On an adaptive preconditioned Crank-Nicolson MCMC algorithm for infinite dimensional Bayesian inferences
Year: 2015
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Hu, Zixi, Yao, Zhewei, Li, Jinglai
Institution: Shanghai Jiao Tong University
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G7095888214
OpenAlex ID: W2256005783