Pubished in Contemporary Physics, vol. 49, issue 2, pp. 71-104, 2008.
http://arxiv.org/abs/0803.4089

For a PDF version of the article, click here.

Abstract: The application of Bayesian methods in cosmology and astrophysics has flourished over the past decade, spurred by data sets of increasing size and complexity. In many respects, Bayesian methods have proven to be vastly superior to more traditional statistical tools, offering the advantage of higher efficiency and of a consistent conceptual basis for dealing with the problem of induction in the presence of uncertainty. This trend is likely to continue in the future, when the way we collect, manipulate and analyse observations and compare them with theoretical models will assume an even more central role in cosmology.

This review is an introduction to Bayesian methods in cosmology and astrophysics and recent results in the field. I first present Bayesian probability theory and its conceptual underpinnings, Bayes' Theorem and the role of priors. I discuss the problem of parameter inference and its general solution, along with numerical techniques such as Monte Carlo Markov Chain methods. I then review the theory and application of Bayesian model comparison, discussing the notions of Bayesian evidence and effective model complexity, and how to compute and interpret those quantities. Recent developments in cosmological parameter extraction and Bayesian cosmological model building are summarized, highlighting the challenges that lie ahead.

Keywords : Bayesian methods; model comparison; cosmology; parameter inference; data analysis; statistical methods.

Table of Contents

• INTRODUCTION
• BAYESIAN PROBABILITY THEORY
• BAYESIAN PARAMETER INFERENCE
• The general problem and its solution
• Markov Chain Monte Carlo techniques for parameter inference
• BAYESIAN MODEL COMPARISON
• Shaving theories with Occam's razor
• The Bayesian evidence
• Computation and interpretation of the evidence
• COSMOLOGICAL PARAMETER INFERENCE
• The "vanilla" CDM cosmological model
• Cosmological observations
• Constraining cosmological parameters
• Caveats and common pitfalls
• COSMOLOGICAL BAYESIAN MODEL BUILDING
• Evidence for the cosmological concordance model
• Other uses of the Bayesian evidence
• CONCLUSIONS
• REFERENCES