TY - JOUR
T1 - Bayesian calibration of a large-scale geothermal reservoir model by a new adaptive delayed acceptance Metropolis Hastings algorithm
AU - Cui, T.
AU - Fox, C.
AU - Sullivan, M J
PY - 2011
Y1 - 2011
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=80055063784&partnerID=8YFLogxK
U2 - 10.1029/2010WR010352
DO - 10.1029/2010WR010352
M3 - Article
AN - SCOPUS:80055063784
SN - 0043-1397
VL - 47
JO - Water Resources Research
JF - Water Resources Research
IS - 10
M1 - W10521
ER -