Gaussian Variational Approximate Inference for Generalized Linear Mixed Models BY J.T. ORMEROD AND M.P. WAND

Variational approximation methods have become a mainstay of contemporary Machine Learn-ing methodology, but currently have little presence in Statistics. We devise an effective vari-ational approximation strategy for fitting generalized linear mixed models (GLMM) appro-priate for grouped data. It involves Gaussian approximation to the distributions of random effects vectors, conditional on the responses. We show that Gaussian variational approximation is a relatively simple and natural alternative to Laplace approximation for fast, non-Monte Carlo, GLMM analysis. Numerical studies show Gaussian variational approximation to be very accu-rate in grouped data GLMM contexts. Finally, we point to some recent theory on consistency of Gaussian variational approximation in this context