Please use this identifier to cite or link to this item: https://doi.org/10.1214/13-STS418
Title: Variational inference for generalized linear mixed models using partially noncentered parametrizations
Authors: Tan, L.S.L.
Nott, D.J. 
Keywords: Hierarchical centering
Longitudinal data analysis.
Nonconjugate models
Variational bayes
Variational message passing
Issue Date: May-2013
Citation: Tan, L.S.L., Nott, D.J. (2013-05). Variational inference for generalized linear mixed models using partially noncentered parametrizations. Statistical Science 28 (2) : 168-188. ScholarBank@NUS Repository. https://doi.org/10.1214/13-STS418
Abstract: The effects of different parametrizations on the convergence of Bayesian computational algorithms for hierarchical models are well explored. Techniques such as centering, noncentering and partial noncentering can be used to accelerate convergence in MCMC and EM algorithms but are still not well studied for variational Bayes (VB) methods. As a fast deterministic approach to posterior approximation, VB is attracting increasing interest due to its suitability for large high-dimensional data. Use of different parametrizations for VB has not only computational but also statistical implications, as different parametrizations are associated with different factorized posterior approximations. We examine the use of partially noncentered parametrizations in VB for generalized linear mixed models (GLMMs). Our paper makes four contributions. First, we show how to implement an algorithm called nonconjugate variational message passing for GLMMs. Second, we show that the partially noncentered parametrization can adapt to the quantity of information in the data and determine a parametrization close to optimal. Third, we show that partial noncentering can accelerate convergence and produce more accurate posterior approximations than centering or noncentering. Finally, we demonstrate how the variational lower bound, produced as part of the computation, can be useful for model selection. © Institute of Mathematical Statistics, 2013.
Source Title: Statistical Science
URI: http://scholarbank.nus.edu.sg/handle/10635/105461
ISSN: 08834237
DOI: 10.1214/13-STS418
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