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Statistica Sinica 21 (2011), 369-389





THEORY OF GAUSSIAN VARIATIONAL APPROXIMATION

FOR A POISSON MIXED MODEL


Peter Hall, J. T. Ormerod and M. P. Wand


University of Melbourne, University of Sydney and University of Wollongong


Abstract: 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.



Key words and phrases: Asymptotic theory, generalized linear mixed models, Kullback-Liebler divergence, longitudinal data analysis, maximum likelihood estimation.

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