458 citations · 2.3k across the 71 of their papers we have counts for
8 papers · 1 filter
Transport map accelerated Markov chain Monte Carlo
Matthew Parno, Youssef Marzouk
We introduce a new framework for efficient sampling from complex probability distributions, using a combination of optimal transport maps and the Metropolis-Hastings rule. The core…
Dimension-independent likelihood-informed MCMC
Tiangang Cui, Kody J. H. Law, Youssef M. Marzouk
Many Bayesian inference problems require exploring the posterior distribution of high-dimensional parameters that represent the discretization of an underlying function. This work…
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…
Spectral tensor-train decomposition
Daniele Bigoni, Allan P. Engsig-Karup, Youssef M. Marzouk
The accurate approximation of high-dimensional functions is an essential task in uncertainty quantification and many other fields. We propose a new function approximation scheme ba…
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.…
Data-Driven Model Reduction for the Bayesian Solution of Inverse Problems
Tiangang Cui, Youssef M. Marzouk, Karen E. Willcox
One of the major challenges in the Bayesian solution of inverse problems governed by partial differential equations (PDEs) is the computational cost of repeatedly evaluating numeri…