Asymptotic normality and valid inference for Gaussian variational approximation

Abstract

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.

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

References in corpus (1)

• Expectation Propagation for approximate Bayesian inference

Cited by in corpus (12)

• Variational Inference: A Review for Statisticians
• Frequentist Consistency of Variational Bayes
• Semiparametric Regression using Variational Approximations
• Bayesian Model Selection via Mean-Field Variational Approximation
• Variational Inference in high-dimensional linear regression
• Statistical Inference in Mean-Field Variational Bayes
• On the use of bootstrap with variational inference: Theory, interpretation, and a two-sample test example
• Variational Bayes under Model Misspecification
• Local convexity of the TAP free energy and AMP convergence for Z2-synchronization
• Variational Discriminant Analysis with Variable Selection
• Approximation Properties of Variational Bayes for Vector Autoregressions
• Supervised Multiscale Dimension Reduction for Spatial Interaction Networks