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Bayes in the sky: Bayesian inference and model selection in cosmology
Open accessAbstract
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.
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Planck 2018 results: X. Constraints on inflation
Planck Collaboration, Akrami, Y., Arroja, F., Ashdown, M., Aumont, J., Baccigalupi, C., Ballardini, M., Banday, A. J., Barreiro, R. B., Bartolo, N., et al. (2020) · Astronomy & Astrophysics · doi:10.1051/0004-6361/201833887 · Cited by 2,442
Cosmology and Fundamental Physics with the Euclid Satellite
The Euclid Theory Working Group, Amendola, L., Appleby, S., Bacon, D., Baker, T., Baldi, M., Bartolo, N., Blanchard, A., Bonvin, C., Borgani, S., et al. (2013) · Living Reviews in Relativity · doi:10.12942/lrr-2013-6 · Cited by 899
Self-citationDESI DR2 results. II. Measurements of baryon acoustic oscillations and cosmological constraints
Abdul Karim, M., Aguilar, J., Ahlen, S., Alam, S., Allen, L., Prieto, C. A., Alves, O., Anand, A., Andrade, U., Armengaud, E., et al. (2025) · Physical Review D · doi:10.1103/tr6y-kpc6 · Cited by 856
Planck evidence for a closed Universe and a possible crisis for cosmology
Di Valentino, E., Melchiorri, A., & Silk, J. (2019) · Nature Astronomy · doi:10.1038/s41550-019-0906-9 · Cited by 673
Event Horizon Telescope Collaboration, Akiyama, K., Alberdi, A., Alef, W., Algaba, J. C., Anantua, R., Asada, K., Azulay, R., Bach, U., Baczko, A.-K., et al. (2022) · The Astrophysical Journal Letters · doi:10.3847/2041-8213/ac6736 · Cited by 369
“The value of serves as a model comparison metric that naturally balances improvements in fit quality against increases in model complexity, with larger values of indicating preferred models (see, e.g., Trotta 2008).”
Background
Metadata
- Authors
- Trotta, R.
- Venue
- Contemporary Physics
- Publisher
- Informa UK Limited
- Published
- 2008-03
- Volume
- 49
- Issue
- 2
- Pages
- 71-104
- ISSN
- 0010-7514 (ISSN-L)
- 1366-5812
- OpenAlex
- W2021748112
- Cited by
- 1,253
- References
- 4
- FWCI
- 18.27
- Type
- journal article
- Language
- en
- Open access
- green
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