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

详细信息    查看全文

• 作者：Zixi Hu^a ; ^{hzx@sjtu.edu.cn} ; Zhewei Yao^a ; ^{zyaosjtu@gmail.com} ; Jinglai Li^b ; ^{jinglaili@sjtu.edu.cn}
• 关键词：Bayesian inference ; Infinite dimensional inverse problems ; Adaptive Markov Chain Monte Carlo
• 刊名：Journal of Computational Physics
• 出版年：2017
• 出版时间：1 March 2017
• 年：2017
• 卷：332
• 期：Complete
• 页码：492-503
• 全文大小：618 K
• 卷排序：332

文摘

Many scientific and engineering problems require to perform Bayesian inference 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.