A noisy Monte Carlo algorithm

We propose a Monte Carlo algorithm to promote the Kennedy-Kuti linear accept-reject algorithm which accommodates unbiased stochastic estimates of the probability to an exact one. This is achieved by adopting the Metropolis accept-reject steps for both the dynamical and noise configurations. We test it on the five state model and obtain desirable results even for the case with large noise. We also discuss its application to lattice QCD with stochastically estimated fermion determinants.