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A note on inverse probability

Published online by Cambridge University Press:  24 October 2008

J. B. S. Haldane
Affiliation:
Trinity College

Extract

The problem of statistical investigation is the description of a population, or Kollektiv, of which a sample has been observed. At best we can only state the probability that certain parameters of this population lie within assigned limits, i.e. specify their probability density. It has been shown, e.g. by von Mises(1), that this is only possible if we know the probability distribution of the parameter before the sample is taken. Bayes' theorem is based on the assumption that all values of the parameter in the neighbourhood of that observed are equally probable a priori. It is the purpose of this paper to examine what more reasonable assumption may be made, and how it will affect the estimate based on the observed sample.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1932

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References

REFERENCES

(1)von Mises, R., Wahrscheinlichkeitsrechnung (1931).CrossRefGoogle Scholar
(2)Blackett, P. M. S., Proc. Roy. Soc. 107 A, p. 349 (1925).Google Scholar
(3)Pearson, K., Tables of the incomplete Γ-function (1922).CrossRefGoogle Scholar
(4)Fisher, R. A., Phil. Trans. Roy. Soc.. 222 A, p. 309 (1922).Google Scholar