  The Horodecki family employed the Jaynes maximum-entropy principle, fitting
the mean (b_{1}) of the Bell-CHSH observable (B). This model was extended by
Rajagopal by incorporating the dispersion (\sigma_{1}^2) of the observable, and
by Canosa and Rossignoli, by generalizing the observable (B_{\alpha}). We
further extend the Horodecki one-parameter model in both these manners,
obtaining a three-parameter (b_{1},\sigma_{1}^2,\alpha) two-qubit model, for
which we find a highly interesting/intricate continuum (-\infty < \alpha <
\infty) of Hilbert-Schmidt (HS) separability probabilities -- in which, the
golden ratio is featured. Our model can be contrasted with the three-parameter
(b_{q}, \sigma_{q}^2,q) one of Abe and Rajagopal, which employs a
q(Tsallis)-parameter rather than $\alpha$, and has simply q-invariant HS
separability probabilities of 1/2. Our results emerge in a study initially
focused on embedding certain information metrics over the two-level quantum
systems into a q-framework. We find evidence that Srednicki's recently-stated
biasedness criterion for noninformative priors yields rankings of priors fully
consistent with an information-theoretic test of Clarke, previously applied to
quantum systems by Slater.
