Statistical techniques in cosmology

Abstract

In these lectures I cover a number of topics in cosmological data analysis. I concentrate on general techniques which are common in cosmology, or techniques which have been developed in a cosmological context. In fact they have very general applicability, for problems in which the data are interpreted in the context of a theoretical model, and thus lend themselves to a Bayesian treatment. We consider the general problem of estimating parameters from data, and consider how one can use Fisher matrices to analyse survey designs before any data are taken, to see whether the survey will actually do what is required. We outline numerical methods for estimating parameters from data, including Monte Carlo Markov Chains and the Hamiltonian Monte Carlo method. We also look at Model Selection, which covers various scenarios such as whether an extra parameter is preferred by the data, or answering wider questions such as which theoretical framework is favoured, using General Relativity and braneworld gravity as an example. These notes are not a literature review, so there are relatively few references.

Typos corrected and exercises added

Cited by in corpus (28)

• Constraining $M_{\nu }$ with the Bispectrum II: The Total Information Content of the Galaxy Bispectrum
• Galaxy bispectrum, primordial non-Gaussianity and redshift space distortions
• QSFit: Automatic analysis of optical AGN spectra
• Cosmological parameter inference with Bayesian statistics
• Cosmology Without Windows: Quadratic Estimators for the Galaxy Power Spectrum
• Search for CII Emission on Cosmological Scales at Redshift Z~2.6
• Analytic study of the effect of dark energy-dark matter interaction on the growth of structures
• Forecast constraints on $f(T)$ gravity with gravitational waves from compact binary coalescences
• Testing cosmic geometry without dynamic distortions using voids
• 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
• BAO from angular clustering: optimization and mitigation of theoretical systematics
• An Estimator for statistical anisotropy from the CMB bispectrum
• Neutrino Signatures on the High Transmission Regions of the Lyman-alpha Forest
• Cosmology with the largest galaxy cluster surveys: Going beyond Fisher matrix forecasts
• Improving Fisher matrix forecasts for galaxy surveys: window function, bin cross-correlation, and bin redshift uncertainty
• Galactic Double Neutron Star total masses and Gaussian mixture model selection
• A single parameterization for dark energy and modified gravity models
• Generalized models of unification of dark matter and dark energy
• Shot noise in multi-tracer constraints on $f_{\text{NL}}$ and relativistic projections: Power Spectrum
• The gravitational and lensing-ISW bispectrum of 21cm radiation
• Geometric and growth rate tests of General Relativity with recovered linear cosmological perturbations
• Toward optimal cluster power spectrum analysis
• Statistical Nuances in BAO Analysis: Likelihood Formulations and Non-Gaussianities
• Reionization relics in the cross-correlation between the Ly$\alpha$ forest and 21 cm intensity mapping in the post-reionization era
• Origin & evolution of the Universe
• Measuring the stellar atmosphere parameters using follow-up polarimetry microlensing observations
• Theoretical and observational aspects of cosmological inflation