Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-24T08:08:51.884Z Has data issue: false hasContentIssue false

Error Probabilities in Error

Published online by Cambridge University Press:  01 April 2022

Colin Howson*
Affiliation:
London School of Economics
*
Department of Philosophy, London School of Economics, Houghton Street, London WC2A 2AE, England.

Abstract

The Bayesian theory is outlined and its status as a logic defended. In this it is contrasted with the development and extension of Neyman-Pearson methodology by Mayo in her recently published book (1996). It is shown by means of a simple counterexample that the rule of inference advocated by Mayo is actually unsound. An explanation of why error-probablities lead us to believe that they supply a sound rule is offered, followed by a discussion of two apparently powerful objections to the Bayesian theory, one concerning old evidence and the other optional stopping.

Type
Symposium: Philosophy of Statistics and Epistemology of Experiment: Bayesian vs. Error Statistical Approaches
Copyright
Copyright © Philosophy of Science Association 1997

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Thanks are due to Lawrence Jackson, Milo Schield, and Peter Urbach for their help, and to the British Academy for financial assistance.

References

BMJ (1996), British Medical Journal 313: 569.10.1136/bmj.313.7057.569CrossRefGoogle Scholar
Earman, J. (1992), Bayes or Bust? A Critical Examination of Bayesian Confirmation Theory. Cambridge, MA: MIT Press.Google Scholar
Garber, D. (1983), “Old Evidence and Logical Omniscience in Bayesian Confirmation Theory”, in Earman, J. (ed.), Testing Scientific Theories. Minneapolis: University of Minnesota Press, pp. 99131.Google Scholar
Glymour, C. (1980), Theory and Evidence. Princeton: Princeton University Press.Google Scholar
Good, I.J. (1983), Good Thinking: The Foundations of Probability and its Applications. Minneapolis: University of Minnesota Press.Google Scholar
Howson, C. and Urbach, P. (1993), Scientific Reasoning: The Bayesian Approach. 2nd ed. Chicago: Open Court.Google Scholar
Kadane, J.B., Schervish, M. J., and Seidenfeld, T. (1996), “When Several Bayesians Agree that There Will Be No Reasoning to a Foregone Conclusion”, Philosophy of Science 63 (Proceedings): S281S289.10.1086/289962CrossRefGoogle Scholar
Korb, K. (1991), “Explaining Science”, British Journal for the Philosophy of Science 42: 239253.10.1093/bjps/42.2.239CrossRefGoogle Scholar
Mayo, D. (1996), Error and the Growth of Experimental Knowledge. Chicago: University of Chicago Press.10.7208/chicago/9780226511993.001.0001CrossRefGoogle Scholar
Popper, K.R. (1972), Objective Knowledge. Oxford: Clarendon Press.Google Scholar
Rosenkrantz, R. (1977), Inference, Method and Decision: Toward A Bayesian Philosophy of Science. Dordrecht: Reidel.10.1007/978-94-010-1237-9CrossRefGoogle Scholar
Savage, L.J. (ed.), (1962), The Foundations of Statistical Inference: A Discussion. London: Methuen.Google Scholar
Schield, M. (1996), “Using Bayesian Inference in Classical Hypothesis Testing”. Proceedings of the Statistical Education Section. Washington, D.C.: American Statistical Association.Google Scholar
Seidenfeld, T. (1979), “Why I am not an Objective Bayesian; Some Reflections Prompted by Rosenkrantz”, Theory and Decision 11: 413440.10.1007/BF00139451CrossRefGoogle Scholar