  Motivated by the desire to numerically calculate rigorous upper and lower
bounds on deviation probabilities over large classes of probability
distributions, we present an adaptive algorithm for the reconstruction of
increasing real-valued functions. While this problem is similar to the
classical statistical problem of isotonic regression, the optimisation setting
alters several characteristics of the problem and opens natural algorithmic
possibilities. We present our algorithm, establish sufficient conditions for
convergence of the reconstruction to the ground truth, and apply the method to
synthetic test cases and a real-world example of uncertainty quantification for
aerodynamic design.

Numerical Analysis;Numerical Analysis;Optimization and Control;Other Statistics