The Metropolis–Hastings algorithm allows one to sample asymptotically from any probability distribution π that admits a density w.r.t to a reference measure which can be evaluated pointwise up to a normalizing constant. There has been recently much work devoted to the development of variants of Metropolis–Hastings which can handle scenarios where such an evaluation is impossible . The most popular approach which has emerged is arguably the pseudo-marginal Metropolis–Hastings algorithm which substitutes an unbiased estimate of π for π. In this talk, we explore an alternative class of pseudo-marginal algorithms relying instead on unbiased estimates of the Metropolis–Hastings ratio. We establish some theoretical properties for these schemes and demonstrate them on various inference problems involving doubly intractable distributions and latent variable models.