153 citations · 153 across the 1 of their papers we have counts for
4 papers
Optimal low-rank approximations of Bayesian linear inverse problems
Alessio Spantini, Antti Solonen, Tiangang Cui +3
In the Bayesian approach to inverse problems, data are often informative, relative to the prior, only on a low-dimensional subspace of the parameter space. Significant computationa…
Likelihood-informed dimension reduction for nonlinear inverse problems
Tiangang Cui, James Martin, Youssef M. Marzouk +2
The intrinsic dimensionality of an inverse problem is affected by prior information, the accuracy and number of observations, and the smoothing properties of the forward operator.…
A computational framework for infinite-dimensional Bayesian inverse problems. Part I: The linearized case, with application to global seismic inversion
Tan Bui-Thanh, Omar Ghattas, James Martin +1
We present a computational framework for estimating the uncertainty in the numerical solution of linearized infinite-dimensional statistical inverse problems. We adopt the Bayesian…
A computational framework for infinite-dimensional Bayesian inverse problems: Part II. Stochastic Newton MCMC with application to ice sheet flow inverse problems
Noemi Petra, James Martin, Georg Stadler +1
We address the numerical solution of infinite-dimensional inverse problems in the framework of Bayesian inference. In the Part I companion to this paper (arXiv.org:1308.1313), we c…