The problem of efficiently generating random samples from high-dimensional and non-log-concave posterior measures arising from nonlinear regression problems is considered. Extending investigations from arXiv:2009.05298, local and global stability properties of the model are identified under which such posterior distributions can be approximated in Wasserstein distance by suitable log-concave measures. This allows the use of fast gradient based sampling algorithms, for which convergence guarantees are established that scale polynomially in all relevant quantities (assuming `warm' initialisation). The scope of the general theory is illustrated in a non-linear inverse problem from integral geometry for which new stability results are derived.

翻译：考虑从非线性回归问题产生的高维且非对数凹后验测度中高效生成随机样本的问题。通过扩展arXiv:2009.05298中的研究，我们识别了模型在Wasserstein距离下可由合适对数凹测度近似的局部与全局稳定性性质。这使得可以采用基于梯度的快速采样算法，并为其建立了在所有相关量上呈多项式尺度收敛的保证（假设“热启动”初始化）。该通用理论的应用范围通过积分几何中的一个非线性反问题得以阐明，并为此推导了新的稳定性结果。