The stochastic inverse problem is a key ingredient in making inferences, predictions, and decisions for complex science and engineering systems. We formulate and analyze a nonparametric Bayesian solution for the stochastic inverse problem. Key properties of the solution are proved and the convergence and error of a computational solution obtained by random sampling is analyzed. Several applications illustrate the results.

翻译：随机逆问题是复杂科学与工程系统中进行推断、预测和决策的关键要素。本文提出并分析了一种求解随机逆问题的非参数贝叶斯方法。我们证明了该解的关键性质，并通过随机采样分析了计算解的收敛性与误差。若干应用实例展示了该方法的实际效果。