Safe, Scalable, and Accurate Bayes Posterior Sampling for Large-Data Generalized Linear Mixed Models

• URL: http://arxiv.org/abs/2604.26029v1
• Date: Tue, 28 Apr 2026 18:11:19 GMT
• Title: Safe, Scalable, and Accurate Bayes Posterior Sampling for Large-Data Generalized Linear Mixed Models
• Abstract summary: We consider the problem of scalable sampling algorithms to fit generalized linear mixed models on large datasets.<n>We advocate the use of a mirror Langevin dynamics algorithm based on data subsampling and provide concrete guidelines for its use in an inference framework.
• Score: 1.1458853556386799
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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