  Synchronization is a key functionality in wireless network, enabling a wide
variety of services. We consider a Bayesian inference framework whereby network
nodes can achieve phase and skew synchronization in a fully distributed way. In
particular, under the assumption of Gaussian measurement noise, we derive two
message passing methods (belief propagation and mean field), analyze their
convergence behavior, and perform a qualitative and quantitative comparison
with a number of competing algorithms. We also show that both methods can be
applied in networks with and without master nodes. Our performance results are
complemented by, and compared with, the relevant Bayesian Cram\'er-Rao bounds.
