Posterior sampling for high-dimensional Bayesian inverse problems is a common challenge in real-world applications. Randomized Maximum Likelihood (RML) is an optimization based methodology that gives samples from an approximation to the posterior distribution. We develop a high-dimensional Bayesian Optimization (BO) approach based on Gaussian Process (GP) surrogate models to solve the RML problem. We demonstrate the benefits of our approach in comparison to alternative optimization methods on a variety of synthetic and real-world Bayesian inverse problems, including medical and magnetohydrodynamics applications.

翻译：高维贝叶斯逆问题中的后验采样是实际应用中常见挑战。随机最大似然法（RML）是一种基于优化的方法，可从后验分布的近似中获取样本。我们开发了一种基于高斯过程（GP）替代模型的高维贝叶斯优化（BO）方法，用于求解RML问题。通过在包括医学和磁流体动力学应用在内的多种合成及实际贝叶斯逆问题中与替代优化方法进行比较，我们展示了所提出方法的优势。