  In this paper we perform a numerious numerical studies for the problem of
low-rank matrix completion. We compare the Bayesain approaches and a recently
introduced de-biased estimator which provides a useful way to build confidence
intervals of interest. From a theoretical viewpoint, the de-biased estimator
comes with a sharp minimax-optinmal rate of estimation error whereas the
Bayesian approach reaches this rate with an additional logarithmic factor. Our
simulation studies show originally interesting results that the de-biased
estimator is just as good as the Bayesain estimators. Moreover, Bayesian
approaches are much more stable and can outperform the de-biased estimator in
the case of small samples. However, we also find that the length of the
confidence intervals revealed by the de-biased estimator for an entry is
absolutely shorter than the length of the considered credible interval. These
suggest further theoretical studies on the estimation error and the
concentration for Bayesian methods as they are being quite limited up to
present.
