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The article develops a hybrid Variational Bayes algorithm that combines themean-field and fixed-form Variational Bayes methods. The new estimationalgorithm can be used to approximate any posterior without relying on conjugatepriors. We propose a divide and recombine strategy for the analysis of largedatasets, which partitions a large dataset into smaller pieces and thencombines the variational distributions that have been learnt in parallel oneach separate piece using the hybrid Variational Bayes algorithm. The proposedmethod is applied to fitting generalized linear mixed models. The computationalefficiency of the parallel and hybrid Variational Bayes algorithm isdemonstrated on several simulated and real datasets.

Efficient variational inference for generalized linear mixed models with large datasets