Modified Markov Chain Monte Carlo method for dynamic data integration using streamline approach

Yalchin Efendiev*, Akhil Datta-Gupta, Xianlin Ma, Bani Mallick

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

In this paper, the Markov Chain Monte Carlo (MCMC) approach is used for sampling of the permeability field conditioned on the dynamic data. The novelty of the approach consists of using an approximation of the dynamic data based on streamline computations. The simulations using the streamline approach allows us to obtain analytical approximations in the small neighborhood of the previously computed dynamic data. Using this approximation, we employ a two-stage MCMC approach. In the first stage, the approximation of the dynamic data is used to modify the instrumental proposal distribution. The obtained chain correctly samples from the posterior distribution; the modified Markov chain converges to a steady state corresponding to the posterior distribution. Moreover, this approximation increases the acceptance rate, and reduces the computational time required for MCMC sampling. Numerical results are presented.

Original languageEnglish (US)
Pages (from-to)213-232
Number of pages20
JournalMathematical Geosciences
Volume40
Issue number2
DOIs
StatePublished - Dec 1 2008

Keywords

  • MCMC
  • Markov chain
  • Streamline approach

ASJC Scopus subject areas

  • Mathematics (miscellaneous)
  • Earth and Planetary Sciences(all)

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