Thomson scattering analysis with the Bayesian probability theory

Electron density and electron temperature profiles are reconstructed from Thomson scattering data on the stellarator Wendelstein 7-AS by means of systematic statistical modelling employing the Bayesian probability theory (BPT). The BPT allows for systematic combination of all information entering the measurement descriptive model considering all uncertainties of the measured data, calibration measurements, physical model parameters and measurement nuisance parameters. The BPT results are consistent with the ratio-evaluation method (REM) which is used to determine the electron temperature from the ratios of scattering signals. If compared to the sequential REM, the Bayesian error analysis is much more informative because it yields probability density functions of the quantities of interest. Moreover, systematic consideration of all the obtainable raw data, in particular those data suffering from low signal levels, results in an improved evaluation for weakly informative data. Sensitivity analysis of model parameters allows for finding crucial uncertainties which has impact on both diagnostic improvement and design.