  Supermassive binary black holes at sub-parsec orbital separations have yet to
be discovered, with the possible exception of blazar OJ~287. In parallel to the
global hunt for nanohertz gravitational waves from supermassive binaries using
pulsar timing arrays, there has been a growing sample of candidates reported
from electromagnetic surveys, particularly searches for periodic variations in
optical light curves of quasars. However, the periodicity search is prone to
false positives from quasar red noise and quasi-periodic oscillations from the
accretion disc of a single supermassive black hole---especially when the data
span fewer than a few signal cycles. We present a Bayesian method for the
detection of quasar (quasi-)periodicity in the presence of red noise. We apply
this method to the binary candidate PG1302$-$102, and show that a) there is
very strong support (Bayes factor $>10^6$) for quasi-periodicity, and b) the
data slightly favour a quasi-periodic oscillation over a sinusoidal signal,
which we interpret as modest evidence against the binary black hole hypothesis.
We also find that the prevalent damped random walk red-noise model is
disfavored with more than 99.9\% credibility. Finally, we outline future work
that may enable the unambiguous identification of supermassive binary black
holes.
