  The aim of this paper is to firmly establish subjective fiducial inference as
a rival to the more conventional schools of statistical inference, and to show
that Fisher's intuition concerning the importance of the fiducial argument was
correct. In this regard, methodology outlined in an earlier paper is modified,
enhanced and extended to deal with general inferential problems in which
various parameters are unknown. As a key part of what is put forward, the joint
fiducial distribution of all the parameters of a given model is determined on
the basis of the full conditional fiducial distributions of these parameters by
using an analytical approach or a Gibbs sampling method, the latter of which
does not require these conditional distributions to be compatible. Although the
resulting theory is classified as being "subjective", this is essentially due
to the argument that all probability statements made about fixed but unknown
parameters must be inherently subjective. In particular, it is systematically
argued that, in general, there is no need to place a great emphasis on the
difference between the fiducial probabilities derived by using this theory of
inference and objective probabilities. Some important examples of the
application of this theory are presented.
