Safe, Scalable, and Accurate Bayes Posterior Sampling for Large-Data Generalized Linear Mixed Models
Year: 2026
Type: preprint
Abstract: We consider the problem of scalable sampling algorithms to fit Bayesian generalized linear mixed models on large datasets. Stochastic gradient Langevin dynamics, coupled with smooth re-parameterizations of variance parameters, produces divergent Markov chains and cannot be reliably used for sampling covariance parameters of random effects. We advocate the use of a mirror Langevin dynamics algorithm, propose the novel stochastic mirror Langevin dynamics based on data subsampling, and provide concrete guidelines for its use in a Bayesian inference framework. Based on an explicit Wasserstein distance error bound between the posterior and its algorithmic approximation, we propose a post-processing step that yields an asymptotic, order-wise correct estimation of the posterior variance, eliminating the irreducible posterior variance estimation bias due to subsampling. Empirical performance of the method is evaluated through simulated experiments and a longitudinal study of pain trajectories in a study of breast cancer survivors.
Source: arXiv (Cornell University)
Authors: Baek, Youngsoo, Berchuck, Samuel I.
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7159164275
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