Applications of Bayesian model selection to cosmological parameters

By Roberto Trotta. 2005

296 citations recorded by the source corpus.

Bayesian model selection is a tool to decide whether the introduction of a new parameter is warranted by data. I argue that the usual sampling statistic significance tests for a null hypothesis can be misleading, since they do not take into account the information gained through the data, when updating the prior distribution to the posterior. On the contrary, Bayesian model selection offers a quantitative implementation of Occam’s razor. I introduce the Savage–Dickey density ratio, a computationally quick method to determine the Bayes factor of two nested models and hence perform model selection. As an illustration, I consider three key parameters for our understanding of the cosmological concordance model. By using WMAP 3–year data complemented by other cosmological measurements, I show that a non–scale invariant spectral index of perturbations is favoured for any sensible choice of prior. It is also found that a flat Universe is favoured with odds of 29 : 1 over non–flat models, and that there is strong evidence against a CDM isocurvature component to the initial conditions which is totally (anti)correlated with the adiabatic mode (odds of about 2000 : 1), but that this is strongly dependent on the prior adopted. These results are contrasted with the analysis of WMAP 1–year data, which were not informative enough to allow a conclusion as to the status of the spectral index. In a companion paper, a new technique to forecast the Bayes factor of a future observation is presented.

Subfields: Astronomy and Astrophysics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/84a18b54eea649ad4488a516024a3cc20fd2d8f5

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Citations in the corpus

MultiNest: an efficient and robust Bayesian inference tool for cosmology and particle physics (2008, methodology): “…1996), which is extremely computationally intensive but has been used successfully in astronomical applications (see e.g. Hobson & McLachlan 2003; Marshall et al. 2003; Slosar A. et al. 2003; Niarchou et al. 2004; Bassett et al. 2004; Trotta 2007; Beltrán et al. 2005; Bridges et al. 2006).”
On model selection forecasting, Dark Energy and modified gravity (2007, methodology): “A special case of this was recently presented by Trotta (2007).”
EIGHT ULTRA-FAINT GALAXY CANDIDATES DISCOVERED IN YEAR TWO OF THE DARK ENERGY SURVEY (2015, background): “The majority of objects show no significant evidence for ellipticity, which is confirmed by calculating the Bayes factor (BF) via the Savage–Dickey density ratio (Dickey 1971; Trotta 2007).”
Cosmic Discordance: Are Planck CMB and CFHTLenS weak lensing measurements out of tune? (2014, background): “…p is given by P(d|M0) P(d|M1) = P(d|M1, p = 0)∫ dpP(d|M1, p)Pr(p|M1) (9) where P (d|M1, p) is the likelihood of the data d marginalised over all other parameters apart from p and Pr(p|M1) is the normalised prior on p (e.g. see Lewis & Bridle (2010), Trotta (2007) and references therein).”
Confronting Lemaitre–Tolman–Bondi models with observational cosmology (2008, methodology): “ral independent analysis based on the Bayesian evidence associated with a given likelihood and a given cosmological model, within some given priors, both theoretical and observational, see e.g. Refs. [49, 50, 51, 52]. The Bayesian evidence is based on Bayes theorem, which relates the posterior distr”
Curvature tension: Evidence for a closed universe (2019, background): “[23] Roberto Trotta.”
Cosmology and Fundamental Physics with the Euclid Satellite (2012, methodology): “Image reproduced from 2005 preprint of [1166].”
BEASTS OF THE SOUTHERN WILD: DISCOVERY OF NINE ULTRA FAINT SATELLITES IN THE VICINITY OF THE MAGELLANIC CLOUDS (2015, methodology): “To check whether the ellipticity of an object is significant, the Bayes Factor is calculated using the Savage-Dickey ratio (Verdinelli & Wassermann 1995; Trotta 2007).”
Surrogate Science (2015, background): “…of the Bayes factor, for which the so-called “Jeffreys’ scale” gives empirically calibrated levels of significance for the strength of evidence... (Trotta, 2007: 73) Fisher and Neyman and Pearson have been victims of social scientists’ desire for a single tool, a desire that produced a surrogate…”
Model selection in finite element model updating using the Bayesian evidence statistic (2011, methodology): “The algorithm has been successfully applied and further modified in a number of recent astronomy and cosmology papers [11,25,26,34].”
Fitting the Phenomenological MSSM (2009, methodology): “scale we use for the interpretation of model probabilities. Here the log represents the natural logarithm. Gaussian approximation at each mode). The Savage–Dickey density ratio has also been proposed [42] as an exact, and potentially faster, means of evaluating evidences, but is restricted to the sp”
Putting the precision in precision cosmology: How accurate should your data covariance matrix be? (2012, background): “…if we want to differentiate between theoretical models in a Bayesian framework, ⋆ ant@roe.ac.uk as well as estimate their parameter value, we also need to accurately integrate over the model parameter-space (e.g., Trotta, 2007; Liddle, Mukherjee, Parkinson, 2006; Taylor & Kitching, 2010).”