2021/01/31 by John O’Leary, O'Leary, John, Guanyang Wang +1 · 1 citation
Mathematics · Medicine · #60J22 #62D05 #65C05 #Advanced MRI Techniques and Applications #Computation (stat.CO) #FOS: Computer and information sciences #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2102.00366
openalex publication_date 2021/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Couplings play a central role in the analysis of Markov chain convergence and in the construction of novel Markov chain Monte Carlo estimators, diagnostics, and variance reduction techniques. The set of possible couplings is often intractable, frustrating the search for tight bounds and efficient estimators. To address this challenge for algorithms in the Metropolis-Hastings (MH) family, we establish a simple characterization of the set of MH transition kernel couplings. We then extend this result to describe the set of maximal couplings of the MH kernel, resolving an open question of O'Leary et al.. Our results represent an advance in understanding the MH transition kernel and a step forward for coupling this popular class of algorithms.