  The article develops a hybrid Variational Bayes algorithm that combines the
mean-field and fixed-form Variational Bayes methods. The new estimation
algorithm can be used to approximate any posterior without relying on conjugate
priors. We propose a divide and recombine strategy for the analysis of large
datasets, which partitions a large dataset into smaller pieces and then
combines the variational distributions that have been learnt in parallel on
each separate piece using the hybrid Variational Bayes algorithm. The proposed
method is applied to fitting generalized linear mixed models. The computational
efficiency of the parallel and hybrid Variational Bayes algorithm is
demonstrated on several simulated and real datasets.
