An adaptive independence sampler MCMC algorithm for Bayesian inferences of functions

Zhe Feng, Jinglai Li

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


Many scientific and engineering problems require one to perform Bayesian inferences in function spaces, in which the unknowns are of infinite dimension. In such problems, many standard Markov chain Monte Carlo (MCMC) algorithms become arbitrarily slow under the mesh refinement, which is referred to as being dimension dependent. In this work we develop an independence sampler based MCMC method for the Bayesian inferences of functions. We represent the proposal distribution as a mixture of a finite number of specially parametrized Gaussian measures. We also design an efficient adaptive algorithm to adjust the parameter values of the mixtures from the previous samples. Finally we provide numerical examples to demonstrate the efficiency and robustness of the proposed method, even for problems with multimodal posterior distributions.
Original languageEnglish
Pages (from-to)A1301–A1321
JournalSIAM Journal on Scientific Computing
Issue number3
Publication statusPublished - 8 May 2018


  • adaptive Markov chain Monte Carlo
  • Bayesian inference
  • Gaussian mixture
  • independence sampler
  • inverse problem


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