Inductive Inference and the Maximum Entropy Principle

Dalkey, N. C.

doi:10.1007/978-94-017-2221-6_16

N. C. Dalkey³

Part of the book series: Fundamental Theories of Physics ((FTPH,volume 14))

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Abstract

A conventional schema for an inference consists of a set of premises and a conclusion, as in the diagram:

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Notes and References

This appears to be the approach followed by the ‘logical’ school of probability, exemplified by H. Jeffries (1939, Theory of Probability Oxford Univ. Press), J. M. Keynes (1921, A Treatise on Probability London: MacMillan), and R. Carnap (1950, Logical Foundations of Probability University of Chicago Press). The distinction between probability as a physical property of systems and as a logical construct was recognized by Carnap, who labeled the logical notion “degree of confirmation.’
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Proper scoring rules are an increasingly important topic in a variety of information sciences. Associated with important early work on the subject are the names B. de Finetti, I. J. Good, L. J. Savage, E. H. Shuford, E. H. Massengill, G. W. Brier, M. Toda, and R. W. Winkler.
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Shuford, E. H., A. Albert, and E. H. Massengill (1966) Admissible probability measurement procedures, Psychometrika, 31, 2.
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The game against nature as a statistical inference tool was initiated by A. Wald (1950, Statistical Decision Functions New York: John Wiley and Sons) and pursued by D. Blackwell and M. A. Girshick (1954, Theory of Games and Statistical Decisions New York: John Wiley and Sons).
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The game against nature has been criticized from all sides, by objectivists, e.g., H. Reichenbach ( 1949, The Theory of Probability Berkeley: Univ. of Calif. Press), subjectivists, e.g., B. de Finetti (1975, Theory of Probability vols. I and II, New York: John Wiley and Sons), and logical probabilists, e.g., Carnap (op. cit. ).
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The caveats relate to a kind of decoupling that must be assumed between actions and events. One aspect of this decoupling is examined by I. H. LaValle ( 1980, On value and strategic role of information in semi-normalized decisions, Operations Research, 28 (1), 129–138). A somewhat more general treatment is pursued in N. Dalkey (to be published, Group Decision Theory Addison-Wesley).
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Compare N. Dalkey ( 1980, The aggregation of probability estimates, UCLA- ENG-CSL-8025).
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Cognitive Systems Laboratory, University of California at Los Angeles, Los Angeles, California, 90024, USA
N. C. Dalkey

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N. C. Dalkey
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Department of Physics and Astronomy, The University of Wyoming, Laramie, Wyoming, USA
C. Ray Smith & W. T. Grandy Jr. &

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Dalkey, N.C. (1985). Inductive Inference and the Maximum Entropy Principle. In: Smith, C.R., Grandy, W.T. (eds) Maximum-Entropy and Bayesian Methods in Inverse Problems. Fundamental Theories of Physics, vol 14. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2221-6_16

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DOI: https://doi.org/10.1007/978-94-017-2221-6_16
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-8418-7
Online ISBN: 978-94-017-2221-6
eBook Packages: Springer Book Archive

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