Some remarks on pivotal models and the fiducial argument in relation to structural models

A recent paper (Barnard, 1995) gives a ''sketch of the ... fiducial argument ... accompanied by a version of ... 'pivotal inference' which ... may give a consistent revised version of the (inference) ideas involved'', The literature on invariant fiducial and on structural models was not discussed or cited. As the invariant fiducial method deals directly with the consistency and interpretation of the fiducial argument and as structural models and pivotal models are, in wide generality, mathematically isomorphic, this note is to provide a brief outline of these omitted topics and their relevance to the inference ideas addressed in the recent paper.