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

被引:847
作者
Trotta, Roberto [1 ]
机构
[1] Univ Oxford, Dept Astrophys, Oxford OX1 3RH, England
关键词
Bayesian methods; model comparison; cosmology; parameter inference; data analysis; statistical methods;
D O I
10.1080/00107510802066753
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
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.
引用
收藏
页码:71 / 104
页数:34
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