  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.
