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The problem of efficiently generating random samples from high-dimensionaland non-log-concave posterior measures arising from nonlinear regressionproblems is considered. Extending investigations from arXiv:2009.05298, localand global stability properties of the model are identified under which suchposterior distributions can be approximated in Wasserstein distance by suitablelog-concave measures. This allows the use of fast gradient based samplingalgorithms, for which convergence guarantees are established that scalepolynomially in all relevant quantities (assuming `warm' initialisation). Thescope of the general theory is illustrated in a non-linear inverse problem fromintegral geometry for which new stability results are derived.

On log-concave approximations of high-dimensional posterior measures and stability properties in non-linear inverse problems