Manifold lifting: scaling Markov chain Monte Carlo to the vanishing noise regime
流形提升：将 MCMC 扩展到观测噪声趋零的情形
Abstract Standard Markov chain Monte Carlo methods struggle to explore distributions that concentrate in the neighbourhood of low-dimensional submanifolds. This pathology naturally occurs in Bayesian inference settings when there is a high signal-to-noise ratio in the observational data but the model is inherently over-parametrised or nonidentifiable. In this paper, we propose a strategy that transforms the original sampling problem into the task of exploring a distribution…