TEASING: a fast and accurate approximation for the low multipole likelihood of the Cosmic Microwave Background temperature

Abstract

We explore the low-l likelihood of the angular spectrum C(l) of masked CMB temperature maps using an adaptive importance sampler. We find that, in spite of a partial sky coverage, the likelihood distribution of each C(l) closely follows an inverse gamma distribution. Our exploration is accurate enough to measure the inverse gamma parameters along with the correlation between multipoles. Those quantities are used to build an approximation of the joint posterior distribution of the low-l likelihood. The accuracy of the proposed approximation is established using both statistical criteria and a mock cosmological parameter fit. When applied to the WMAP5 data set, this approximation yields cosmological parameter estimates at the same level of accuracy as the best current techniques but with very significant speed gains.

10 pages, 10 figures, submitted to MNRAS

References in corpus (10)

• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Likelihoods and Parameters from the WMAP data
• Three-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Temperature Analysis
• Likelihood Analysis of CMB Temperature and Polarization Power Spectra
• Adaptive Importance Sampling in General Mixture Classes
• Estimation of cosmological parameters using adaptive importance sampling
• A re-analysis of the three-year WMAP temperature power spectrum and likelihood
• Fast optimal CMB power spectrum estimation with Hamiltonian sampling
• Hybrid Estimation of CMB Polarization Power Spectra
• Likelihood methods for the combined analysis of CMB temperature and polarisation power spectra
• CMB likelihood approximation by a Gaussianized Blackwell-Rao estimator

Cited by in corpus (28)

• Planck 2018 results. V. CMB power spectra and likelihoods
• Planck intermediate results. LI. Features in the cosmic microwave background temperature power spectrum and shifts in cosmological parameters
• Reionization optical depth determination from Planck HFI data with ten percent accuracy
• A new model to predict weak-lensing peak counts II. Parameter constraint strategies
• Constructing a bivariate distribution function with given marginals and correlation: application to the galaxy luminosity function
• Gamma ray burst constraints on cosmological models from the improved Amati correlation
• Copula Cosmology: Constructing a Likelihood Function
• From Finance to Cosmology: The Copula of Large-Scale Structure
• Determining the core radio luminosity function of radio AGNs via copula
• Planck constraints on cross-correlations between anisotropic cosmic birefringence and CMB polarization
• The improved Amati correlations from Gaussian copula
• Likelihood methods for CMB experiments
• Cylinders out of a top hat: counts-in-cells for projected densities
• Bayesian model comparison in cosmology with Population Monte Carlo
• A comparison of CMB Angular Power Spectrum Estimators at Large Scales: the TT case
• Dust polarization spectral dependence from Planck HFI data. Turning point on CMB polarization foregrounds modelling
• Lack-of-correlation anomaly in CMB large scale polarisation maps
• A novel CMB polarization likelihood package for large angular scales built from combined WMAP and Planck LFI legacy maps
• Sufficiency of a Gaussian power spectrum likelihood for accurate cosmology from upcoming weak lensing surveys
• Residual noise covariance for Planck low-resolution data analysis
• Bayesian angular power spectrum analysis of interferometric data
• 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
• Inference of the optical depth to reionization $\tau$ from $\text{Planck}$ CMB maps with convolutional neural networks
• Non-Gaussian likelihood of weak lensing power spectra
• Accurate and efficient likelihood modeling for large-scale CMB data