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Classical versus Bayesian Statistics

Published online by Cambridge University Press:  01 January 2022

Eric Johannesson
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Abstract

In statistics, there are two main paradigms: classical and Bayesian statistics. The purpose of this article is to investigate the extent to which classicists and Bayesians can (in some suitable sense of the word) agree. My conclusion is that, in certain situations, they cannot. The upshot is that, if we assume that the classicist is not allowed to have a higher degree of belief (credence) in a null hypothesis after he has rejected it than before, then (in certain situations) he has to either have trivial or incoherent credences to begin with or fail to update his credences by conditionalization.

Type
Articles
Information
Philosophy of Science , Volume 87 , Issue 2 , April 2020 , pp. 302 - 318
Copyright
Copyright © The Philosophy of Science Association

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References

Barnett, V. 1999. Comparative Statistical Inference. 3rd ed. Probability and Mathematical Statistics. Chichester, NY: Wiley.CrossRefGoogle Scholar
Berger, J. O. and Sellke, T. 1987. “Testing a Point Null Hypothesis: The Irreconcilability of P Values and Evidence.” Journal of the American Statistical Association 82 (397): 112–22.Google Scholar
Casella, G., and Berger, R. L. 1987. “Reconciling Bayesian and Frequentist Evidence in the One-Sided Testing Problem.” Journal of the American Statistical Association 82 (397): 106–11.CrossRefGoogle Scholar
Fisher, R. A. 1925. Statistical Methods for Research Workers. Edinburgh: Oliver & Boyd.Google Scholar
Jeffreys, H. 1980. “Some General Points in Probability Theory.” In Studies in Bayesian Econometrics: Essays in Honor of Harold Jeffreys, ed. Zellner, A., 451–53. Amsterdam: North-Holland.Google Scholar
Lewis, D. 1980. “A Subjectivist’s Guide to Objective Chance.” In Studies in Inductive Logic and Probability, ed. Jeffrey, R. C., 83–132. Berkeley: University of California Press.Google Scholar
Lindley, D. V. 1957. “A Statistical Paradox.” Biometrika 44 (1/2): 187–92.CrossRefGoogle Scholar
Mayo, D. G., and Spanos, A. 2006. “Severe Testing as a Basic Concept in a Neyman-Pearson Philosophy of Induction.” British Journal for the Philosophy of Science 57 (2): 323–57.CrossRefGoogle Scholar
Mayo, D. G., and Spanos, A. 2011. “Error Statistics.” In Philosophy of Statistics, ed. Bandyopadhyay, P. S. and Forster, M. R., 153–98. Handbook of the Philosophy of Science 7. Amsterdam: North-Holland.Google Scholar
Neyman, J., and Pearson, E. S. 1933a. “On the Problem of the Most Efficient Tests of Statistical Hypotheses.” Philosophical Transactions of the Royal Society of London A 231:289–337.Google Scholar
Neyman, J., and Pearson, E. S. 1933b. “The Testing of Statistical Hypotheses in Relation to Probabilities a Priori.” Mathematical Proceedings of the Cambridge Philosophical Society 29 (4): 492–510.CrossRefGoogle Scholar
Pérez, M.-E., and Pericchi, L. R. 2014. “Changing Statistical Significance with the Amount of Information: The Adaptive α Significance Level.” Statistics and Probability Letters 85:20–24.CrossRefGoogle Scholar
Spanos, A. 2013. “Who Should Be Afraid of the Jeffreys-Lindley Paradox?” Philosophy of Science 80 (1): 73–93.CrossRefGoogle Scholar
Sprenger, J. 2013. “Testing a Precise Null Hypothesis: The Case of Lindley’s Paradox.” Philosophy of Science 80 (5): 733–44.CrossRefGoogle Scholar