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A Bayesian Account of Independent Evidence with Applications

Published online by Cambridge University Press:  01 April 2022

Branden Fitelson
Branden Fitelson*
Affiliation:
University of Wisconsin-Madison
*
†This paper won the PSA 2000 Graduate Student Essay Contest. Send requests for reprints to the author, Philosophy Department, University of Wisconsin, 600 N. Park St., Madison, WI 53706; email: [email protected].
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Abstract

A Bayesian account of independent evidential support is outlined. This account is partly inspired by the work of C. S. Peirce. I show that a large class of quantitative Bayesian measures of confirmation satisfy some basic desiderata suggested by Peirce for adequate accounts of independent evidence. I argue that, by considering further natural constraints on a probabilistic account of independent evidence, all but a very small class of Bayesian measures of confirmation can be ruled out. In closing, another application of my account to the problem of evidential diversity is also discussed.

Type
Bayesian Methodology
Information
Philosophy of Science , Volume 68 , Issue S3: No. 3 Supplement: Proceedings of the 2000 Biennial Meeting of the Philosophy of Science Association. Part I: Contributed Papers Sep., 2001 , 2001 , pp. S123 - S140
Copyright
Copyright © Philosophy of Science Association 2001

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Footnotes

‡

Thanks to Marty Barrett, Ellery Eells, Malcolm Forster, Jim Joyce, Mike Kruse, Greg Mougin, Dan Steel, Wayne Myrvold, and, especially, Patrick Maher and Elliott Sober for useful comments and suggestions on previous drafts of this paper.

References

Carnap, Rudolf (1945), “On inductive logic”, Philosophy of Science 12, 72–97.CrossRefGoogle Scholar
Carnap, Rudolf (1962), Logical Foundations of Probability, 2nd ed. Chicago: University of Chicago Press.Google Scholar
Christensen, D. (1999), “Measuring confirmation”. Journal of Philosophy XCVI: 437–461.CrossRefGoogle Scholar
Earman, John (1992), Bayes or Bust: A Critical Examination of Bayesian Confirmation Theory. Cambridge: MIT Press.Google Scholar
Eells, Ellery (1982), Rational Decision and Causality. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Eells, Ellery and Fitelson, Branden (2000a), “Measuring confirmation and evidence”, Journal of Philosophy XCVII(12): 663–672.CrossRefGoogle Scholar
Eells, Ellery and Fitelson, Branden (2000b), “Symmetries and Asymmetries in Evidential Support”, forthcoming in Philosophical Studies.Google Scholar
Fitelson, Branden (1996), “Wayne, Horwich, and Evidential Diversity”, Philosophy of Science 63, 652–660.CrossRefGoogle Scholar
Fitelson, Branden (1999), “The Plurality of Bayesian Measures of Confirmation and the Problem of Measure Sensitivity”, Philosophy of Science 66 (Proceedings): S362–S378.CrossRefGoogle Scholar
Forster, Malcolm (1995), “Bayes and Bust: Simplicity as a Problem for a Probabilist's Approach to Confirmation”, British Journal for the Philosophy of Science 46:399–424.CrossRefGoogle Scholar
Gillies, D. (1986), “In Defense of the Popper-Miller Argument”, Philosophy of Science 53:110–113.CrossRefGoogle Scholar
Good, Irving (1983), Good Thinking. Minneapolis: University of Minnesota Press.Google Scholar
Good, Irving (1984), “The best explicatum for weight of evidence”, Journal of Statistical Computation and Simulation 19:294–299.CrossRefGoogle Scholar
Halpern, J. (1996), “A counterexample to theorems of Cox and Fine”, in AAAI-96. Cambridge, MA: MIT Press, 1313–1319.Google Scholar
Heckerman, D. (1988), “An axiomatic framework for belief updates”, in Kanal, L. and Lemmer, J. (eds.). Uncertainty in Artificial Intelligence 2. New York: Elsevier Science Publishers, 11–22.CrossRefGoogle Scholar
Horvitz, E. and Heckerman, D. (1986), “The inconsistent use of certainty measures in artificial intelligence research”, in Kanal, L. and Lemmer, J. (eds.), Uncertainty in Artificial Intelligence 1. New York: Elsevier Science Publishers, 137–151.CrossRefGoogle Scholar
Horwich, Paul (1982), Probability and Evidence. Cambridge: Cambridge University Press.Google Scholar
Howson, Colin and Urbach, Peter (1993), Scientific Reasoning: The Bayesian Approach. La Salle: Open Court.Google Scholar
Jeffrey, Richard (1992), Probability and the Art of Judgment. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Joyce, James (1999), The Foundations of Causal Decision Theory. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Kemeny, J. and Oppenheim, P. (1952), “Degrees of Factual Support”, Philosophy of Science 19:307–324.CrossRefGoogle Scholar
Keynes, J. (1921), A Treatise on Probability. London: Macmillan.Google Scholar
Kyburg, H. (1983), “Recent work in inductive logic”, in Machan, T. and Lucey, K. (eds.), Recent Work in Philosophy. Lanham: Rowman & Allanheld, 87–150.Google Scholar
Mackie, J. (1969), “The Relevance Criterion of Confirmation”, British Journal for the Philosophy of Science 20:27–40.CrossRefGoogle Scholar
Milne, Peter (1996), “log[p(h/eb)/p(h/b)] is the One True Measure of Confirmation”, Philosophy of Science 63:21–26.CrossRefGoogle Scholar
Myrvold, Wayne (1996), “Bayesianism and Diverse Evidence: A Reply to Andrew Wayne”, Philosophy of Science 63:661–665.CrossRefGoogle Scholar
Pearl, Judea (1988), Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. San Francisco: Morgan Kauffman.Google Scholar
Peirce, Charles Sanders (1878), “The Probability of Induction”, Popular Science Monthly 12:705–718.Google Scholar
Pollard, S. (1999), “Milne's Measure of Confirmation”, Analysis 59:335–337.CrossRefGoogle Scholar
Reichenbach, Hans (1956), The Direction of Time. Berkeley: University of California Press.CrossRefGoogle Scholar
Rosenkrantz, R. (1994), “Bayesian Confirmation: Paradise Regained”, British Journal for the Philosophy of Science 45:467–476.CrossRefGoogle Scholar
Schlesinger, G. (1995), “Measuring Degrees of Confirmation”, Analysis 55:208–212.CrossRefGoogle Scholar
Schum, David (1994), The Evidential Foundations of Probabilistic Reasoning. New York: John Wiley & Sons.Google Scholar
Sober, Elliott (1989), “Independent Evidence About a Common Cause”, Philosophy of Science 56:275–287.CrossRefGoogle Scholar