Bayesian statistics provides a powerful tool for the analysis of data. The methods are flexible enough to permit a realistic modelling of complex measurements. Prior information about the experiment, as well as knowledge from other sources can be used in a natural way. All relevant quantities concerning the measurement, as e. g. the expected values and their associated uncertainties are obtained from probability density functions. Bayesian data analysis strictly follows the rules of probability theory, thus ensuring that the procedure is free of inconsistencies and is in accordance with the Guide to the Expression of Uncertainty in Measurement (GUM).