Asymptotic normality and valid inference for Gaussian variational approximation

Details Asymptotic normality and valid inference for Gaussian variational approximation Asymptotic normality and valid inference for Gaussian variational approximation

2012-02-23

arxiv.org/abs/1202.5183v1

Annals of Statistics 2011, Vol. 39, No. 5, 2502-2532

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/11-AOS908 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

10.1214/11-AOS908

We derive the precise asymptotic distributional behavior of Gaussian variational approximate estimators of the parameters in a single-predictor Poisson mixed model. These results are the deepest yet obtained concerning the statistical properties of a variational approximation method. Moreover, they give rise to asymptotically valid statistical inference. A simulation study demonstrates that Gaussian variational approximate confidence intervals possess good to excellent coverage properties, and have a similar precision to their exact likelihood counterparts.

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