For plasmas in fusion devices using magnetic field confinement Electron Cyclotron Emission (ECE) is inherent. Thereby, plasma electrons emit an intensity spectrum at the gyration frequency and its harmonics for each polarisation state. For a broad plasma parameter range the plasma is optically thick and acts therefore like a blackbody in the main spectral part of the 2nd harmonic in X-mode polarisation. By utilization of the Rayleigh-Jeans law the electron temperature profile can be determined from the intensities measured by individual spectral channels and the magnetic field along the diagnostic line of sight. At the tokamak JET the described technique is routinely applied in the spectral range 100-200GHz measured by the absolute calibrated Michelson interferometer. For the ECE spectrum in the spectral range of the 4th and 5th harmonic, also covered by the Michelson interferometer at JET, the plasma has become optically thin and thus the blackbody model is not valid anymore. As consequence, the optically thin ranges are influenced by the electron density and each of the spectral channels affected gives separate information about the density profile integrated along the line of sight. Thus, information about the temperature and density profiles can be extracted from the extended spectral range by an improved analysis. Furthermore, by the use of several harmonics probing different regions in the velocity phase space the determined temperature gives an improved ensemble average. For an improved analysis a model predicting the ECE spectrum for given electron temperature and density profile and magnetic field is mandatory. Since the ECE theory is well understood and ECE ray-tracing codes like SPECE have been developed such a model is available. At JET a first order analysis of the optically thin and thick spectral ranges has been achieved already by manual manipulation of the plasma parameters fed to SPECE. To treat the complex inference problem more consistently, a model for the Michelson interferometer has been implemented together with the absolute calibration into the Minerva Bayesian inference framework, previously used for modelling of other JET diagnostics and different equilibrium inference studies. The novel Bayesian technique removes the need for window functions, zero-padding and phase correction associated with Fourier transformation based techniques for the analysis of interferogram data [15]. But the diagnostic model needs to take into account dispersion inside the interferometer itself. The proof of principle for the new approach, as described below, shows the feasibility for the inference of the Te and ne profiles and a 1st order correction of the vacuum toroidal magnetic field independent on other diagnostics.