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A strategy for improved computational efficiency of the method of anchored distributions
Author(s) -
Over Matthew William,
Yang Yarong,
Chen Xingyuan,
Rubin Yoram
Publication year - 2013
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 - 10.1002/wrcr.20182
Subject(s) - computer science , inversion (geology) , parametrization (atmospheric modeling) , likelihood function , algorithm , mathematical optimization , function (biology) , importance sampling , mathematics , estimation theory , statistics , monte carlo method , paleontology , physics , quantum mechanics , structural basin , evolutionary biology , biology , radiative transfer
This paper proposes a strategy for improving the computational efficiency of model inversion using the method of anchored distributions (MAD) by “bundling” similar model parametrizations in the likelihood function. Inferring the likelihood function typically requires a large number of forward model (FM) simulations for each possible model parametrization; as a result, the process is quite expensive. To ease this prohibitive cost, we present an approximation for the likelihood function called bundling that relaxes the requirement for high quantities of FM simulations. This approximation redefines the conditional statement of the likelihood function as the probability of a set of similar model parametrizations “bundle” replicating field measurements, which we show is neither a model reduction nor a sampling approach to improving the computational efficiency of model inversion. To evaluate the effectiveness of these modifications, we compare the quality of predictions and computational cost of bundling relative to a baseline MAD inversion of 3‐D flow and transport model parameters. Additionally, to aid understanding of the implementation we provide a tutorial for bundling in the form of a sample data set and script for the R statistical computing language. For our synthetic experiment, bundling achieved a 35% reduction in overall computational cost and had a limited negative impact on predicted probability distributions of the model parameters. Strategies for minimizing error in the bundling approximation, for enforcing similarity among the sets of model parametrizations, and for identifying convergence of the likelihood function are also presented.