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

09/07/2021

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by   Swarnadip Ghosh, et al.

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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.