  We find, in an analysis involving four prior probabilities (p's), that the
information-theoretic-based comparative noninformativity test devised by
Clarke, and applied by Slater in a quantum setting, yields a ranking
(p_{F_{q=1}} > p_{B} > p_{B_{q=1}trunc} >p_{F}) fully consistent with
Srednicki's recently-stated criterion for priors of ``biasedness to pure
states''. Two of the priors are formed by extending certain metrics of
quantum-theoretic interest from three- to four-dimensions -- by incorporating
the q-parameter (nonextensivity/Tsallis index/escort parameter). The
three-dimensional metrics are the Bures (minimal monotone) metric over the
two-level quantum systems and the Fisher information metric over the
corresponding family of Husimi distributions. The priors p_{B} and p_{F} are
the (independent-of-q) normalized volume elements of these metrics, and
p_{F_{q=1}} is the normalized volume element of the q-extended Fisher
information metric, with q set to 1. While originally intended to similarly be
the q-extension of the Bures metric, with q then set to 1, the prior
p_{B_{q=1}trunc}, actually entails the truncation of the only off-diagonal
entry of the extended Bures metric tensor. Without this truncation, the
q-extended Bures volume element is null, as is also the case in two other
quantum scenarios we examine.
