  We analyse computational efficiency of Metropolis-Hastings algorithms with
stochastic 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 size
for MCMC methods with general stochastic AR(1) process proposals for the case
where the target distribution is absolutely continuous with respect to a
Gaussian and the covariance of the Gaussian is allowed to have off-diagonal
terms. This allows us to extend what is known about several MCMC methods as
well as determining the efficiency of new MCMC methods of this type. In the
special case of Hybrid Monte Carlo, we can determine the optimal integration
time and the effect of the choice of mass matrix.
  By including the effect of Metropolis-Hastings we also extend results by Fox
and Parker, who used matrix splitting techniques to analyse the performance and
improve efficiency of stochastic AR(1) processes for sampling from Gaussian
distributions.
