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Inverse probability and sufficient statistics

Published online by Cambridge University Press:  24 October 2008

V. S. Huzurbazar
Affiliation:
Fitzwilliam HouseCambridge

Extract

1. It is an interesting fact that in many problems of statistical estimation the results given by the theory of inverse probability (as modified by Jeffreys) are indistinguishable from those given by the methods of ‘fiducial probability’ or ‘confidence intervals’. The derivation of some of the important inverse distributions by Jeffreys(3) arouses one's curiosity. It seems that when this agreement is noticed there are usually sufficient statistics for parameters in the distribution. The object of this note is to throw some light, in general terms, on the similarity in form between the posterior probability-density function of the parameters and the probability-density function of the distribution when it admits sufficient statistics. For convenience the following notation in Jeffreys's probability logic is used below:

P(q | p) is the probability of a proposition q on data p.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1949

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References

(1)Bartlett, M. S.Proc. Roy. Soc. A, 160 (1937), 268.CrossRefGoogle Scholar
(2)Fisher, R. A.Proc. Roy. Soc. A, 144 (1934), 285.CrossRefGoogle Scholar
(3)Jeffreys, H.Theory of Probability (Oxford, 1939).Google Scholar
(4)Kendall, M. G.The Advanced Theory of Statistics, 2 (London, 1946).Google Scholar
(5)Koopman, B. O.Trans. American Math. Soc. 39 (1936), 399.CrossRefGoogle Scholar
(6)Pitman, E. J. G.Proc. Cambridge Phil. Soc. 32 (1936), 567.CrossRefGoogle Scholar

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