Statistical methods in cosmology

Abstract

The advent of large data-set in cosmology has meant that in the past 10 or 20 years our knowledge and understanding of the Universe has changed not only quantitatively but also, and most importantly, qualitatively. Cosmologists rely on data where a host of useful information is enclosed, but is encoded in a non-trivial way. The challenges in extracting this information must be overcome to make the most of a large experimental effort. Even after having converged to a standard cosmological model (the LCDM model) we should keep in mind that this model is described by 10 or more physical parameters and if we want to study deviations from it, the number of parameters is even larger. Dealing with such a high dimensional parameter space and finding parameters constraints is a challenge on itself. Cosmologists want to be able to compare and combine different data sets both for testing for possible disagreements (which could indicate new physics) and for improving parameter determinations. Finally, cosmologists in many cases want to find out, before actually doing the experiment, how much one would be able to learn from it. For all these reasons, sophisiticated statistical techniques are being employed in cosmology, and it has become crucial to know some statistical background to understand recent literature in the field. I will introduce some statistical tools that any cosmologist should know about in order to be able to understand recently published results from the analysis of cosmological data sets. I will not present a complete and rigorous introduction to statistics as there are several good books which are reported in the references. The reader should refer to those.

31, pages, 6 figures, notes from 2nd Trans-Regio Winter school in Passo del Tonale. To appear in Lectures Notes in Physics, "Lectures on cosmology: Accelerated expansion of the universe" Feb 2010

References in corpus (5)

• Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology
• Improved Cosmological Constraints from New, Old and Combined Supernova Datasets
• The shape of the SDSS DR5 galaxy power spectrum
• On model selection forecasting, Dark Energy and modified gravity
• Observational bounds on the cosmic radiation density

Cited by in corpus (44)

• Cosmology and Fundamental Physics with the Euclid Satellite
• Cosmology and fundamental physics with the Euclid satellite
• Searching for Dark Matter in the CMB: A Compact Parameterization of Energy Injection from New Physics
• On the theory and applications of modern cosmography
• Galileon Gravity in Light of ISW, CMB, BAO and $H_0$ data
• Constraining $M_{\nu }$ with the Bispectrum II: The Total Information Content of the Galaxy Bispectrum
• Searching for Light Relics with Large-Scale Structure
• Galaxy bispectrum, primordial non-Gaussianity and redshift space distortions
• Detecting Neutrino Mass by Combining Matter Clustering, Halos, and Voids
• Cosmological Parameter Estimation with Large Scale Structure Observations
• The Future of Primordial Features with Large-Scale Structure Surveys
• Cosmological parameter inference with Bayesian statistics
• Could the cosmic acceleration be transient? A cosmographic evaluation
• Constraining the EoR model parameters with the 21cm bispectrum
• Constraint on the cosmological f(R) model from the multipole power spectrum of the SDSS luminous red galaxy sample and prospects for a future redshift survey
• Testing the Early Universe with Anisotropies of the Gravitational Wave Background
• The Hubble Tension, The $M$ Crisis of Late Time $H(z)$ Deformation Models and the Reconstruction of Quintessence Lagrangians
• Non-Gaussianities in the Cosmological Perturbation Spectrum due to Primordial Anisotropy II
• An Estimator for statistical anisotropy from the CMB bispectrum
• Measuring our Peculiar Velocity by "Pre-deboosting" the CMB
• Intrinsic galaxy alignment from angular dependent primordial non-Gaussianity
• Cosmological parameter estimation using Particle Swarm Optimization (PSO)
• Cross-correlations as a Diagnostic Tool for Primordial Gravitational Waves
• EFTofLSS meets simulation-based inference: ${\sigma }_8$ from biased tracers
• On Model Selection in Cosmology
• Observational constraints on the oscillating dark energy cosmologies
• Expected constraints on models of the epoch of reionization with the variance and skewness in redshifted 21cm-line fluctuations
• MADYS: the Manifold Age Determination for Young Stars
• Improved model-independent constraints on the recombination era and development of a direct projection method
• Linear matter density perturbations in the ${\Lambda }_{\mathrm{s}}$CDM model: Examining growth dynamics and addressing the $S_8$ tension
• Exploring neutrino interactions in light of present and upcoming galaxy surveys
• Cosmology with the kinetic Sunyaev-Zeldovich effect: Independent of the optical depth and ${\sigma }_8$
• How Sensitive is the CMB to a Single Lens?
• Toward a test of Gaussianity of a gravitational wave background
• Measuring the matter fluctuations in the Local Universe with the ALFALFA catalog
• Isolating the linear signal when making redshift space distortion measurements
• Signatures of Einstein-Maxwell dilaton-axion gravity from the observed quasi-periodic oscillations in black holes
• Survey design for Spectral Energy Distribution fitting: a Fisher Matrix approach
• Searching for Stringy Topologies in the Cosmic Microwave Background
• Imprints of dark matter-massive neutrino interaction in upcoming post-reionization and galaxy surveys
• Low redshift constraints on scale-covariant models
• Observational constraints on the free parameters of an interacting Bose-Einstein gas as a dark-energy model
• Model independent reconstruction of cosmological accelerated-decelerated phase
• Optimizing Observational Strategy for Future Fgas Constraints