  Metropolis algorithms for approximate sampling of probability measures on
infinite dimensional Hilbert spaces are considered and a generalization of the
preconditioned Crank-Nicolson (pCN) proposal is introduced. The new proposal is
able to incorporate information of the measure of interest. A numerical
simulation of a Bayesian inverse problem indicates that a Metropolis algorithm
with such a proposal performs independent of the state space dimension and the
variance of the observational noise. Moreover, a qualitative convergence result
is provided by a comparison argument for spectral gaps. In particular, it is
shown that the generalization inherits geometric ergodicity from the Metropolis
algorithm with pCN proposal.
