Hostname: page-component-848d4c4894-hfldf Total loading time: 0 Render date: 2024-06-01T17:09:52.319Z Has data issue: false hasContentIssue false
  • English
  • Français

On Indeterminate Updating of Credences

Published online by Cambridge University Press:  01 January 2022

Leendert Huisman
Get access Rights & Permissions [Opens in a new window]

Abstract

The strategy of updating credences by minimizing the relative entropy has been questioned by many authors, most strongly by means of the Judy Benjamin puzzle. I present a new analysis of Judy Benjamin–like forms of new information and defend the thesis that in general the rational posterior is indeterminate, meaning that a family of posterior credence functions rather than a single one is the rational response when that type of information becomes available. The proposed thesis extends naturally to all cases in which new information is traditionally handled by minimizing the relative entropy.

Type
Research Article
Information
Philosophy of Science , Volume 81 , Issue 4 , October 2014 , pp. 537 - 557
Copyright
Copyright © The Philosophy of Science Association

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.)

References

Ali, S. M., and Silvey, S. D.. 1966. “A General Class of Coefficients of Divergence of One Distribution from Another.” Journal of the Royal Statistical Society B 28:131–42.Google Scholar
Bradley, Richard. 2005. “Radical Probabilism and Bayesian Conditioning.” Philosophy of Science 72:342–64.CrossRefGoogle Scholar
Csiszár, Imre, and Shields, Paul C.. 2004. “Information Theory and Statistics: A Tutorial.” Foundations and Trends in Communications and Information Theory 1:417–528.CrossRefGoogle Scholar
Diaconis, Persi, and Zabell, Sandy L.. 1982. “Updating Subjective Probability.” Journal of the American Statistical Association 77:822–30.CrossRefGoogle Scholar
Douven, Igor, and Romeijn, Jan-Willem. 2011. “A New Resolution of the Judy Benjamin Problem.” Mind 120:637–70.CrossRefGoogle Scholar
Grove, Adam J., and Halpern, Joseph Y.. 1997. “Probability Update: Conditioning vs. Cross-Entropy.” In Proceedings of the Thirteenth Annual Conference on Uncertainty in Artificial Intelligence, ed. Geiger, Dan and Shenoy, Prakash. San Francisco: Kaufmann.Google Scholar
Hájek, Allen, and Smithson, Michael. 2012. “Rationality and Indeterminate Probabilities.” Synthese 187:33–48.CrossRefGoogle Scholar
Howson, Colin, and Urbach, Peter. 1993. Scientific Reasoning: The Bayesian Approach. 2nd ed. Chicago: Open Court.Google Scholar
Jaynes, E. T. 2003. Probability Theory: The Logic of Science. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Jeffrey, Richard C. 1983. The Logic of Decision. 2nd ed. Chicago: University of Chicago Press.Google Scholar
Joyce, James M. 2009. “The Development of Subjective Bayesianism.” In Handbook of the History of Logic, Vol. 10, Inductive Logic, ed. Gabbay, Dov, Hartmann, Stephan, and Woods, John, 415–76. Amsterdam: North-Holland.Google Scholar
Gabbay, Dov, Hartmann, Stephan, and Woods, John 2010. “A Defense of Imprecise Credences in Inference and Decision Making.” Philosophical Perspectives 24:281–323.Google Scholar
Levi, Isaac. 1974. “On Indeterminate Probabilities.” Journal of Philosophy 71:391–418.CrossRefGoogle Scholar
Liese, Friedrich, and Vajda, Igor. 2006. “On Divergences and Informations in Statistics and Information Theory.” IEEE Transactions on Information Theory 52:4394–4412.CrossRefGoogle Scholar
Lukits, Stefan. 2014. “The Principle of Maximum Entropy and a Problem in Probability Kinematics.” Synthese 191:1409–31.CrossRefGoogle Scholar
Seidenfeld, Teddy. 1986. “Entropy and Uncertainty.” Philosophy of Science 53:467–91.CrossRefGoogle Scholar
Seidenfeld, Teddy, and Wasserman, Larry. 1993. “Dilation for Sets of Probabilities.” Annals of Statistics 21:1139–54.CrossRefGoogle Scholar
Shore, John E., and Johnson, Rodney W.. 1980. “Axiomatic Derivation of the Principle of Maximum Entropy and the Principle of Minimum Cross-Entropy.” IEEE Transactions on Information Theory 26:26–37.CrossRefGoogle Scholar
Uffink, Jos. 1995. “Can the Maximum Entropy Principle Be Explained as a Consistency Requirement?” Studies in History and Philosophy of Modern Physics B 26:233–61.CrossRefGoogle Scholar
van Fraassen, Bas C. 1981. “A Problem for Relative Information Minimizers in Probability Kinematics.” British Journal for the Philosophy of Science 32:375–79.CrossRefGoogle Scholar
van Fraassen, Bas C. 1989. Laws and Symmetry. Oxford: Oxford University Press.CrossRefGoogle Scholar
van Fraassen, Bas C., Hughes, R. I. G., and Hartman, Gilbert. 1986. “A Problem for Relative Information Minimizers, Continued.” British Journal for the Philosophy of Science 37:453–63.Google Scholar
Williams, P. M. 1980. “Bayesian Conditionalisation and the Principle of Minimum Information.” British Journal for the Philosophy of Science 31:131–44.CrossRefGoogle Scholar