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    Dimension-independent likelihood-informed MCMC

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    1-s2.0-S0021999115006701-main.pdf
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    Type
    Article
    Authors
    Cui, Tiangang
    Law, Kody
    Marzouk, Youssef M.
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2015-10-19
    Online Publication Date
    2015-10-19
    Print Publication Date
    2016-01
    Permanent link to this record
    http://hdl.handle.net/10754/581312
    
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    Abstract
    Many Bayesian inference problems require exploring the posterior distribution of high-dimensional parameters that represent the discretization of an underlying function. This work introduces a family of Markov chain Monte Carlo (MCMC) samplers that can adapt to the particular structure of a posterior distribution over functions. Two distinct lines of research intersect in the methods developed here. First, we introduce a general class of operator-weighted proposal distributions that are well defined on function space, such that the performance of the resulting MCMC samplers is independent of the discretization of the function. Second, by exploiting local Hessian information and any associated low-dimensional structure in the change from prior to posterior distributions, we develop an inhomogeneous discretization scheme for the Langevin stochastic differential equation that yields operator-weighted proposals adapted to the non-Gaussian structure of the posterior. The resulting dimension-independent and likelihood-informed (DILI) MCMC samplers may be useful for a large class of high-dimensional problems where the target probability measure has a density with respect to a Gaussian reference measure. Two nonlinear inverse problems are used to demonstrate the efficiency of these DILI samplers: an elliptic PDE coefficient inverse problem and path reconstruction in a conditioned diffusion.
    Citation
    Dimension-independent likelihood-informed MCMC 2015 Journal of Computational Physics
    Publisher
    Elsevier BV
    Journal
    Journal of Computational Physics
    DOI
    10.1016/j.jcp.2015.10.008
    arXiv
    1411.3688
    Additional Links
    http://linkinghub.elsevier.com/retrieve/pii/S0021999115006701
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.jcp.2015.10.008
    Scopus Count
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    Articles; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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