Spectral gap of Metropolis-within-Gibbs under log-concavity

arXiv:2509.26175 · stat.ML, math.ST, stat.ME, stat.TH · Submitted 2025-09-30 · Read on arXiv

stat.ML, math.ST, stat.ME, stat.TH

Submitted: 2025-09-30

Updated: 2026-09-16

Comments: 23 pages, 7 figure

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Spectral Gap — 23× in this paper · explained in 5 episodes
• Data Augmentation — 2× in this paper · explained in 7 episodes
• Benchmark — 1× in this paper · explained in 2 episodes
• Calibration — 1× in this paper · explained in 7 episodes
• Clustering — 1× in this paper · explained in 2 episodes
• Consistency — 1× in this paper · explained in 3 episodes
• Convergence Guarantees — 1× in this paper · explained in 3 episodes
• Hilbert Space — 1× in this paper · explained in 2 episodes
• MwG with Random Walk Metropolis — 1× in this paper

Sources

• Mixing times of data-augmentation Gibbs samplers for high-dimensional probit regression
• Entropy contraction of the Gibbs sampler under log-concavity
• Scalability of Metropolis-within-Gibbs schemes for high-dimensional Bayesian models
• A practical sequential stopping rule for high-dimensional MCMC and its application to spatial-temporal Bayesian models
• Fast Mixing of Data Augmentation Algorithms: Bayesian Probit, Logit, and Lasso Regression
• Is Gibbs sampling faster than Hamiltonian Monte Carlo on GLMs?
• On spectral gap decomposition for Markov chains
• Spectral gap bounds for reversible hybrid Gibbs chains

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