Inferência bayesiana e seleção de modelo em cosmologia

terça-feira, maio 24, 2011

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

Contemporary Physics

Volume 49, Issue 2, 2008, Pages 71 - 104

Author: Roberto Trottaa

DOI: 10.1080/00107510802066753 


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 summarised, highlighting the challenges that lie ahead.

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

Affiliation: a Astrophysics Department, Oxford University, Oxford, UK


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