Asymptotic normality and valid inference for Gaussian variational approximation

Authors

P. Hall, University of Wollongong
T. Pham, University of Wollongong
M. Wand, University of WollongongFollow
S.S.J. Wang, University of Wollongong

Publication Date

2010

Recommended Citation

Hall, P.; Pham, T.; Wand, M.; and Wang, S.S.J., Asymptotic normality and valid inference for Gaussian variational approximation, Centre for Statistical and Survey Methodology, University of Wollongong, Working Paper 04-10, 2010, 24p.
https://ro.uow.edu.au/cssmwp/55

Abstract

We derive the precise asymptotic distributional behavior of Gaussian variational approximate estimators of the parameters in a singlepredictor 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 with precision similar to their exact likelihood counterparts.