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"
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