Projects per year
Abstract
We propose a dimension reduction technique for Bayesian inverse problems with nonlinear forward operators, nonGaussian priors, and nonGaussian observation noise. The likelihood function is approximated by a ridge function, i.e., a map which depends nontrivially only on a few linear combinations of the parameters. We build this ridge approximation by minimizing an upper bound on the Kullback–Leibler divergence between the posterior distribution and its approximation. This bound, obtained via logarithmic Sobolev inequalities, allows one to certify the error of the posterior approximation. Computing the bound requires computing the second moment matrix of the gradient of the loglikelihood function. In practice, a samplebased approximation of the upper bound is then required. We provide an analysis that enables control of the posterior approximation error due to this sampling. Numerical and theoretical comparisons with existing methods illustrate the benefits of the proposed methodology.
Original language  English 

Pages (fromto)  17891835 
Number of pages  47 
Journal  Mathematics of Computation 
Volume  91 
DOIs  
Publication status  Published  2022 
Projects
 1 Active

Interfaceaware numerical methods for stochastic inverse problems
Badia, S., Droniou, J., Cui, T., Marzouk, Y. & Carrera, J.
23/10/21 → 31/05/25
Project: Research