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Nowadays, numerical models are widely used in most of engineering fields tosimulate the behaviour of complex systems, such as for example power plants orwind turbine in the energy sector. Those models are nevertheless affected byuncertainty of different nature (numerical, epistemic) which can affect thereliability of their predictions. We develop here a new method for quantifyingconditional parameter uncertainty within a chain of two numerical models in thecontext of multiphysics simulation. More precisely, we aim to calibrate theparameters $\theta$ of the second model of the chain conditionally on the valueof parameters $\lambda$ of the first model, while assuming the probabilitydistribution of $\lambda$ is known. This conditional calibration is carried outfrom the available experimental data of the second model. In doing so, we aimto quantify as well as possible the impact of the uncertainty of $\lambda$ onthe uncertainty of $\theta$. To perform this conditional calibration, we setout a nonparametric Bayesian formalism to estimate the functional dependencebetween $\theta$ and $\lambda$, denoted by $\theta(\lambda)$. First, eachcomponent of $\theta(\lambda)$ is assumed to be the realization of a Gaussianprocess prior. Then, if the second model is written as a linear function of$\theta(\lambda)$, the Bayesian machinery allows us to compute analytically theposterior predictive distribution of $\theta(\lambda)$ for any set ofrealizations $\lambda$. The effectiveness of the proposed method is illustratedon several analytical examples.

Nonparametric Bayesian approach for quantifying the conditional uncertainty of input parameters in chained numerical models