Vol. 23, No. 1, 1–37, 1961.
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Mayo, D.G., Kruse, M. (2001). Principles of Inference and Their Consequences. In: Corfield, D., Williamson, J. (eds) Foundations of Bayesianism. Applied Logic Series, vol 24. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1586-7_16
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