  We introduce a class of acquisition functions for sample selection that leads
to faster convergence in applications related to Bayesian experimental design
and uncertainty quantification. The approach follows the paradigm of active
learning, whereby existing samples of a black-box function are utilized to
optimize the next most informative sample. The proposed method aims to take
advantage of the fact that some input directions of the black-box function have
a larger impact on the output than others, which is important especially for
systems exhibiting rare and extreme events. The acquisition functions
introduced in this work leverage the properties of the likelihood ratio, a
quantity that acts as a probabilistic sampling weight and guides the
active-learning algorithm towards regions of the input space that are deemed
most relevant. We demonstrate superiority of the proposed approach in the
uncertainty quantification of a hydrological system as well as the
probabilistic quantification of rare events in dynamical systems and the
identification of their precursors.
