A hybrid adaptive MCMC algorithm in function spaces

Research output: Contribution to journalArticlepeer-review

Authors

Colleges, School and Institutes

Abstract

The preconditioned Crank--Nicolson (pCN) method is a Markov chain Monte Carlo (MCMC) scheme, specifically designed to perform Bayesian inferences in function spaces. Unlike many standard MCMC algorithms, the pCN method can preserve the sampling efficiency under the mesh refinement, a property referred to as being dimension independent. In this work we consider an adaptive strategy to further improve the efficiency of pCN. In particular we develop a hybrid adaptive MCMC method: the algorithm performs an adaptive Metropolis scheme in a chosen finite dimensional subspace and a standard pCN algorithm in the complement space of the chosen subspace. We show that the proposed algorithm satisfies certain important ergodicity conditions. Finally with numerical examples we demonstrate that the proposed method has competitive performance with existing adaptive algorithms.

Details

Original languageEnglish
Pages (from-to)621–639
Number of pages19
JournalSIAM/ASA Journal on Uncertainty Quantification
Volume5
Issue number1
Publication statusPublished - 12 Jul 2017

Keywords

  • adaptive metropolis, Bayesian inference, function space, inverse problems, Markov Chain Monte Carlo