Efficiency and computability of MCMC with Langevin, Hamiltonian, and other matrix-splitting proposals

Abstract: We analyse computational efficiency of Metropolis-Hastings algorithms with AR(1) process proposals. These proposals include, as a subclass, discretized Langevin diffusion (e.g. MALA) and discretized Hamiltonian dynamics (e.g. HMC). By including the effect of Metropolis-Hastings we extend earlier work by Fox and Parker, who used matrix splitting techniques to analyse the performance and improve efficiency of AR(1) processes for targeting Gaussian distributions. Our research enables analysis of MCMC methods that draw samples from non-Gaussian target distributions by using AR(1) process proposals in Metropolis-Hastings algorithms, by analysing the matrix splitting of the precision matrix for a local Gaussian approximation of the non-Gaussian target.