Hall, P.; Ormerod, J. T.; and Wand, M. P., Theory of Gaussian Variational Approximation for a Poisson Mixed Model, Centre for Statistical and Survey Methodology, University of Wollongong, Working Paper 06-09, 2009, 16p.
Likelihood-based inference for the parameters of generalized linear mixed models is hindered by the presence of intractable integrals. Gaussian variational approximation provides a fast and effective means of approximate inference. We provide some theory for this type of approximation for a simple Poisson mixed model. In particular, we establish consistency at rate m−1/2 + n−1, where m is the number of groups and n is the number of repeated measurements.