  We propose a simple, analytic dual-cone accretion model for horizon scale
images of the cores of Low-Luminosity Active Galactic Nuclei (LLAGN), including
those observed by the Event Horizon Telescope (EHT). Our underlying model is of
synchrotron emission from an axisymmetric, magnetized plasma, which is
constrained to flow within two oppositely oriented cones that are aligned with
the black hole's spin axis. We show that this model can accurately reproduce
images for a variety of time-averaged general relativistic magnetohydrodynamic
(GRMHD) simulations, that it accurately recovers both the black hole and
emission parameters from these simulations, and that it is sufficiently
efficient to be used to measure these parameters in a Bayesian inference
framework with radio interferometric data. We show that non-trivial topologies
in the source image can result in non-trivial multi-modal solutions when
applied to observations from a sparse array, such as the EHT 2017 observations
of M87${}^*$. The presence of these degeneracies underscores the importance of
employing Bayesian techniques that adequately sample the posterior space for
the interpretation of EHT measurements. We fit our model to the EHT
observations of M87${}^*$ and find a 95% Highest Posterior Density Interval
(HPDI) for the mass-to-distance ratio of $\theta_g\in(2.84,3.75)\,\mu{\rm as}$,
and give an inclination of $\theta_{\rm o}\in(11^\circ,24^\circ)$. These new
measurements are consistent with mass measurements from the EHT and stellar
dynamical estimates (e.g., Gebhardt et al. 2011; EHTC et al. 2019a,b; Liepold
et al. 2023), and with the spin axis inclination inferred from properties of
the M87${}^*$ jet (e.g., Walker et al. 2018).
