Convergence rate of a collapsed Gibbs sampler for crossed random effects models

2021/09/07 by Swarnadip Ghosh, Ghosh, Swarnadip, Chenyang Zhong +1
Mathematics · #Computation (stat.CO) #FOS: Computer and information sciences #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Methodology (stat.ME) #Random Matrices and Applications #Statistical Methods and Inference #Statistics Theory (math.ST) #math.ST #stat.CO #stat.ME #stat.TH

paper · pdf · doi:10.48550/arxiv.2109.02849

42 pages, 12 figures

openalex publication_date 2021/09/07 · arxiv created 2021/10/21 · arxiv updated 2021/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

In this paper, we analyze the convergence rate of a collapsed Gibbs sampler for crossed random effects models. Our results apply to a substantially larger range of models than previous works, including models that incorporate missingness mechanism and unbalanced level data. The theoretical tools involved in our analysis include a connection between relaxation time and autoregression matrix, concentration inequalities, and random matrix theory.

Citations

• Estimation and Inference for Very Large Linear Mixed Effects Models

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