A Bayesian reference analysis of a typical scenario of high energy physics has recently been performed [Phys. Rev. D 82, 034002 (2010)]. The reference prior with partial information (and hence also the posterior) were found to depend on the sequence of subsets of the parameter space used for a normalization process. A particular choice of the subsets leading to a proper posterior was advocated. Here it is shown that this choice differs from the natural sequence of subsets in the ``original parametrization'' of the problem, which has been generally recommended elsewhere. Although this questions the manner in which the commented result was obtained, the result itself is corroborated because the present derivation based on a different argument yields a reference prior of the same functional form.