  This survey reviews the existing literature on the most relevant Bayesian
inference methods for univariate and multivariate GARCH models. The advantages
and drawbacks of each procedure are outlined as well as the advantages of the
Bayesian approach versus classical procedures. The paper makes emphasis on
recent Bayesian non-parametric approaches for GARCH models that avoid imposing
arbitrary parametric distributional assumptions. These novel approaches
implicitly assume infinite mixture of Gaussian distributions on the
standardized returns which have been shown to be more flexible and describe
better the uncertainty about future volatilities. Finally, the survey presents
an illustration using real data to show the flexibility and usefulness of the
non-parametric approach.
