  The problem of low-rank matrix estimation recently received a lot of
attention due to challenging applications. A lot of work has been done on
rank-penalized methods and convex relaxation, both on the theoretical and
applied sides. However, only a few papers considered Bayesian estimation. In
this paper, we review the different type of priors considered on matrices to
favour low-rank. We also prove that the obtained Bayesian estimators, under
suitable assumptions, enjoys the same optimality properties as the ones based
on penalization.
