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We introduce a class of acquisition functions for sample selection that leadsto faster convergence in applications related to Bayesian experimental designand uncertainty quantification. The approach follows the paradigm of activelearning, whereby existing samples of a black-box function are utilized tooptimize the next most informative sample. The proposed method aims to takeadvantage of the fact that some input directions of the black-box function havea larger impact on the output than others, which is important especially forsystems exhibiting rare and extreme events. The acquisition functionsintroduced in this work leverage the properties of the likelihood ratio, aquantity that acts as a probabilistic sampling weight and guides theactive-learning algorithm towards regions of the input space that are deemedmost relevant. We demonstrate superiority of the proposed approach in theuncertainty quantification of a hydrological system as well as theprobabilistic quantification of rare events in dynamical systems and theidentification of their precursors.

Output-Weighted Optimal Sampling for Bayesian Experimental Design and Uncertainty Quantification