Current challenges in Bayesian model choice

Model selection (and the related issue of model uncertainty) arises in many astronomical problems, and, in particular, has been one of the focal areas of the Exoplanet working group under the SAMSI (Statistics and Applied Mathematical Sciences Institute) Astrostatistcs Exoplanet program. We provide an overview of the Bayesian approach to model selection and highlight the challenges involved in implementing Bayesian model choice in four stylized problems. We review some of the current methods used by statisticians and astronomers and present recent developments in the area. We discuss the applicability, computational challenges, and performance of suggested methods and conclude with recommendations and open questions.