  The cooling phase of thermonuclear (type-I) X-ray bursts can be used to
constrain the neutron star (NS) compactness by comparing the observed cooling
tracks of bursts to accurate theoretical atmosphere model calculations. By
applying the so-called cooling tail method, where the information from the
whole cooling track is used, we constrain the mass, radius, and distance for
three different NSs in low-mass X-ray binaries 4U 1702-429, 4U 1724-307, and
SAX J1810.8-260. Care is taken to only use the hard state bursts where it is
thought that only the NS surface alone is emitting. We then utilize a Markov
chain Monte Carlo algorithm within a Bayesian framework to obtain a
parameterized equation of state (EoS) of cold dense matter from our initial
mass and radius constraints. This allows us to set limits on various nuclear
parameters and to constrain an empirical pressure-density relation for the
dense matter. Our predicted EoS results in NS radius between 10.5-12.8 km (95%
confidence limits) for a mass of 1.4 $M_{\odot}$. Due to systematic errors and
uncertainty in the composition these results should be interpreted as lower
limits for the radius.
