On a generalization of the preconditioned Crank-Nicolson Metropolis algorithm

Daniel Rudolf; Björn Sprungk

doi:10.1007/s10208-016-9340-x

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arXiv · 1504.03461

On a generalization of the preconditioned Crank-Nicolson Metropolis algorithm

Daniel Rudolf·Björn Sprungk

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Abstract

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.

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BibTeX RIS

Daniel Rudolf, Björn Sprungk. 2015-04-14. On a generalization of the preconditioned Crank-Nicolson Metropolis algorithm. https://doi.org/10.1007/s10208-016-9340-x

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