  NOvA is a long-baseline neutrino oscillation experiment that measures
oscillations in charged-current $\nu_{\mu} \rightarrow \nu_{\mu}$
(disappearance) and $\nu_{\mu} \rightarrow \nu_{e}$ (appearance) channels, and
their antineutrino counterparts, using neutrinos of energies around 2 GeV over
a distance of 810 km. In this work we reanalyze the dataset first examined in
our previous paper [Phys. Rev. D 106, 032004 (2022)] using an alternative
statistical approach based on Bayesian Markov Chain Monte Carlo. We measure
oscillation parameters consistent with the previous results. We also extend our
inferences to include the first NOvA measurements of the reactor mixing angle
$\theta_{13}$ and the Jarlskog invariant. We use these results to quantify the
strength of our inferences about CP violation, as well as to examine the
effects of constraints from short-baseline measurements of $\theta_{13}$ using
antineutrinos from nuclear reactors when making NOvA measurements of
$\theta_{23}$. Our long-baseline measurement of $\theta_{13}$ is also shown to
be consistent with the reactor measurements, supporting the general
applicability and robustness of the PMNS framework for neutrino oscillations.
