  Accurate stellar properties are essential for precise stellar astrophysics
and exoplanetary science. In the M-dwarf regime, much effort has gone into
defining empirical relations that can use readily accessible observables to
assess physical stellar properties. Often, these relations for the quantity of
interest are cast as a non-linear function of available data; however, in
Bayesian modeling the reverse is needed. In this article, we introduce a new
Bayesian framework to self-consistently and simultaneously apply multiple
empirical calibrations to fully characterize the mass, luminosity, radius, and
effective temperature of a field age M-dwarf. This framework includes a new
M-dwarf mass-radius relation with a scatter of 3.1% at fixed mass. We further
introduce the M-dwarf Ultraviolet Spectroscopic Sample (MUSS), and apply our
methodology to provide consistent stellar parameters for these nearby low-mass
stars, selected as having available spectroscopic data in the ultraviolet.
These targets are of interest largely as either exoplanet hosts or benchmarks
in multi-wavelength stellar activity. We use the field MUSS stars to define a
low-mass main sequence in the solar neighborhood through Gaussian Process (GP)
regression. These results enable us to empirically measure a feature in the GP
derivative at $\mathcal{M}_{b} = 0.337 \pm ^{0.013}_{0.026}$ $M_{\odot}$ that
indicates where the M-dwarf Ultraviolet Spectroscopic Sample transitions from
fully to partly convective interiors.
