Cosmological bayesian model selection: Recent advances and open challenges

The cosmology community has been increasingly focusing on Bayesian model selection as a tool to discriminate between competing theories to explain a large amount of data about our Universe. In this paper, I summarize the conceptual underpinnings and the algorithmic implementations of Bayesian model comparison. I then discuss two representative applications of Bayesian model comparison to cosmological problems: determining whether the Universe is infinite and selecting the "best" model of inflation. I conclude by offering some reflections about open challenges and interpretational issues. Help and suggestions from the statistics community would be appreciated in further developing the field. © Springer Science+Business Media New York 2013.