  We suggest a new Bayesian analysis (BA) using disjunct M-R constraints for
extracting probability measures for cold, dense matter equations of state
(EoS). One of the key issues of such an analysis is the question of a
deconfinement transition in compact stars and whether it proceeds as a
crossover or rather as a first order transition. We show by postulating results
of not yet existing radius measurements for the known pulsars with a mass of
$2M_\odot$ that a radius gap of about 3 km would clearly select an EoS with a
strong first order phase transition as the most probably one. This would
support the existence of a critical endpoint in the QCD phase diagram under
scrutiny in present and upcoming heavy-ion collision experiments.
