Bayesian modelling of multiple plasma diagnostics at Wendelstein 7-X

Consistent inference of the electron density and temperature has been carried out with multiple heterogeneous plasma diagnostic data sets at Wendelstein 7-X. The predictive models of the interferometer, Thomson scattering and helium beam emission spectroscopy systems have been developed in the Minerva framework and combined to a single joint model. The electron density and temperature profiles are modelled by Gaussian processes with their hyperparameters. The model parameters such as the calibration factor of the Thomson scattering system and the model predictive uncertainties are regarded as additional unknown parameters. The joint posterior probability distribution of the electron density and temperature profiles, hyperparameters of the Gaussian processes and model parameters is explored by Markov chain Monte Carlo algorithms. The posterior samples drawn from the joint posterior distribution are numerically marginalised over the hyperparameters and model parameters to obtain the marginal posterior distributions of the electron density and temperature profiles. The inference of these profiles is performed with different combinations of the interferometer and Thomson scattering data as well as either the empirical electron density and temperature constraints at the limiter/divertor positions introduced by \textit{virtual observations} or the edge density and temperature from the helium beam emission data. Furthermore, the addition of the X-ray imaging crystal spectrometers to the joint model for the ion temperature profiles is demonstrated. All these profiles presented in this work are inferred with the optimal hyperparameters and model parameters by exploring the full joint posterior distribution which intrinsically embodies Bayesian Occam's razor.