  The three and five-dimensional convex sets of two-level complex and
quaternionic quantum systems are studied in the Bayesian thermostatistical
framework introduced by Lavenda. Associated with a given parameterization of
each such set is a quantum Fisher (Helstrom) information matrix. The square
root of its determinant (adopting an ansatz of Harold Jeffreys) provides a
reparameterization-invariant prior measure over the set. Both such measures can
be properly normalized and their univariate marginal probability distributions
(which serve as structure functions) obtained. Gibbs (posterior) probability
distributions can then be found, using Poisson's integral representation of the
modified spherical Bessel functions. The square roots of the (classical) Fisher
information of these Gibbs distributions yield (unnormalized) priors over the
inverse temperature parameters.
