Fitting and Comparison of Models of Radio Spectra

I describe an approach to fitting and comparison of radio spectra based on Bayesian anal-ysis and realised using a new implementation of the nested sampling algorithm. Such an approach improves on the commonly used maximum-likelihood fitting of radio spectra by allowing objective model selection, calculation of the full probability distributions of the model parameters and provides a natural mechanism for including information other than the measured spectra through priors. In this paper I cover the theoretical background, the algorithms used and the implementation details of the computer code. I also briefly illus-trate the method with some previously published data for three near-by galaxies. In forth-coming papers we will present the results of applying this analysis larger data sets, includ-ing some new observations, and the physical conclusions that can be made. The computer code as well as the overall approach described here may also be useful for analysis of other multi-chromatic broad-band observations and possibly also photometric redshift estimation. All of the code is publicly available, licensed under the GNU General Public License, a