Dimension free convergence rates for Gibbs samplers for Bayesian linear mixed models

The emergence of big data has led to a growing interest in so-called convergence complexity analysis, which is the study how rate Monte Carlo Markov chain (for an intractable Bayesian posterior distribution) scales as underlying set grows size. Convergence analysis practical chains on continuous state spaces quite challenging, and there have been very few successful analyses such chains. One fruitful was recently presented by Qin Hobert (2022), who studied Gibbs sampler for simple random effects model. These authors showed that, under regularity conditions, geometric this converges zero It shown herein that similar behavior exhibited samplers more general models possess both traditional covariates, mixed models. employs Wasserstein-based techniques introduced (2022).