Asymptotic normality and valid inference for Gaussian variational approximation

Authors

Peter Hall, University of Melbourne
Tung Pham, University of WollongongFollow
M P. Wand, University of Technology, SydneyFollow
S S.J Wang, University of WollongongFollow

RIS ID

44472

Publication Details

Hall, P., Pham, T., Wand, M. P.. & Wang, S. (2011). Asymptotic normality and valid inference for Gaussian variational approximation. Annals of Statistics, 39 (5), 2502-2532.

Abstract

We derive the precise asymptotic distributional behavior of Gaussianvariational approximate estimators of the parameters in a single-predictorPoisson mixed model. These results are the deepest yet obtained concerningthe statistical properties of a variational approximation method. Moreover,they give rise to asymptotically valid statistical inference. A simulation studydemonstrates that Gaussian variational approximate confidence intervals possessgood to excellent coverage properties, and have a similar precision totheir exact likelihood counterparts.

Grant Number

ARC/DP0877055

Additional Grant Number

http://purl.org/au-research/grants/arc/DP0877055