Copula Cosmology: Constructing a Likelihood Function

Abstract

To estimate cosmological parameters from a given dataset, we need to construct a likelihood function, which sometimes has a complicated functional form. We introduce the copula, a mathematical tool to construct an arbitrary multivariate distribution function from one-dimensional marginal distribution functions with any given dependence structure. It is shown that a likelihood function constructed by the so-called Gaussian copula can reproduce very well the n-dimensional probability distribution of the cosmic shear power spectrum obtained from a large number of ray-tracing simulations. This suggests that the Copula likelihood will be a powerful tool for future weak lensing analyses, instead of the conventional multivariate Gaussian likelihood.

9 pages, 4 figures. Maches version published by the Physical Review D

References in corpus (20)

• Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology
• Cosmological parameters from CMB and other data: a Monte-Carlo approach
• Detection of weak gravitational lensing distortions of distant galaxies by cosmic dark matter at large scales
• Detection of Weak Gravitational Lensing by Large-scale Structure
• Very weak lensing in the CFHTLS Wide: Cosmology from cosmic shear in the linear regime
• Evidence for the accelerated expansion of the Universe from weak lensing tomography with COSMOS
• Likelihood Analysis of CMB Temperature and Polarization Power Spectra
• Simulations of Wide-Field Weak Lensing Surveys I: Basic Statistics and Non-Gaussian Effects
• Cosmic Shear Analysis with CFHTLS Deep data
• Simulations of Baryon Acoustic Oscillations II: Covariance matrix of the matter power spectrum
• Cosmic shear statistics in the Suprime-Cam 2.1 sq deg field: Constraints on Omega_m and sigma_8
• Dark Energy Constraints from the CTIO Lensing Survey
• Constraints on Neutrino Masses from Weak Lensing
• The non-Gaussianity of the cosmic shear likelihood - or: How odd is the Chandra Deep Field South?
• Application of the Information Criterion to the Estimation of Galaxy Luminosity Function
• TEASING: a fast and accurate approximation for the low multipole likelihood of the Cosmic Microwave Background temperature
• From Finance to Cosmology: The Copula of Large-Scale Structure
• Precise Estimation of Cosmological Parameters Using a More Accurate Likelihood Function
• Weak lensing and dark energy: the impact of dark energy on nonlinear dark matter clustering
• Construction of Coupled Period-Mass Functions in Extrasolar Planets through the Nonparametric Approach

Cited by in corpus (31)

• Revising the Halofit Model for the Nonlinear Matter Power Spectrum
• Cosmology with cosmic shear observations: a review
• Probability Distribution Functions of Cosmological Lensing: Convergence, Shear, and Magnification
• SPICY: The Spitzer/IRAC Candidate YSO Catalog for the Inner Galactic Midplane
• Cosmic shear covariance: The log-normal approximation
• A new model to predict weak-lensing peak counts II. Parameter constraint strategies
• Simulations of Wide-Field Weak Lensing Surveys II: Covariance Matrix of Real Space Correlation Functions
• Impact of the non-Gaussian covariance of the weak lensing power spectrum and bispectrum on cosmological parameter estimation
• Cosmological information in Gaussianised weak lensing signals
• Determining the core radio luminosity function of radio AGNs via copula
• Machine Learning for Observational Cosmology
• The improved Amati correlations from Gaussian copula
• Gaussianizing the non-Gaussian lensing convergence field I: the performance of the Gaussianization
• Non-Gaussianity in the Weak Lensing Correlation Function Likelihood -- Implications for Cosmological Parameter Biases
• Galaxy And Mass Assembly (GAMA): Bivariate functions of H$\alpha$ star forming galaxies
• CFHTLenS: A Gaussian likelihood is a sufficient approximation for a cosmological analysis of third-order cosmic shear statistics
• Sufficiency of a Gaussian power spectrum likelihood for accurate cosmology from upcoming weak lensing surveys
• Modeling of weak lensing statistics. I. Power spectrum and bispectrum
• Constrained probability distributions of correlation functions
• Redshift-evolutionary X-ray and UV luminosity relation of quasars from Gaussian copula
• Far-Ultraviolet and Far-Infrared Bivariate Luminosity Function of Galaxies: Complex Relation between Stellar and Dust Emission
• Constructing a multivariate distribution function with a vine copula: toward multivariate luminosity and mass functions
• Exact joint likelihood of pseudo-$C_{\ell }$ estimates from correlated Gaussian cosmological fields
• A quasi-Gaussian approximation for the probability distribution of correlation functions
• Modeling of weak lensing statistics. II. Configuration-space statistics
• The copula of the cosmological matter density field is non-Gaussian
• J-PLUS: A catalogue of globular cluster candidates around the M81/M82/NGC3077 triplet of galaxies
• Deep Learning and genetic algorithms for cosmological Bayesian inference speed-up
• A possible explanation of vanishing halo velocity bias
• Modeling high-dimensional dependence among astronomical data
• Copula approach to exchange-correlation hole in many-electron systems with strong correlations