On a Generalization of the Preconditioned Crank–Nicolson Metropolis Algorithm

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 on the measure of interest. a numerical simulation of a bayesian inverse problem indicates that a metropolis algorithm with such a proposal performs independently 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 convergence from the metropolis algorithm with pcn proposal.