Bayes in the sky: Bayesian inference and model selection in cosmology

TL;DR

This paper reviews Bayesian inference and model selection techniques in cosmology, emphasizing their advantages over traditional methods and discussing recent advances, challenges, and future prospects in the field.

Contribution

It provides a comprehensive introduction to Bayesian methods in cosmology, including recent developments in parameter inference and model comparison, with practical insights into their application.

Findings

Bayesian methods outperform traditional statistical tools in cosmology.

Recent advances include improved parameter extraction techniques.

Challenges involve computational complexity and model interpretation.

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.