May 2006
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) Astrostatics 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.
Keywords: Adaptive Importance Sampling, Bayes Factors, Bayesian Model Averaging, Nested Sampling, Path Sampling, Ratio Importance Sampling, Reversible Jump Markov chain Monte Carlo, Thermodynamic Integration
The manuscript is available in PostScript and PDF formats.
To be presented at Statistical Challenges in Modern Astronomy IV (SCMA IV), June 12-15, 2006. This material is based upon work supported by the National Science Foundation under Grants 0112069, 0422400, and 0507481. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.