Certified dimension reduction in nonlinear Bayesian inverse problems

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