  Likelihood-to-evidence ratio estimation is usually cast as either a binary
(NRE-A) or a multiclass (NRE-B) classification task. In contrast to the binary
classification framework, the current formulation of the multiclass version has
an intrinsic and unknown bias term, making otherwise informative diagnostics
unreliable. We propose a multiclass framework free from the bias inherent to
NRE-B at optimum, leaving us in the position to run diagnostics that
practitioners depend on. It also recovers NRE-A in one corner case and NRE-B in
the limiting case. For fair comparison, we benchmark the behavior of all
algorithms in both familiar and novel training regimes: when jointly drawn data
is unlimited, when data is fixed but prior draws are unlimited, and in the
commonplace fixed data and parameters setting. Our investigations reveal that
the highest performing models are distant from the competitors (NRE-A, NRE-B)
in hyperparameter space. We make a recommendation for hyperparameters distinct
from the previous models. We suggest two bounds on the mutual information as
performance metrics for simulation-based inference methods, without the need
for posterior samples, and provide experimental results. This version corrects
a minor implementation error in $\gamma$, improving results.
