BAYESIAN MODEL COMPARISON IN ASTRONOMY AND COSMOLOGY
Daniel Mortlock (Imperial College London)

Bayesian inference provides a self-consistent method of model comparison, provided that i) there are at least two models under consideration and ii) all the models in question have fully-specified and proper parameter priors.  Unfortunately, these requirements are not always satisfied in astronomy and cosmology: despite the existence of exquisitely-characterised measurements and quantitative physical models (i.e., sufficient to compute a believable likelihood), these models generally have parameters without well-motivated priors, making completely rigorous model comparison a formal impossibility.  Still, huge advances have been made in cosmology, in particular, in the last few decades, implying that model comparison (and testing) is possible in practice even without fully specified priors.  I will discuss the above principles and then illustrate some test cases of varying rigour, outlining some schemes for formalising heuristic approaches to model testing within a Bayesian framework.