  Discrepancies between cosmological parameter estimates from cosmic shear
surveys and from recent Planck cosmic microwave background measurements
challenge the ability of the highly successful $\Lambda$CDM model to describe
the nature of the Universe. To rule out systematic biases in cosmic shear
survey analyses, accurate redshift calibration within tomographic bins is key.
In this paper, we improve photo-$z$ calibration via Bayesian hierarchical
modeling of full galaxy photo-$z$ conditional densities, by employing
$\textit{StratLearn}$, a recently developed statistical methodology, which
accounts for systematic differences in the distribution of the spectroscopic
training/source set and the photometric target set. Using realistic simulations
that were designed to resemble the KiDS+VIKING-450 dataset, we show that
$\textit{StratLearn}$-estimated conditional densities improve the galaxy
tomographic bin assignment, and that our $\textit{StratLearn}$-Bayesian
framework leads to nearly unbiased estimates of the target population means.
This leads to a factor of $\sim 2$ improvement upon the previously best
photo-$z$ calibration method. Our approach delivers a maximum bias per
tomographic bin of $\Delta \langle z \rangle = 0.0095 \pm 0.0089$, with an
average absolute bias of $0.0052 \pm 0.0067$ across the five tomographic bins.
