  Bayesian models of axisymmetric plasmas using Gaussian processes and force
balance equations have been developed. These models give the full joint
posterior probability distributions over plasma current distributions and
pressure profiles given the magnetic field and pressure measurements
simultaneously. The toroidal currents such as plasma and magnetic field coil
currents are modelled as a grid of toroidal current carrying solid beams. The
plasma pressure and poloidal current flux profiles are given as a function of
the poloidal magnetic flux surface, determined by the toroidal currents.
Inference of all these physics parameters is a tomographic problem, thus, in
order to exclude unreasonable solutions, two different prior distributions have
been exploited: a Gaussian process prior and an equilibrium prior. The Gaussian
process prior constrains the plasma current distributions by their covariance
(smoothness) function whose hyperparameters have been optimally selected by
Bayesian Occam's razor. On the other hand, the equilibrium prior imposes the
magnetohydrodynamic force balance by introducing observations that the
differences between the magnetic force and the plasma pressure gradient are
almost zero at every plasma current beam. These \textit{virtual} observations
emphasise equilibrium solutions \textit{a~priori} as a part of the prior
knowledge. These models with the two different priors employ predictive models
of magnetic sensors and other plasma diagnostics in order to find all possible
solutions consistent with all the measurements. The complex, high dimensional
posterior distributions are explored by a new method based on the Gibbs
sampling scheme.
