Journal
GEM-INTERNATIONAL JOURNAL ON GEOMATHEMATICS
Volume 11, Issue 1, Pages -Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s13137-020-00163-x
Keywords
Markov chain Monte Carlo (MCMC); Inverse problem; Geothermal reservoir; Capacitance tomography; Reduced model; Adaptive MCMC; Delayed acceptance
Categories
Funding
- ARC [LP170100985]
- Australian Research Council [LP170100985] Funding Source: Australian Research Council
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Bayesian modelling and computational inference by Markov chain Monte Carlo (MCMC) is a principled framework for large-scale uncertainty quantification, though is limited in practice by computational cost when implemented in the simplest form that requires simulating an accurate computer model at each iteration of the MCMC. The delayed acceptance Metropolis-Hastings MCMC leverages a reduced model for the forward map to lower the compute cost per iteration, though necessarily reduces statistical efficiency that can, without care, lead to no reduction in the computational cost of computing estimates to a desired accuracy. Randomizing the reduced model for the forward map can dramatically improve computational efficiency, by maintaining the low cost per iteration but also avoiding appreciable loss of statistical efficiency. Randomized maps are constructed bya posterioriadaptive tuning of a randomized and locally-corrected deterministic reduced model. Equivalently, the approximated posterior distribution may be viewed as induced by a modified likelihood function for use with the reduced map, with parameters tuned to optimize the quality of the approximation to the correct posterior distribution. Conditions for adaptive MCMC algorithms allow practical approximations and algorithms that have guaranteed ergodicity for the target distribution. Good statistical and computational efficiencies are demonstrated in examples of calibration of large-scale numerical models of geothermal reservoirs and electrical capacitance tomography.
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