Journal article
Distributed Bayesian Inference in Linear Mixed-Effects Models
Journal of computational and graphical statistics, Vol.30(3), pp.594-611
09/16/2021
DOI: 10.1080/10618600.2020.1869025
Abstract
Linear mixed-effects models play a fundamental role in statistical methodology. A variety of Markov chain Monte Carlo (MCMC) algorithms exist for fitting these models, but they are inefficient in massive data settings because every iteration of any such MCMC algorithm passes through the full data. Many divide-and-conquer methods have been proposed to solve this problem, but they lack theoretical guarantees, impose restrictive assumptions, or have complex computational algorithms. Our focus is one such method called the Wasserstein Posterior (WASP), which has become popular due to its optimal theoretical properties under general assumptions. Unfortunately, practical implementation of the WASP either requires solving a complex linear program or is limited to one-dimensional parameters. The former method is inefficient and the latter method fails to capture the joint posterior dependence structure of multivariate parameters. We develop a new algorithm for computing the WASP of multivariate parameters that is easy to implement and is useful for computing the WASP in any model where the posterior distribution of parameter belongs to a location-scatter family of probability measures. The algorithm is introduced for linear mixed-effects models with both implementation details and theoretical properties. Our algorithm outperforms the current state-of-the-art method in inference on the functions of the covariance matrix of the random effects across diverse numerical comparisons. Supplemental materials for this article are available online.
Details
- Title: Subtitle
- Distributed Bayesian Inference in Linear Mixed-Effects Models
- Creators
- SanveshB Srivastava - Univ Iowa, Dept Stat & Actuarial Sci, Iowa City, IA 52242 USAYixiang Xu - University of California, Berkeley
- Resource Type
- Journal article
- Publication Details
- Journal of computational and graphical statistics, Vol.30(3), pp.594-611
- DOI
- 10.1080/10618600.2020.1869025
- ISSN
- 1061-8600
- eISSN
- 1537-2715
- Publisher
- Taylor & Francis
- Number of pages
- 18
- Grant note
- DMS-1854667/1854662 / National Science Foundation; National Science Foundation (NSF) ONR-BAA N000141812741 / Office of Naval Research; Office of Naval Research
- Language
- English
- Date published
- 09/16/2021
- Academic Unit
- Statistics and Actuarial Science
- Record Identifier
- 9984257743802771
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