Statistical classics in the big data era. When (astro-physical) models are nonregular

The hundreds of thousands of γ-ray counts collected by the Fermi Large Area Telescope (LAT) contribute uniquely to the study of the most extreme phenomena in our Universe such as active galactic nuclei, supernova remnants and pulsar wind nebula. Likelihood is currently been used to analyse these extensive data sets. The aim of this contribution is to raise awareness among the readers about the possible non-regularities inherent the corresponding parametric models and about the failures of the underlying likelihood-based theory. Especially practitioners may be less familiar with the resulting limiting distributions.