Uncertainty quantification via codimension-one partitioning

We consider uncertainty quantification in the context of certification, i.e. showing that that the probability of some “failure” event is acceptably small. In this paper, we derive a new method for rigorous uncertainty quantification and conservative certification by combining McDiarmid’s inequality with input domain partitioning and a new concentration-ofmeasure inequality. We show that arbitrarily sharp upper bounds on the probability of failure can be obtained by partitioning the input parameter space appropriately; in contrast, the bound provided by McDiarmid’s inequality is usually not sharp. We prove an error estimate for the method (proposition 3.2); we define a codimension-one recursive partitioning scheme and prove its convergence properties (theorem 4.1); finally, we apply a new concentration-of-measure inequality to give confidence levels when empirical means are used in place of exact ones (section 5).