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Inverse Probability and Modern Statisticians

Published online by Cambridge University Press:  14 March 2022

Robert Dean Gordon*
Affiliation:
Scripps Institution of Oceanography La Jolla, California

Extract

Introduction: Purpose of this essay is to draw attention to some points which are relevant to the underlying philosophy of modern statistics, but which the writer feels have been largely overlooked both by the defenders and the opponents of the classic conceptions of Laplace. There is no quarrel with methodologies as such which have found their introduction under the heads of “maximum likelihood”, “fiducial limits”, etc. But the writer cannot accept arguments (e.g. Fisher (1)) which would make of such procedures an absolute sine qua non for all decisions based on evidence, and which would relegate human judgment (a priori probabilities) and all considerations of the intended use of a decision to the rubbish heap of outmoded conceptions. To assume that two rational minds, having different backgrounds and different objectives, must necessarily find themselves in agreement in their appraisal of a given objective situation, is simply absurd; yet this is the basis which underlies, so far as I can make out, all the “criticisms” of Laplace and Bayes which constitute the excuses put forward for attempting to displace those procedures in Statistics which involve “inverse probability”. Also the so-called “paradoxes” which have been invented by many writers in order to assail Laplace, contradict only this one assumption; without it they are not paradoxes.

Type
Research Article
Copyright
Copyright © The Philosophy of Science Association 1940

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References

(1) Fisher, R. A., On the mathematical foundations of theoretical statistics. Philosophical Transactions, Royal Society of London, Sec. A, 222, pp. 309368 (1921).Google Scholar
Fisher, R. A., Theory of statistical estimation. Proceedings, Cambridge Philosophical Society, XXII, V; pp. 700725 (1925).CrossRefGoogle Scholar
Fisher, R. A., Probability, likelihood, and quantity of information in the logic of uncertain inference; Proceedings of the Royal Society, Sec. A, 146 (1934).Google Scholar
(2) Uspensky, J. V., Introduction to Mathematical Probability. McGraw-Hill, New York, 1937.Google Scholar
(3) Montague, W. P., The Ways of Knowing. Macmillan, New York, 1928; pp. 99105.Google Scholar
(4) Gordon, R. D., Note on estimating bacterial populations by the dilution method. Proceedings of the National Academy of Sciences, Vol. 24, No. 5, pp. 212215. May, 1938.CrossRefGoogle Scholar
Gordon, R. D., Estimating bacterial populations by the dilution method. Biometrika, vol. XXXI, parts I and II. July, 1939, pp. 167180.CrossRefGoogle Scholar
(5) Halvorson and Ziegler, Quantitative Bacteriology. Burgess Publishing Co., Minneapolis, Minnesota (1933).Google Scholar
(6) Gordon, R. D. and ZoBell, C. E., Note on the successive dilution method for estimating bacterial populations. Zentralblatt für Bakteriologie, II. Abteilung, Bd. 99 (1938), pp. 318320.Google Scholar
(7) Jeffreys, H., Scientific Inference. Cambridge University Press, 1937.Google Scholar
(8) Curti, Mrs. M. W., Child Psychology. Cf. also Pepper, S. C., The conceptual framework of Tolman's Purposive Behaviorism. Psychological Review, Vol. 41, No. 2 (March, 1934) pp. 108133.Google Scholar