
Reducedorder modeling for nonlinear Bayesian statistical inverse problems
Bayesian statistical inverse problems are often solved with Markov chain...
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Scaling Up Bayesian Uncertainty Quantification for Inverse Problems using Deep Neural Networks
Due to the importance of uncertainty quantification (UQ), Bayesian appro...
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Contamination mapping in Bangladesh using a multivariate spatial Bayesian model for leftcensored data
Arsenic (As) and other toxic elements contamination of groundwater in Ba...
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Adversarial Numerical Analysis for Inverse Problems
Many scientific and engineering applications are formulated as inverse p...
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Likelihood informed dimension reduction for inverse problems in remote sensing of atmospheric constituent profiles
We use likelihood informed dimension reduction (LIS) (T. Cui et al. 2014...
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Novel Deep neural networks for solving Bayesian statistical inverse
We consider the simulation of Bayesian statistical inverse problems gove...
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Adaptive Dimension Reduction to Accelerate InfiniteDimensional Geometric Markov Chain Monte Carlo
Bayesian inverse problems highly rely on efficient and effective inferen...
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SplineBased Bayesian Emulators for Large Scale Spatial Inverse Problems
A Bayesian approach to nonlinear inverse problems is considered where the unknown quantity (input) is a random spatial field. The forward model is complex and nonlinear, therefore computationally expensive. An emulatorbased methodology is developed, where the Bayesian multivariate adaptive regression splines (BMARS) are used to model the function that maps the inputs to the outputs. Discrete cosine transformation (DCT) is used for dimension reduction of the input spatial field. The posterior sampling is carried out using transdimensional Markov Chain Monte Carlo (MCMC) methods. Numerical results are presented by analyzing simulated as well as real data on hydrocarbon reservoir characterization.
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