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A multi-fidelity simulator is a numerical model, in which one of the inputscontrols a trade-off between the realism and the computational cost of thesimulation. Our goal is to estimate the probability of exceeding a giventhreshold on a multi-fidelity stochastic simulator. We propose a fully Bayesianapproach based on Gaussian processes to compute the posterior probabilitydistribution of this probability. We pay special attention to thehyper-parameters of the model. Our methodology is illustrated on an academicexample.

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