Inversion of GPS radio occultation signals to temperature and humidity profiles is a mathematical exercise which is conceptually simple, and at the same time rather complex when one starts questioning the basic assumptions of the method. In this talk I will describe the 1D-Var method used for retrieval of the ROM SAF operational atmospheric products, including also a discussion of the background fields and their error characteristics. This will be used as an example for a more general exercise, which should be of broader interest: Can we by Bayseian inference estimate the error covariance of the observation data and the background data from the data series themselves? Generally: Given two data sets representing the same quantity, but with independent errors, can one derive the error covariances of the two without any prior knowledge?