Gaussian Approximations of SDES in Metropolis-Adjusted Langevin Algorithms

Markov chain Monte Carlo (MCMC) methods are a cornerstone of Bayesian inference and stochastic simulation. The Metropolis-adjusted Langevin algorithm (MALA) is an MCMC method that relies on the simulation of a stochastic differential equation (SDE) whose stationary distribution is the desired target density using the Euler-Maruyama algorithm and accounts for simulation errors using a Metropolis step. In this paper we propose a modification of the MALA which uses Gaussian assumed density approximations for the integration of the SDE. The effectiveness of the algorithm is illustrated on simulated and real data sets.