  Proposals for Metropolis-Hastings MCMC derived by discretizing Langevin
diffusion or Hamiltonian dynamics are examples of stochastic autoregressive
proposals that form a natural wider class of proposals with equivalent
computability. We analyze Metropolis-Hastings MCMC with stochastic
autoregressive proposals applied to target distributions that are absolutely
continuous with respect to some Gaussian distribution to derive expressions for
expected acceptance probability and expected jump size, as well as measures of
computational cost, in the limit of high dimension. Thus, we are able to unify
existing analyzes for these classes of proposals, and to extend the theoretical
results that provide useful guidelines for tuning the proposals for optimal
computational efficiency. For the simplified Langevin algorithm we find that it
is optimal to take at least three steps of the proposal before the
Metropolis-Hastings accept-reject step, and for Hamiltonian/hybrid Monte Carlo
we provide new guidelines for the optimal number of integration steps and
criteria for choosing the optimal mass matrix.
