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.
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