  In the present paper we examine the effects of noise on Monte Carlo
algorithms, a problem raised previously by Kennedy and Kuti (Phys. Rev. Lett.
{\bf 54}, 2473 (1985)). We show that the effects of introducing unbiased noise
into the acceptance/rejection phase of the conventional Metropolis approach are
surprisingly modest, and, to a significant degree, largely controllable. We
present model condensed phase numerical applications to support these
conclusions.
