  We develop a Bayesian analysis method for selecting the most probable
equation of state under a set of constraints from compact star physics, which
now include the tidal deformability from GW170817. We apply this method for the
first time to a two-parameter family of hybrid equations of state that is based
on realistic models for the hadronic phase (KVORcut02) and the quark matter
phase (SFM$\alpha$) which produce a third family of hybrid stars in the
mass-radius diagram. One parameter ($\alpha$) characterizes the screening of
the string tension in the string-flip model of quark matter while the other
($\Delta_P$) belongs to the mixed phase construction that mimics the
thermodynamics of pasta phases and includes the Maxwell construction as a
limiting case for $\Delta_P=0$. We present the corresponding results for
compact star properties like mass, radius and tidal deformabilities and use
empirical data for them in the newly developed Bayesian analysis method to
obtain the probabilities for the model parameters within their considered
range.
