  We introduce SimBAL, a novel spectral-synthesis procedure that uses large
grids of ionic column densities generated by the photoionization code Cloudy
and a Bayesian model calibration to forward-model broad absorption line quasar
spectra. We used SimBAL to analyze the HST COS spectrum of the low-redshift
BALQ SDSS J085053.12+445122.5. SimBAL analysis yielded velocity-resolved
information about the physical conditions of the absorbing gas. We found that
the ionization parameter and column density increase, and the covering fraction
decreases as a function of velocity. The total log column density is 22.9
(22.4) [cm^-2] for solar (Z=3Z_\odot) metallicity. The outflow lies 1--3
parsecs from the central engine, consistent with the estimated location of the
torus. The mass outflow rate is 17--28 M_\odot yr^-1, the momentum flux is
consistent with L_Bol/c, and the ratio of the kinematic to bolometric
luminosity is 0.8--0.9%. The outflow velocity is similar to the escape velocity
at the absorber's location, and force multiplier analysis indicates that part
of the outflow could originate in resonance-line driving. The location near the
torus suggests that dust scattering may play a role in the acceleration,
although the lack of reddening in this UV-selected object indictes a relatively
dust-free line of sight. The low accretion rate (0.06 L_Edd) and compact
outflow suggests that SDSS~J0850+4451 might be a quasar past its era of
feedback, although since its mass outflow is about 8 times the accretion rate,
the wind is likely integral to the accretion physics of the central engine.
