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

Researchers Youngsoo Baek and Samuel I. Berchuck have developed a novel stochastic mirror Langevin dynamics (SMLD) algorithm for safe, scalable, and accurate Bayesian posterior sampling in generalized linear mixed models (GLMMs) on large datasets. Traditional stochastic gradient Langevin dynamics (SGLD) often produce divergent Markov chains when coupled with smooth re-parameterizations of variance parameters, making them unreliable for sampling covariance parameters of random effects. The new SMLD method replaces this with a mirror Langevin framework, which uses data subsampling to maintain scalability while ensuring chain stability. The authors provide concrete implementation guidelines for Bayesian inference, including a post-processing step that leverages an explicit Wasserstein distance error bound between the posterior and its approximation. This step yields an asymptotic, order-wise correct estimation of posterior variance, eliminating the irreducible bias caused by subsampling—a key limitation of existing methods.

The method's empirical performance was validated through simulated experiments and a real-world longitudinal study of pain trajectories in breast cancer survivors. By enabling accurate Bayesian inference on large datasets without the computational cost of full MCMC, SMLD opens new possibilities for analyzing complex hierarchical data in fields like healthcare, ecology, and social sciences. The paper, published on arXiv (2604.26029), spans 19 pages with 5 figures and is categorized under statistics methodology, computation, and machine learning. This work addresses a critical bottleneck in Bayesian statistics, making posterior sampling practical for big-data applications while preserving theoretical guarantees.