title: Streamlined mean field variational Bayes for longitudinal and multilevel data analysis.
abstract: Streamlined mean field variational Bayes algorithms for efficient fitting and inference in large models for longitudinal and multilevel data analysis are obtained. The number of operations is linear in the number of groups at each level, which represents a two orders of magnitude improvement over the naïve approach. Storage requirements are also lessened considerably. We treat models for the Gaussian and binary response situations. Our algorithms allow the fastest ever approximate Bayesian analyses of arbitrarily large longitudinal and multilevel datasets, with little degradation in accuracy compared with Markov chain Monte Carlo. The modularity of mean field variational Bayes allows relatively simple extension to more complicated scenarios.
authors.affiliation: School of Mathematical and Physical Sciences, University of Technology Sydney, P.O. Box 123, Broadway, New South Wales 2007, Australia.
authors.forename: Cathy Yuen Yi
authors.initials: CY
authors.lastname: Lee
authors.affiliation: School of Mathematical and Physical Sciences, University of Technology Sydney, P.O. Box 123, Broadway, New South Wales 2007, Australia.
authors.forename: Matt P
authors.initials: MP
authors.lastname: Wand
mesh_terms: D000465:Algorithms; D001499:Bayes Theorem; D001699:Biometry / Q000379:methods*; D003627:Data Interpretation, Statistical; D008390:Markov Chains; D009010:Monte Carlo Method; D016011:Normal Distribution
keywords: Bayesian computing; Longitudinal data; Matrix decomposition; Multilevel model; Variational approximations