The Parameter-Level Performance of Covariance Matrix Conditioning in Cosmic Microwave Background Data Analyses

Abstract

Empirical estimates of the band power covariance matrix are commonly used in cosmic microwave background (CMB) power spectrum analyses. While this approach easily captures correlations in the data, noise in the resulting covariance estimate can systematically bias the parameter fitting. Conditioning the estimated covariance matrix, by applying prior information on the shape of the eigenvectors, can reduce these biases and ensure the recovery of robust parameter constraints. In this work, we use simulations to benchmark the performance of four different conditioning schemes, motivated by contemporary CMB analyses. The simulated surveys measure the $TT$, $TE$, and $EE$ power spectra over the angular multipole range $300\le \ell \le 3500$ in $\Delta \ell =50$ wide bins, for temperature map-noise levels of $10,6.4$ and $2\mu$K-arcmin. We divide the survey data into $N_{\mathrm{real}}=30,50,$ or 100 uniform subsets. We show the results of different conditioning schemes on the errors in the covariance estimate, and how these uncertainties on the covariance matrix propagate to the best-fit parameters and parameter uncertainties. The most significant effect we find is an additional scatter in the best-fit point, beyond what is expected from the data likelihood. For a minimal conditioning strategy, $N_{\mathrm{real}}=30$, and a temperature map-noise level of 10$\mu$K-arcmin, we find the uncertainty on the recovered best fit parameter to be $\times 1.3$ larger than the apparent posterior width from the likelihood ($\times 1.2$ larger than the uncertainty when the true covariance is used). Stronger priors on the covariance matrix reduce the misestimation of parameter uncertainties to $<1\%$. As expected, empirical estimates perform better with higher $N_{\mathrm{real}}$, ameliorating the adverse effects on parameter constraints.

arXiv comment11 pages, 4 figures, submitted to MNRAS

References in corpus (35)

• The NumPy array: a structure for efficient numerical computation
• Efficient Computation of CMB anisotropies in closed FRW models
• Cosmological parameters from CMB and other data: a Monte-Carlo approach
• Planck 2018 results. I. Overview and the cosmological legacy of Planck
• Planck 2018 results. V. CMB power spectra and likelihoods
• A Joint Analysis of BICEP2/Keck Array and Planck Data
• Why your model parameter confidences might be too optimistic -- unbiased estimation of the inverse covariance matrix
• MASTER of the CMB Anisotropy Power Spectrum: A Fast Method for Statistical Analysis of Large and Complex CMB Data Sets
• Cobaya: Code for Bayesian Analysis of hierarchical physical models
• The Atacama Cosmology Telescope: DR4 Maps and Cosmological Parameters
• A Measurement of the Cosmic Microwave Background B-Mode Polarization Power Spectrum at Sub-Degree Scales with POLARBEAR
• The Atacama Cosmology Telescope: Temperature and Gravitational Lensing Power Spectrum Measurements from Three Seasons of Data
• Neutrino Physics from the Cosmic Microwave Background and Large Scale Structure
• The Atacama Cosmology Telescope: A Measurement of the Cosmic Microwave Background Power Spectra at 98 and 150 GHz
• Measurements of the E-Mode Polarization and Temperature-E-Mode Correlation of the CMB from SPT-3G 2018 Data
• Parameter inference with estimated covariance matrices
• The Atacama Cosmology Telescope: Two-Season ACTPol Spectra and Parameters
• Putting the Precision in Precision Cosmology: How accurate should your data covariance matrix be?
• The Effect of Covariance Estimator Error on Cosmological Parameter Constraints
• Measurements of the Temperature and E-Mode Polarization of the CMB from 500 Square Degrees of SPTpol Data
• Measurements of Secondary Cosmic Microwave Background Anisotropies with the South Pole Telescope
• COSMOPOWER: emulating cosmological power spectra for accelerated Bayesian inference from next-generation surveys
• Xspect, estimation of the angular power spectrum by computing cross-power spectra with analytical error bars
• An Improved Measurement of the Secondary Cosmic Microwave Background Anisotropies from the SPT-SZ + SPTpol Surveys
• Performance of internal Covariance Estimators for Cosmic Shear Correlation Functions
• Massive data compression for parameter-dependent covariance matrices
• Measurements of E-Mode Polarization and Temperature-E-Mode Correlation in the Cosmic Microwave Background from 100 Square Degrees of SPTpol Data
• CARPool: fast, accurate computation of large-scale structure statistics by pairing costly and cheap cosmological simulations
• Fast generation of ensembles of cosmological N-body simulations via mode-resampling
• Properties and use of CMB power spectrum likelihoods
• On estimating cosmology-dependent covariance matrices
• Dark Energy Survey Year 1 Results: Cross-correlation between DES Y1 galaxy weak lensing and SPT+Planck CMB weak lensing
• Simulations and cosmological inference: A statistical model for power spectra means and covariances
• A Bayesian method for combining theoretical and simulated covariance matrices for large-scale structure surveys
• Pico: Parameters for the Impatient Cosmologist