A SUR version of the Bichon criterion for excursion set estimation

Many model inversion problems occur in industry. These problems consist in finding the set of parameter values such that a certain quantity of interest respects a constraint, for example remains below a threshold. In general, the quantity of interest is the output of a simulator, costly in computation time. An effective way to solve this problem is to replace the simulator by a Gaussian process regression, with an experimental design enriched sequentially by a well chosen acquisition criterion. Different inversion-adapted criteria exist such as the Bichon criterion (also known as expected feasibility function) and deviation number . There also exist a class of enrichment strategies (stepwise uncertainty reduction—SUR) which select the next point by measuring the expected uncertainty reduction induced by its selection. In this paper we propose a SUR version of the Bichon criterion. An explicit formulation of the criterion is given and test comparisons show good performances on classical test functions.