The accurate determination of electron density ne and temperature Te is important for many areas of Tokamak research. At JET, several different systems make measurements which depend on these but are based on very different physics, have different spatial resolutions and observe different regions of the plasma. Bayesian analysis and forward modelling provide a conceptually simple method to obtain and represent the information that can be inferred from the combination of an arbitrary number of observations and prior assumptions about all the physical quantities on which they depend. This paper gives results from the Bayesian Inversion for a typical JET plasma using models developed for the Interferometry, core LIDAR and edge LIDAR diagnostics.