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When Several Bayesians Agree that There will be no Reasoning to a Foregone Conclusion

Published online by Cambridge University Press:  01 April 2022

Joseph B. Kadane ,
Mark J. Schervish  and
Teddy Seidenfeld
Joseph B. Kadane
Affiliation:
Carnegie Mellon University
Mark J. Schervish
Affiliation:
Carnegie Mellon University
Teddy Seidenfeld
Affiliation:
Carnegie Mellon University
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Abstract

When can a Bayesian investigator select an hypothesis H and design an experiment (or a sequence of experiments) to make certain that, given the experimental outcome(s), the posterior probability of H will be lower than its prior probability? We report an elementary result which establishes sufficient conditions under which this reasoning to a foregone conclusion cannot occur. Through an example, we discuss how this result extends to the perspective of an onlooker who agrees with the investigator about the statistical model for the data but who holds a different prior probability for the statistical parameters of that model. We consider, specifically, one-sided and two-sided statistical hypotheses involving i.i.d. Normal data with conjugate priors. In a concluding section, using an “improper” prior, we illustrate how the preceding results depend upon the assumption that probability is countably additive.

Type
Confirmation
Information
Philosophy of Science , Volume 63 , Issue S3 , 1996 , pp. S281 - S289
Copyright
Copyright © Philosophy of Science Association 1996

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Footnotes

†

This research was supported by ONR contract N00014-89-J-1851, and NSF grants DMS-9303557 and SES-9123370.

‡

Department of Philosophy, Carnegie Mellon University, Schenley Park, Pittsburgh, PA 152133890.

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