CMB likelihood approximation by a Gaussianized Blackwell-Rao estimator

Abstract

We introduce a new CMB temperature likelihood approximation called the Gaussianized Blackwell-Rao (GBR) estimator. This estimator is derived by transforming the observed marginal power spectrum distributions obtained by the CMB Gibbs sampler into standard univariate Gaussians, and then approximate their joint transformed distribution by a multivariate Gaussian. The method is exact for full-sky coverage and uniform noise, and an excellent approximation for sky cuts and scanning patterns relevant for modern satellite experiments such as WMAP and Planck. A single evaluation of this estimator between l=2 and 200 takes ~0.2 CPU milliseconds, while for comparison, a single pixel space likelihood evaluation between l=2 and 30 for a map with ~2500 pixels requires ~20 seconds. We apply this tool to the 5-year WMAP temperature data, and re-estimate the angular temperature power spectrum, $C_{\ell }$, and likelihood, L(C_l), for l<=200, and derive new cosmological parameters for the standard six-parameter LambdaCDM model. Our spectrum is in excellent agreement with the official WMAP spectrum, but we find slight differences in the derived cosmological parameters. Most importantly, the spectral index of scalar perturbations is n_s=0.973 +/- 0.014, 1.9 sigma away from unity and 0.6 sigma higher than the official WMAP result, n_s = 0.965 +/- 0.014. This suggests that an exact likelihood treatment is required to higher l's than previously believed, reinforcing and extending our conclusions from the 3-year WMAP analysis. In that case, we found that the sub-optimal likelihood approximation adopted between l=12 and 30 by the WMAP team biased n_s low by 0.4 sigma, while here we find that the same approximation between l=30 and 200 introduces a bias of 0.6 sigma in n_s.

10 pages, 7 figures, submitted to ApJ

References in corpus (15)

• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Data Processing, Sky Maps, and Basic Results
• Distributions generated by perturbation of symmetry with emphasis on a multivariate skew $t$ distribution
• Three-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Temperature Analysis
• Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Galactic Foreground Emission
• Joint Bayesian component separation and CMB power spectrum estimation
• Likelihood Analysis of CMB Temperature and Polarization Power Spectra
• Bayesian analysis of sparse anisotropic universe models and application to the 5-yr WMAP data
• Fast cosmological parameter estimation using neural networks
• A re-analysis of the three-year WMAP temperature power spectrum and likelihood
• Estimation of Polarized Power Spectra by Gibbs sampling
• The joint large-scale foreground-CMB posteriors of the 3-year WMAP data
• Bayesian analysis of the low-resolution polarized 3-year WMAP sky maps
• Marginal distributions for cosmic variance limited CMB polarization data
• Pico: Parameters for the Impatient Cosmologist

Cited by in corpus (22)

• Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Power Spectra and WMAP-Derived Parameters
• Planck 2018 results. V. CMB power spectra and likelihoods
• Planck 2015 results. XI. CMB power spectra, likelihoods, and robustness of parameters
• Hunting for Primordial Non-Gaussianity in the Cosmic Microwave Background
• Estimation of cosmological parameters using adaptive importance sampling
• Planck Intermediate Results. IX. Detection of the Galactic haze with Planck
• New estimates of the CMB angular power spectra from the WMAP 5 yrs low resolution data
• Bayesian component separation and CMB estimation for the 5-year WMAP temperature data
• TEASING: a fast and accurate approximation for the low multipole likelihood of the Cosmic Microwave Background temperature
• Properties and use of CMB power spectrum likelihoods
• Likelihood methods for CMB experiments
• Foreground Separation and Constraints on Primordial Gravitational Waves with the PICO Space Mission
• BeyondPlanck I. Global Bayesian analysis of the Planck Low Frequency Instrument data
• Cosmoglobe DR1 results. I. Improved Wilkinson Microwave Anisotropy Probe maps through Bayesian end-to-end analysis
• BeyondPlanck XI. Bayesian CMB analysis with sample-based end-to-end error propagation
• BeyondPlanck XII. Cosmological parameter constraints with end-to-end error propagation
• Analysis of WMAP 7-year Temperature Data: Astrophysics of the Galactic Haze
• Cosmo++: An Object-Oriented C++ Library for Cosmology
• Cosmological Parameters from a re-analysis of the WMAP-7 low resolution maps
• CMB likelihood approximation for banded probability distributions
• Nearly Full-Sky Low-Multipole Cosmic Microwave Background Temperature Anisotropy: III. CMB Temperature Anomalies
• Cosmological measurements from the CMB and BAO are insensitive to the tail probability in the assumed likelihood