Modern nuclear fusion experiments utilise a large number of sophisticated plasma diagnostics, which are sensitive to overlapping subsets of the physics parameters of interest. The mapping between the set of all physics parameters (the plasma 'state') and the raw observations of each diagnostic, will depend on the particular physics model used, and will also be inherently probabilistic. Uncertainty enters into the mapping between model parameters and observations through the inability of most models to predict the precise value of an observation, and also through aspects of the diagnostic itself, such as calibrations, instrument functions etc. To optimally utilise observations from multiple diagnostics and properly deal with all aspects of model uncertainties is very difficult with today's data analysis infrastructures. For this work, the Minerva analysis framework has been used, which implements a flexible and general way of modelling and carrying out analysis on this type of interconnected probabilistic systems by modelling of diagnostics, physics models and their dependencies through the use of Bayesian graphical models. To date about 10 diagnostic systems have been modelled in this way at JET, which has already led to a number of new results, including the reconstruction of flux surface topology and q profiles without an equilibrium assumption, profile inversions including uncertainty in the positions of flux surfaces, first experimental verification of relativistic effects to explain polarimetry measurements, and a substantial increase in accuracy of JET electron density and temperature profiles, including improved pedestal resolution, through the joint analysis of three different diagnostic systems.