  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.
