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

By Roberto Trotta. 2008

1,095 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Astronomy and Astrophysics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/de323f482046b891e957d5810301075b4be65ce4

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Citations in the corpus

Planck2018 results (2018, methodology): “We apply Bayesian statistical methods to infer the posterior probability distributions of the model parameters and select between competing models (Trotta 2008), using either the Metropolis-Hastings Markov-chain Monte Carlo (MCMC) sampling algorithm, as implemented in CosmoMC (Lewis & Bridle 2002)…”
Neutrino physics with the PTOLEMY project: active neutrino properties and the light sterile case (2019, background): “[49], for its application in determining the neutrino mass ordering see [6, 50].”
Constraints on the sum of the neutrino masses in dynamical dark energy models with w(z)≥−1 are tighter than those obtained in ΛCDM (2018, background): “Indeed these tighter bounds are a result of our use of a Bayesian statistical approach [217, 218].”
KiDS-450: testing extensions to the standard cosmological model (2016, methodology): “…this aim, we follow Joudaki et al. (2017) in using the DIC (Spiegelhalter, Best & Carlin 2002, also see Kunz, Trotta & Parkinson 2006; Liddle 2007; Trotta 2008, and Spiegelhalter et al. 2014), given by the sum of two terms: DIC ≡ χ2eff (θ̂) + 2pD. (1) Here, the first term consists of the…”
Curvature tension: Evidence for a closed universe (2019, neutral): “[20] R.”
A novel determination of the local dark matter density (2009, positive): “Our data analysis is based on a Bayesian probabilistic inference (see [19] for a recent review on the subject).”
Galileon gravity in light of ISW, CMB, BAO and H0 data (2017, methodology): “More robust model comparison analyses can be performed by computing the actual Bayesian evidence [98] of the competing models.”
Complex Faraday depth structure of active galactic nuclei as revealed by broad‐band radio polarimetry (2012, methodology): “…fits to the data, we then used the Bayesian information criterion (BIC) to distinguish the goodness of fit between different models with different degrees of freedom (Schwarz 1978; Trotta 2008): BIC ≡ −2 log P (d|k) ≈ −2 log L + k log N, (14) where k is the number of free parameters in the model.”
A NICER View of the Massive Pulsar PSR J0740+6620 Informed by Radio Timing and XMM-Newton Spectroscopy (2021, background): “…2020); the three nucleon potential (Maselli et al. 2020); relativistic mean-field models (Traversi et al. 2020); muon fraction content (Zhang 1 For an introduction to the concept of conditional probabilities within Bayesian inference see Sivia & Skilling (2006); Trotta (2008); Clyde et al. (2021).”
New physics in light of the H0 tension: An alternative view (2019, background): “Finally, the fact that the number of free parameters in these physical theories remains the same as in ΛCDM might play in favour of the models themselves when computing the Bayesian evidence: the latter is in fact generally known to disfavour models with extra parameters, unless the improvement in f”
KiDS-450 + 2dFLenS: Cosmological parameter constraints from weak gravitational lensing tomography and overlapping redshift-space galaxy clustering (2017, background): “Best & Carlin 2002, also see Liddle 2007; Trotta 2008; Spiegelhalter et al. 2014; Joudaki et al. 2017a), given by DIC ≡ χ2eff (θ̂ ) + 2pD. (19) The first term of the DIC is the best-fit effective χ2eff (θ̂ ) = −2 lnLmax, where θ̂ is the vector of varied parameters at the maximum likelihoodLmax of…”