A replica exchange preconditioned Crank-Nicolson Langevin dynamic MCMC method for Bayesian inverse problems

Understand

This paper proposes a replica exchange preconditioned Langevin diffusion discretized by the Crank-Nicolson scheme (repCNLD) to handle high-dimensional and multi-modal distribution problems.

• Sampling from high-dimensional and multi-modal distributions is a challenging question.
• The performance of many standard MCMC chains deteriorates as the dimension of parameters increases, and many MCMC algorithms cannot capture all modes if the energy function is not convex.
• The proposed repCNLD can accelerate the convergence of the single-chain pCNLD, and can capture all modes of the multi-modal distributions.