Joint Seminar with MPIK/ Cosmology has the ambition to probe fundamental physical laws in astrophysical systems such as the cosmic microwave background or the large-scale distribution of galaxies. Inference, as the exact process of isolating physical information from observations is tasked with dealing with non-Gaussian statistics, systematic errors and biased observations. I would like to report on a few developments for using partition functions in the inference process as an embodiment of Bayes’ law, and draw analogies between thermodynamics and the theory of information. In fact, information partition functions are well-suited to understand the information content of an experiment and are able to deal with non-Gaussian statistics in an analytic formalism. I’ll illustrate the application of these partition functions to cosmological data sets and discuss promising extensions for more involved inference problems.