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Scalable inference for crossed random effects models
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Papaspiliopoulos, O., Roberts, Gareth O. and Zanella, G. (2019) Scalable inference for crossed random effects models. Biometrika . doi:10.1093/biomet/asz058 ISSN 0006-3444.
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Official URL: https://doi.org/10.1093/biomet/asz058
Abstract
We develop methodology and complexity theory for Markov chain Monte Carlo algorithms used in inference for crossed random effect models in modern analysis of variance. We consider 15 a plain Gibbs sampler and a simple modification we propose here, a collapsed Gibbs sampler. Under some balancedness assumptions on the data designs and assuming that precision hyperparameters are known, we demonstrate that the plain Gibbs sampler is not scalable, in the sense that its complexity is worse than proportional to the number of parameters and data, but that the collapsed Gibbs sampler is scalable. In simulated and real datasets we show that the explicit 20 convergence rates our theory predicts match remarkably the computable but non-explicit rates in cases where the design assumptions are violated. We also show empirically that the collapsed Gibbs sampler, extended to sample precision hyperparameters, outperforms significantly, often by orders of magnitude, alternative state of the art algorithms. Supplementary material includes some proofs, additional simulations, implementation details and the R code to implement the 25 algorithms considered in the article.
Item Type: | Journal Article | |||||||||||||||
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Subjects: | Q Science > QA Mathematics | |||||||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | |||||||||||||||
Library of Congress Subject Headings (LCSH): | Bayesian statistical decision theory -- Data processing, Analysis of variance, Markov processes, Multilevel models (Statistics) | |||||||||||||||
Journal or Publication Title: | Biometrika | |||||||||||||||
Publisher: | Biometrika Trust | |||||||||||||||
ISSN: | 0006-3444 | |||||||||||||||
Official Date: | 15 November 2019 | |||||||||||||||
Dates: |
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DOI: | 10.1093/biomet/asz058 | |||||||||||||||
Status: | Peer Reviewed | |||||||||||||||
Publication Status: | Published | |||||||||||||||
Reuse Statement (publisher, data, author rights): | This is a pre-copyedited, author-produced version of an article accepted for publication in Biometrika following peer review. The version of record O Papaspiliopoulos, G O Roberts, G Zanella, Scalable inference for crossed random effects models, Biometrika, , asz058 is available online at: https://doi.org/10.1093/biomet/asz058 | |||||||||||||||
Access rights to Published version: | Restricted or Subscription Access | |||||||||||||||
Date of first compliant deposit: | 18 April 2019 | |||||||||||||||
Date of first compliant Open Access: | 15 November 2020 | |||||||||||||||
RIOXX Funder/Project Grant: |
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