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.

BAYES IN THE SKY: BAYESIAN INFERENCE AND MODEL SELECTION IN COSMOLOGY

Roberto Trotta


Oxford University, Astrophysics Department
Denys Wilkinson Building, Keble Rd, Oxford, OX1 3RH, UK


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" LambdaCDM 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

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