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Bayesian calibration of a large‐scale geothermal reservoir model by a new adaptive delayed acceptance Metropolis Hastings algorithm
Author(s) -
Cui T.,
Fox C.,
O'Sullivan M. J.
Publication year - 2011
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2010wr010352
Subject(s) - metropolis–hastings algorithm , markov chain monte carlo , algorithm , sampling (signal processing) , computer science , bayesian inference , posterior probability , bayesian probability , geothermal gradient , scale (ratio) , inference , mathematical optimization , mathematics , artificial intelligence , geology , physics , filter (signal processing) , quantum mechanics , geophysics , computer vision
The aim of this research is to estimate the parameters of a large‐scale numerical model of a geothermal reservoir using Markov chain Monte Carlo (MCMC) sampling, within the framework of Bayesian inference. All feasible parameters that are consistent with the measured data are summarized by the posterior distribution, and hence parameter estimation and uncertainty quantification are both given by calculating expected values of statistics of interest over the posterior distribution. It appears to be computationally infeasible to use the standard Metropolis‐Hastings algorithm (MH) to sample the high dimensional computationally expensive posterior distribution. To improve the sampling efficiency, a new adaptive delayed‐acceptance MH algorithm (ADAMH) is implemented to adaptively build a stochastic model of the error introduced by the use of a reduced‐order model. This use of adaptivity differs from existing adaptive MCMC algorithms that tune proposal distributions of the Metropolis‐Hastings algorithm (MH), though ADAMH also implements that technique. For the 3‐D geothermal reservoir model we present here, ADAMH shows a great improvement in the computational efficiency of the MCMC sampling, and promising results for parameter estimation and uncertainty quantification are obtained. This algorithm could offer significant improvement in computational efficiency when implementing sample‐based inference in other large‐scale inverse problems.