  Approximate inference methods like the Laplace method, Laplace approximations
and variational methods, amongst others, are popular methods when exact
inference is not feasible due to the complexity of the model or the abundance
of data. In this paper we propose a hybrid approximate method called Low-Rank
Variational Bayes correction (VBC), that uses the Laplace method and
subsequently a Variational Bayes correction in a lower dimension, to the joint
posterior mean. The cost is essentially that of the Laplace method which
ensures scalability of the method, in both model complexity and data size.
Models with fixed and unknown hyperparameters are considered, for simulated and
real examples, for small and large datasets.
