  We consider the application of active subspaces to inform a
Metropolis-Hastings algorithm, thereby aggressively reducing the computational
dimension of the sampling problem. We show that the original formulation, as
proposed by Constantine, Kent, and Bui-Thanh (SIAM J. Sci. Comput.,
38(5):A2779-A2805, 2016), possesses asymptotic bias. Using pseudo-marginal
arguments, we develop an asymptotically unbiased variant. Our algorithm is
applied to a synthetic multimodal target distribution as well as a Bayesian
formulation of a parameter inference problem for a Lorenz-96 system.
