  Sampling of sharp posteriors in high dimensions is a challenging problem,
especially when gradients of the likelihood are unavailable. In low to moderate
dimensions, affine-invariant methods, a class of ensemble-based gradient-free
methods, have found success in sampling concentrated posteriors. However, the
number of ensemble members must exceed the dimension of the unknown state in
order for the correct distribution to be targeted. Conversely, the
preconditioned Crank-Nicolson (pCN) algorithm succeeds at sampling in high
dimensions, but samples become highly correlated when the posterior differs
significantly from the prior. In this article we combine the above methods in
two different ways as an attempt to find a compromise. The first method
involves inflating the proposal covariance in pCN with that of the current
ensemble, whilst the second performs approximately affine-invariant steps on a
continually adapting low-dimensional subspace, while using pCN on its
orthogonal complement.
