Efficient Bayesian inference of subsurface flow models using nested sampling and sparse polynomial chaos surrogates

Ahmed H Elsheikh, Ibrahim Hoteit, Mary F Wheeler

    Research output: Contribution to journalArticle

    65 Citations (Scopus)

    Abstract

    An efficient Bayesian calibration method based on the nested sampling (NS) algorithm and non-intrusive polynomial chaos method is presented. Nested sampling is a Bayesian sampling algorithm that builds a discrete representation of the posterior distributions by iteratively re-focusing a set of samples to high likelihood regions. NS allows representing the posterior probability density function (PDF) with a smaller number of samples and reduces the curse of dimensionality effects. The main difficulty of the NS algorithm is in the constrained sampling step which is commonly performed using a random walk Markov chain Monte-Carlo (MCMC) algorithm. In this work, we perform a two–stage sampling using a polynomial chaos response surface to filter out rejected samples in the Markov chain Monte-Carlo method. The combined use of nested sampling and the two–stage MCMC based on approximate response surfaces provides significant computational gains in terms of the number of simulation runs. The proposed algorithm is applied for calibration and model selection of subsurface flow models.
    Original languageEnglish
    Pages (from-to)515-537
    Number of pages23
    JournalComputer Methods in Applied Mechanics and Engineering
    Volume269
    Early online date18 Nov 2013
    DOIs
    Publication statusPublished - Feb 2014

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