On an adaptive preconditioned Crank-Nicolson MCMC algorithm for infinite dimensional Bayesian inference

Hu, Zixi, Yao, Zhewei and Li, Jinglai ORCID: 0000-0001-7980-6901 (2017) On an adaptive preconditioned Crank-Nicolson MCMC algorithm for infinite dimensional Bayesian inference. JOURNAL OF COMPUTATIONAL PHYSICS, 332. pp. 492-503.

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Abstract

Many scientific and engineering problems require to perform Bayesian inferences for unknowns of infinite dimension. In such problems, many standard Markov Chain Monte Carlo (MCMC) algorithms become arbitrary slow under the mesh refinement, which is referred to as being dimension dependent. To this end, a family of dimensional independent MCMC algorithms, known as the preconditioned Crank-Nicolson (pCN) methods, were proposed to sample the infinite dimensional parameters. In this work we develop an adaptive version of the pCN algorithm, where the covariance operator of the proposal distribution is adjusted based on sampling history to improve the simulation efficiency. We show that the proposed algorithm satisfies an important ergodicity condition under some mild assumptions. Finally we provide numerical examples to demonstrate the performance of the proposed method.

Item Type:	Article
Uncontrolled Keywords:	Bayesian inference, Infinite dimensional inverse problems, Adaptive Markov Chain Monte Carlo
Depositing User:	Symplectic Admin
Date Deposited:	04 Dec 2018 09:40
Last Modified:	19 Jan 2023 01:11
DOI:	10.1016/j.jcp.2016.11.024
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3029238