  Velocity offsets in the broad Balmer lines of quasars and their temporal
variations serve as indirect evidence for bound supermassive black hole
binaries (SBHBs) at sub-parsec separations. In this work, we test the SBHB
hypothesis for 14 quasars with double-peaked broad emission lines using their
long-term (14--41 years) radial velocity curves. We improve on previous work by
(a) using elliptical instead of circular orbits for the SBHBs, (b) adopting a
statistical model for radial velocity jitter, (c) employing a Markov Chain
Monte Carlo method to explore the orbital parameter space efficiently and build
posterior distributions of physical parameters and (d) incorporating new
observations. We determine empirically that jitter comprises approximately
Gaussian distributed fluctuations about the smooth radial velocity curves that
are larger than the measurement errors by factors of order a few. We initially
treat jitter by enlarging the effective error bars and then verify this
approach via a variety of Gaussian process models for it. We find lower mass
limits for the hypothesized SBHBs in the range $10^8$--$10^{11}\;M_{\odot}$.
For seven objects the SBHB scenario appears unlikely based on goodness-of-fit
tests. For two additional objects the minimum SBHB masses are unreasonably
large ($>10^{10}\;M_{\odot}$), strongly disfavoring the SBHB scenario. Using
constraints on the orbital inclination angle (which requires some assumptions)
makes the minimum masses of four more objects unreasonably large. We also cite
physical and observational arguments against the SBHB hypothesis for nine
objects. We conclude that the SBHB explanation is not the favoured explanation
of double-peaked broad emission lines.
