On Direct Probabilities

Abstract

SUMMARY The concept of a direct probability argument is introduced. This is a means of assigning distributions a posteriori which satisfies the requirement that such distributions shall be valid conditional on the observations, but which differs from the inverse probability argument in that distributions a priori are not needed. Direct probabilities are closely related to fiducial probabilities. This theory requires a generalized concept of sampling a family Fθ of distributions which is discussed in Section 3. Direct inference from a sample of n is discussed in Section 4 for a single continuous parameter and in Section 5 for the non-parametric case.