The concepts of inverse probability and fiducial probability referring to unknown parameters

Abstract In a paper published in these 'Proceedings' Jeffreys puts forward a form of reasoning purporting to resolve in a particular case the primitive difficulty which besets all attempts to derive valid results of practical application from the theory of Inverse Probability. For a normally distributed variate, x, the frequency element may be written df = h/√π e-h2(x-μ)2dx, where μ is the mean of the distribution, and h the precision constant. For the convenience of the majority of statisticians who prefer to use the standard deviation, σ, of the distribution, in place of the precision constant, we may note that h2 = 1/2σ2, and that this substitution may be made at any stage of the argument.