  We report Bayesian inference of the mass, radius and hot X-ray emitting
region properties - using data from the Neutron Star Interior Composition
ExploreR (NICER) - for the brightest rotation-powered millisecond X-ray pulsar
PSR J0437$\unicode{x2013}$4715. Our modeling is conditional on informative
tight priors on mass, distance and binary inclination obtained from radio
pulsar timing using the Parkes Pulsar Timing Array (PPTA) (Reardon et al.
2024), and we use NICER background models to constrain the non-source
background, cross-checking with data from XMM-Newton. We assume two distinct
hot emitting regions, and various parameterized hot region geometries that are
defined in terms of overlapping circles; while simplified, these capture many
of the possibilities suggested by detailed modeling of return current heating.
For the preferred model identified by our analysis we infer a mass of $M =
1.418 \pm 0.037$ M$_\odot$ (largely informed by the PPTA mass prior) and an
equatorial radius of $R = 11.36^{+0.95}_{-0.63}$ km, each reported as the
posterior credible interval bounded by the 16% and 84% quantiles. This radius
favors softer dense matter equations of state and is highly consistent with
constraints derived from gravitational wave measurements of neutron star binary
mergers. The hot regions are inferred to be non-antipodal, and hence
inconsistent with a pure centered dipole magnetic field.
