Asymptotic normality and valid inference for Gaussian variational approximation

Institute of Mathematical Statistics (IMS)
Publication Type:
Journal Article
Annals of Statistics, 2011, 39 (5), pp. 2502 - 2532
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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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