Data assimilation
A central research challenge for the mathematical sciences in the twenty-first century is the
development of principled methodologies for the seamless integration of (often vast) data …
development of principled methodologies for the seamless integration of (often vast) data …
MCMC methods for functions: modifying old algorithms to make them faster
Many problems arising in applications result in the need to probe a probability distribution
for functions. Examples include Bayesian nonparametric statistics and conditioned diffusion …
for functions. Examples include Bayesian nonparametric statistics and conditioned diffusion …
A hierarchical multilevel Markov chain Monte Carlo algorithm with applications to uncertainty quantification in subsurface flow
In this paper we address the problem of the prohibitively large computational cost of existing
Markov chain Monte Carlo methods for large-scale applications with high-dimensional …
Markov chain Monte Carlo methods for large-scale applications with high-dimensional …
Convergence of Gaussian process regression with estimated hyper-parameters and applications in Bayesian inverse problems
AL Teckentrup - SIAM/ASA Journal on Uncertainty Quantification, 2020 - SIAM
This work is concerned with the convergence of Gaussian process regression. A particular
focus is on hierarchical Gaussian process regression, where hyper-parameters appearing in …
focus is on hierarchical Gaussian process regression, where hyper-parameters appearing in …
[HTML][HTML] Evaluating data assimilation algorithms
Evaluating Data Assimilation Algorithms in: Monthly Weather Review Volume 140 Issue 11 (2012)
Jump to Content Jump to Main Navigation Logo Logo Logo Logo Logo Logo JOURNALS …
Jump to Content Jump to Main Navigation Logo Logo Logo Logo Logo Logo JOURNALS …
Besov priors for Bayesian inverse problems
M Dashti, S Harris, A Stuart - arXiv preprint arXiv:1105.0889, 2011 - arxiv.org
We consider the inverse problem of estimating a function $ u $ from noisy, possibly
nonlinear, observations. We adopt a Bayesian approach to the problem. This approach has …
nonlinear, observations. We adopt a Bayesian approach to the problem. This approach has …
Uncertainty quantification and weak approximation of an elliptic inverse problem
M Dashti, AM Stuart - SIAM Journal on Numerical Analysis, 2011 - SIAM
We consider the inverse problem of determining the permeability from the pressure in a
Darcy model of flow in a porous medium. Mathematically the problem is to find the diffusion …
Darcy model of flow in a porous medium. Mathematically the problem is to find the diffusion …
Well-posed Bayesian geometric inverse problems arising in subsurface flow
MA Iglesias, K Lin, AM Stuart - Inverse Problems, 2014 - iopscience.iop.org
In this paper, we consider the inverse problem of determining the permeability of the
subsurface from hydraulic head measurements, within the framework of a steady Darcy …
subsurface from hydraulic head measurements, within the framework of a steady Darcy …
Multilevel markov chain monte carlo
In this paper we address the problem of the prohibitively large computational cost of existing
Markov chain Monte Carlo methods for large-scale applications with high-dimensional …
Markov chain Monte Carlo methods for large-scale applications with high-dimensional …
Bayesian estimation of the observation‐error covariance matrix in ensemble‐based filters
G Ueno, N Nakamura - Quarterly Journal of the Royal …, 2016 - Wiley Online Library
We develop a Bayesian technique for estimating the parameters in the observation‐noise
covariance matrix Rt for ensemble data assimilation. We design a posterior distribution by …
covariance matrix Rt for ensemble data assimilation. We design a posterior distribution by …