Integrating hyper-parameter uncertainties in a multi-fidelity Bayesian model for the estimation of a probability of failure

Rémi Stroh (1, 2, 3) , Julien Bect (2, 3) , Séverine Demeyer (1) , Nicolas Fischer (1) , Emmanuel Vazquez (2, 3)

1 LNE - Laboratoire National de Métrologie et d'Essais [Trappes]
2 L2S - Laboratoire des signaux et systèmes
3 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques

A multi-fidelity simulator is a numerical model, in which one of the inputs controls a trade-off between the realism and the computational cost of the simulation. Our goal is to estimate the probability of exceeding a given threshold on a multi-fidelity stochastic simulator. We propose a fully Bayesian approach based on Gaussian processes to compute the posterior probability distribution of this probability. We pay special attention to the hyper-parameters of the model. Our methodology is illustrated on an academic example.

Domaines: Méthodologie [stat.ME]; Calcul [stat.CO]

Rémi Stroh, Julien Bect, Séverine Demeyer, Nicolas Fischer, Emmanuel Vazquez. Integrating hyper-parameter uncertainties in a multi-fidelity Bayesian model for the estimation of a probability of failure. 11th International Conference on Advanced Mathematical and Computational Tools in Metrology and Testing (AMTCM 2017) , Aug 2017, Glasgow, United Kingdom. ⟨hal-01590748⟩