Abstract
The paper provides a formal proof that efficient estimates of parameters, which vary as as little as possible when measurements are repeated, may be expected to provide more accurate predictions. The definition of predictive accuracy is motivated by the work of Akaike (1973). Surprisingly, the same explanation provides a novel solution for a well known problem for standard theories of scientific confirmation — the Ravens Paradox. This is significant in light of the fact that standard Bayesian analyses of the paradox fail to account for the predictive utility of universal laws like “All ravens are black.”
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References
Akaike, H.: 1973, ‘Information Theory and an Extension of the Maximum Likelihood Principle’ in B. N. Petrov and F. Csaki (eds.),2nd International Symposium on Information Theory, Akademiai Kiado, Budapest, pp. 267–81.
Cartwright, N.: 1983,How the Laws of Physics Lie, Oxford University Press, Oxford.
Cramér, H.: 1946,Mathematical Methods of Statistics, Princeton University Press, Princeton.
Earman, J.: 1992,Bayes or Bust? A Critical Examination of Bayesian Confirmation Theory, The MIT Press, Cambridge.
Eells, E.: 1982,Rational Decision and Causality, Cambridge University Press, Cambridge.
Forster, M.: 1988a, ‘Confirmation of Component Causes’ in A. Fine & J Leplin (eds.)PSA 1988, Philosophy of Science Association, E. Lansing, Michigan, pp. 3–9.
Forster, M.: 1988b, ‘Unification, Explanation, and the Composition of Causes in Newtonian Mechanics’,Studies in the History and Philosophy of Science 19, pp. 55–101.
Forster, M.: 1988c, ‘Sober's Principle of Common Cause and the Problem of Incomplete Hypotheses’,Philosophy of Science 55, 538–59.
Forster, M.: 1993, ‘Progress Towards the Truth’, in preparation.
Forster, M. and E. Sober: 1994, ‘How To Tell When Simpler, More Unified, or Less Ad Hoc Theories Will Provide More Accurate Predictions’,The British Journal for the Philosophy of Science, March 1994.
Giere, R.: 1991,Understanding Scientific Reasoning, Third Edition, Holt, Rinehart and Winston, Inc., Orlando, Florida.
Good, I. J.: 1975, ‘Comments on David Miller’,Synthese 30, 205–6.
Good, I. J.: 1983,Good Thinking, University of Minnesota Press, Minneapolis.
Harper, W.: 1989, ‘Consilience and Natural Kind Reasoning’, in J. R. Brown and J. Mittelstrass (eds.),An Intimate Relation, Kluwer Academic Publishers, Dordrecht, pp. 115–52.
Hempel, C.: 1945, ‘Studies in the Logic of Confirmation’,Mind,54. Reprinted in Hempel, G.: 1965,Aspects of Scientific Explanation, The Free Press, New York.
Hintikka, J. and P. Suppes (eds.): 1966,Aspects of Inductive Logic, North-Holland, Amsterdam.
Hosiasson-Lindenbaum, J.: 1940, ‘On Confirmation’,Journal of Symbolic Logic, 133–48.
Horwich, P.: 1982,Probability and Evidence, Cambridge University Press, Cambridge.
Howson, C. and Urbach, P.: 1989,Scientific Reasoning: The Bayesian Approach, Open Court, La Salle, Illinois.
Kullback, S. and R. A., Leibler: 1951, ‘On Information and Sufficiency’,Annals of Mathematical Statistics 22, 79–86.
Meyer, S. L.: 1977, ‘Urning a Resolution of Hempel's Paradox’,Philosophy of Science 44, 292–96.
Miller, D.: 1975, ‘The Accuracy of Predictions’,Synthese 30, pp. 159–91.
Rosenkrantz, R.: 1977,Inference, Method, and Decision, D. Reidel, Dordrecht.
Sakamoto, Y., M. Ishiguro, and G. Kitagawa: 1986,Akaike Information Criterion Statistics, Kluwer Academic Publishers, Dordrecht.
Skyrms, B.: 1980,Causal Necessity: A Pragmatic Investigation of the Necessity of Laws, Yale University Press, New Haven.
Sober, E.: 1988a, ‘Likelihood and Convergence’,Philosophy of Science 55, 228–37.
Sober, E.: 1988b,Reconstructing the Past: Parsimony, Evolution, and Inference, MIT Press, Cambridge.
Suppes, P.: 1966, ‘A Bayesian Approach to the Paradoxes of Confirmation’, in Hintikka and Suppes (1966), pp. 198–207.
Williams, P. M.: 1980, ‘Bayesian Conditionalization and the Principle of Minimum Information’,British Journal for the Philosophy of Science 31, 131–44.
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I wish to thank Martin Barrett, Ellery Eells, Berent Enç, Branden Fitelson, Dan Hausman, Eric Saidel, Brian Skyrms, Elliott Sober, Mariam Thalos, as well as anonymous reviewer, for helpful suggestions. This research was supported by NSF grant DIR-8822278, and by the Graduate School at the University of Wisconsin, Madison.
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Forster, M.R. Non-bayesian foundations for statistical estimation, prediction, and the ravens example. Erkenntnis 40, 357–376 (1994). https://doi.org/10.1007/BF01128904
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DOI: https://doi.org/10.1007/BF01128904