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Belief, Evidence, and Conditioning

Published online by Cambridge University Press:  01 January 2022

Henry E. Kyburg Jr.
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Abstract

Since Ramsey, much discussion of the relation between probability and belief has taken for granted that there are degrees of belief, i.e., that there is a real-valued function, B, that characterizes the degree of belief that an agent has in each statement of his language. It is then supposed that B is a probability. It is then often supposed that as the agent accumulates evidence, this function should be updated by conditioning:$B^{E}(\cdot) $ should be$B(\cdot \wedge E) / B(E) $ . Probability is also important in classical statistics, where it is generally supposed that probabilities are frequencies, and that inference proceeds by controlling error and not by conditioning. I will focus on the tension between these two approaches to probability, and in the main part of the paper show where and when Bayesian conditioning conflicts with error based statistics and how to resolve these conflicts.

Type
Research Article
Information
Philosophy of Science , Volume 73 , Issue 1 , January 2006 , pp. 42 - 65
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

‡

This material is based upon work supported by NASA, and by NSF award IIS-0328849.

References

Buehler, R. J. (1959), “Some Validity Criteria for Statistical Inference”, Some Validity Criteria for Statistical Inference 30:845–863.Google Scholar
de Campos, Luis M., Heute, Juan F., and Moral, Serafin (1993), “Probability Intervals: A Tool for Uncertain Reasoning”, Technical Report, University of Grenada.Google Scholar
de Finetti, Bruno ([1937] 1964), “Foresight, Its Logical Laws; Its Subjective Sources”, in Kyburg, Henry and Smoklee, Howard (eds.), Studies in Subjective Probability. New York: John Wiley, 93–158. Reprint. Translated by Henry Kyburg. Originally published as “La prevision: Ses lois logiques, ses sources subjectives”, Annales de l’Institute Henri Poincare 7:1–68.Google Scholar
de Finetti, Bruno (1972), Probability, Induction, and Statistics. New York: John Wiley.Google Scholar
Fisher, Ronald A. (1956), Statistical Methods and Scientific Inference. New York: Hafner.Google Scholar
Fisher, Ronald A. (1971), The Design of Experiments. New York: Hafner.Google Scholar
Keynes, John Maynard (1952), A Treatise on Probability. London: Macmillan.Google Scholar
Kyburg, Henry E. Jr. (1959), “Probability and Randomness I and II”, Probability and Randomness I and II 24:316–318.Google Scholar
Kyburg, Henry E. Jr (1990), “Theories as Mere Conventions”, in Savage, Wade (ed.), Scientific Theories, Vol. 14. Minneapolis: University of Minnesota Press, 158–174.Google Scholar
Kyburg, Henry E. Jr (2003), “Are There Degrees of Belief?”, Are There Degrees of Belief? 1:139–149.Google Scholar
Kyburg, Henry E. Jr., and Teng, Choh Man (2001), Uncertain Inference. New York: Cambridge University Press.CrossRefGoogle Scholar
Levi, Isaac (1967), Gambling with Truth. New York: Knopf.Google Scholar
Levi, Isaac (1980), The Enterprise of Knowledge. Cambridge, MA: MIT Press.Google Scholar
Neyman, Jerzy (1957), “‘Inductive behavior’ as a Basic Concept of Philosophy of Science”, ‘Inductive behavior’ as a Basic Concept of Philosophy of Science 25:7–22.Google Scholar
Pollock, John L. (1990), Nomic Probability and the Foundations of Induction. New York: Oxford University Press.CrossRefGoogle Scholar
Ramsey, Frank P. (1931), The Foundations of Mathematics and Other Essays. New York: Humanities Press.Google Scholar
Reichenbach, Hans (1949), The Theory of Probability. Berkeley: University of California Press.Google Scholar
Savage, L. J., Edwards, W., and Lindeman, H. (1963), “Bayesian Statistical Inference for Psychological Research”, Bayesian Statistical Inference for Psychological Research 70:193–242.Google Scholar
Smith, C. A. B. (1961), “Consistency in Statistical Inference and Decision”, Consistency in Statistical Inference and Decision 23:1–37.Google Scholar
Smith, C. A. B. (1965), “Personal Probability and Statistical Analysis”, Personal Probability and Statistical Analysis 128:468–499.Google Scholar
Walley, Peter (1991), Statistical Reasoning with Imprecise Probabilities. London: Chapman and Hall.CrossRefGoogle Scholar