  Data driven modelling is vital to many analyses at collider experiments,
however the derived inference of physical properties becomes subject to details
of the model fitting procedure. This work brings a principled Bayesian picture,
based on the marginal likelihood, of both data modelling and signal extraction
to a common collider physics scenario. First the marginal likelihood based
method is used to propose a more principled construction of the background
process, systematically exploring a variety of candidate shapes. Second the
picture is extended to propose the marginal likelihood as a useful tool for
anomaly detection challenges in particle physics. This proposal offers insight
into both precise background model determination and demonstrates a flexible
method to extend signal determination beyond a simple bump hunt.
