6 papers
Directional subset simulation method for reliability analysis
Oindrila Kanjilal, Julien Bect
Estimating the probabilities of rare failure events is a key challenge in the reliability analysis of physical systems. Subset simulation (SS) is a very popular adaptive Monte Carl…
Uncertainty functionals revisited: Concavity and Jensen's inequality
Julien Bect, Xujia Zhu
This article presents a theoretical study of uncertainty functionals on general measurable spaces. These functionals are fundamental in experimental design and global sensitivity a…
Relaxed Gaussian process interpolation: a goal-oriented approach to Bayesian optimization
Sébastien Petit, Julien Bect, Emmanuel Vazquez
This work presents a new procedure for obtaining predictive distributions in the context of Gaussian process (GP) modeling, with a relaxation of the interpolation constraints outsi…
Bayesian Active Learning of (small) Quantile Sets through Expected Estimator Modification
Romain Ait Abdelmalek-Lomenech, Julien Bect, Emmanuel Vazquez
Given a multivariate function taking deterministic and uncertain inputs, we consider the problem of estimating a quantile set: a set of deterministic inputs for which the probabili…
Bayesian sequential design of computer experiments for quantile set inversion
Romain Ait Abdelmalek-Lomenech, Julien Bect, Vincent Chabridon +1
We consider an unknown multivariate function representing a system-such as a complex numerical simulator-taking both deterministic and uncertain inputs. Our objective is to estimat…
Rational kernel-based interpolation for complex-valued frequency response functions
Julien Bect, Niklas Georg, Ulrich Römer +1
This work is concerned with the kernel-based approximation of a complex-valued function from data, where the frequency response function of a partial differential equation in the f…