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We analyse computational efficiency of Metropolis-Hastings algorithms withstochastic AR(1) process proposals. These proposals include, as a subclass,discretized Langevin diffusion (e.g. MALA) and discretized Hamiltonian dynamics(e.g. HMC).  We derive expressions for the expected acceptance rate and expected jump sizefor MCMC methods with general stochastic AR(1) process proposals for the casewhere the target distribution is absolutely continuous with respect to aGaussian and the covariance of the Gaussian is allowed to have off-diagonalterms. This allows us to extend what is known about several MCMC methods aswell as determining the efficiency of new MCMC methods of this type. In thespecial case of Hybrid Monte Carlo, we can determine the optimal integrationtime and the effect of the choice of mass matrix.  By including the effect of Metropolis-Hastings we also extend results by Foxand Parker, who used matrix splitting techniques to analyse the performance andimprove efficiency of stochastic AR(1) processes for sampling from Gaussiandistributions.

Metropolis-Hastings algorithms with autoregressive proposals, and a few examples