# Accelerating MCMC with active subspaces

@inproceedings{Constantine2015AcceleratingMW, title={Accelerating MCMC with active subspaces}, author={Paul G. Constantine and Carson Kent and Tan Bui-Thanh}, year={2015} }

The Markov chain Monte Carlo (MCMC) method is the computational workhorse for Bayesian inverse problems. However, MCMC struggles in high-dimensional parameter spaces, since its iterates must sequentially explore the high-dimensional space. This struggle is compounded in physical applications when the nonlinear forward model is computationally expensive. One approach to accelerate MCMC is to reduce the dimension of the state space. Active subspaces are part of an emerging set of tools for…

## 12 Citations

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- Computer Science, MathematicsJ. Comput. Phys.
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- Computer Science
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This work proposes a new methodology for tackling the RML optimization problem based on the high-dimensional Bayesian optimization literature, and demonstrates the beneﬁts of the methodology in comparison with the solutions obtained by alternative optimization methods on a variety of synthetic and real-world problems, including medical anduid dynamics applications.

### Applications of Bayesian computational statistics and modeling to large-scale geoscientific problems

- Environmental Science, Computer Science
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The particular geoscientific problems considered are finding the spatio-temporal distribution of atmospheric carbon dioxide based on sparse remote sensing data, quantifying uncertainties in modeling methane emissions from boreal wetlands, analyzing and quantifying the effect of climate change on growing season in the boreal region, and using statistical methods to calibrate a terrestrial ecosystem model.

### Line source estimation of environmental pollutants using super-Gaussian geometry model and Bayesian inference.

- Computer ScienceEnvironmental research
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### Bayesian model calibration on active subspaces

- Mathematics2017 American Control Conference (ACC)
- 2017

A Delayed Rejection Adaptive Metropolis algorithm is employed to infer parameter distributions on the active subspace and then map these distributions back to the full space.

### A review and assessment of importance sampling methods for reliability analysis

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- Computer ScienceAerospace Science and Technology
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### Conditioning by Projection for the Sampling from Prior Gaussian Distributions

- Computer Science, MathematicsICCSA
- 2021

A Bayesian statistical framework with a preconditioned Markov Chain Monte Carlo (MCMC) algorithm for the solution of the inverse problem for absolute permeability characterization and presents a new method to condition Gaussian fields to available sparse measurements.

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