Daniel Mortlock: BAYESIAN MODEL COMPARISON IN ASTRONOMY

Abstract: 
Astronomers often want to test which of two very different models is supported by their data: Is some faint object a star or a galaxy or a quasars? Do measurements of supernovae require imply that the cosmological expansion is accelerating due to “dark energy"?  Is the deviation of Mercury’s orbit from the Newtonian prediction a sign of the breakdown of gravitational theory or indicative of the presence of some unseen planet?  Bayesian inference provides a self-consistent method of answering such questions through 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 real world problems, as is generally the case in astronomy.  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.