Convergence of Dirichlet Forms for MCMC Optimal Scaling with General Target Distributions on Large Graphs. (arXiv:2210.17042v1 [math.ST])

Markov chain Monte Carlo (MCMC) algorithms have played a significant role in
statistics, physics, machine learning and others, and they are the only known
general and efficient approach for some high-dimensional problems. The
Metropolis-Hastings (MH) algorithm as the most classical MCMC algorithm, has
had a great influence on the development and practice of science and
engineering. The behavior of the MH algorithm in high-dimensional problems is
typically investigated through a weak convergence result of diffusion
processes. In this paper, we …

arxiv convergence general graphs math mcmc scaling