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Simulation-based optimal Bayesian experimental design for nonlinear systems
Dimensionality reduction and polynomial chaos acceleration of Bayesian inference in inverse problems
Stochastic spectral methods for efficient Bayesian solution of inverse problems
A stochastic collocation approach to Bayesian inference in inverse problems
We present an efficient numerical strategy for the Bayesian solution of inverse problems. Stochastic collocation methods, based on generalized polynomial chaos (gPC), are used to construct a…
Bayesian inference with optimal maps
Dimension-independent likelihood-informed MCMC
Transport Map Accelerated Markov Chain Monte Carlo
We introduce a new framework for efficient sampling from complex probability distributions, using a combination of transport maps and the Metropolis--Hastings rule. The core idea is to use determin...
Adaptive Smolyak Pseudospectral Approximations
This paper describes an adaptive method for non-intrusive pseudospectral approximation, based on Smolyak's algorithm with generalized sparse grids, and introduces a greedy heuristic for adaptive refinement of the pseudospectsral approximation.
Likelihood-informed dimension reduction for nonlinear inverse problems
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. From a Bayesian…
A Stein variational Newton method
- Gianluca Detommaso, T. Cui, Y. Marzouk, Robert Scheichl, A. Spantini
- Computer ScienceNeurIPS
- 8 June 2018
This paper accelerates and generalizes the SVGD algorithm by including second-order information, thereby approximating a Newton-like iteration in function space and shows how second- order information can lead to more effective choices of kernel.