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In Part I (arXiv:1911.00619) of this article, we proposed an importancesampling algorithm to compute rare-event probabilities in forward uncertaintyquantification problems. The algorithm, which we termed the "Bayesian InverseMonte Carlo (BIMC) method", was shown to be optimal for problems in which theinput-output operator is nearly linear. But applying the original BIMC tohighly nonlinear systems can lead to several different failure modes. In thispaper, we modify the BIMC method to extend its applicability to a wider classof systems. The modified algorithm, which we call "Adaptive-BIMC (A-BIMC)", hastwo stages. In the first stage, we solve a sequence of optimization problems toroughly identify those regions of parameter space which trigger the rare-event.In the second stage, we use the stage one results to construct a mixture ofGaussians that can be then used in an importance sampling algorithm to estimaterare event probability. We propose using a local surrogate that minimizescostly forward solves. The effectiveness of A-BIMC is demonstrated via severalsynthetic examples. Yet again, the modified algorithm is prone to failure. Wesystematically identify conditions under which it fails to lead to an effectiveimportance sampling distribution.

BIMC: The Bayesian Inverse Monte Carlo method for goal-oriented uncertainty quantification. Part II