Likelihood, Fisher information, and systematics of cosmic microwave background experiments
arXiv:1205.0810 · doi:10.1051/0004-6361/201219293
Abstract
Every experiment is affected by systematic effects that hamper the data analysis and have the potential to ultimately degrade its performance. In the case of probes of the cosmic microwave background (CMB) radiation, a minimal set of issues to consider includes asymmetric beam functions, correlated noise, and incomplete sky coverage. Presuming a simplified scanning strategy that allows for an exact analytical treatment of the problem, we study the impact of systematic effects on the likelihood function of the CMB power spectrum. We use the Fisher matrix, a measure of the information content of a data set, for a quantitative comparison of different experimental configurations. In addition, for various power spectrum coefficients, we explore the functional form of the likelihood directly, and obtain the following results: The likelihood function can deviate systematically from a Gaussian distribution up to the highest multipole values considered in our analysis. Treated exactly, realistic levels of asymmetric beam functions and correlated noise do not by themselves decrease the information yield of CMB experiments nor do they induce noticeable coupling between multipoles. Masking large fractions of the sky, on the other hand, results in a considerably more complex correlation structure of the likelihood function. Combining adjacent power spectrum coefficients into bins can partially mitigate these problems.
arXiv comment10 pages, 14 figures. Accepted for publication in Astronomy and Astrophysics
References in corpus (36)
- Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
- First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Preliminary Maps and Basic Results
- Cosmological parameters from CMB and other data: a Monte-Carlo approach
- Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Data Processing, Sky Maps, and Basic Results
- Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Sky Maps, Systematic Errors, and Basic Results
- Three-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Temperature Analysis
- A measurement by BOOMERANG of multiple peaks in the angular power spectrum of the cosmic microwave background
- MASTER of the CMB Anisotropy Power Spectrum: A Fast Method for Statistical Analysis of Large and Complex CMB Data Sets
- First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Parameter Estimation Methodology
- Planck Early Results: The Planck mission
- A Measurement of the Damping Tail of the Cosmic Microwave Background Power Spectrum with the South Pole Telescope
- Cosmological-Parameter Determination with Microwave Background Maps
- Estimating the Power Spectrum of the Cosmic Microwave Background
- Estimating spinning binary parameters and testing alternative theories of gravity with LISA
- The Atacama Cosmology Telescope: Cosmological Parameters from the 2008 Power Spectra
- How to measure CMB power spectra without losing information
- High Resolution Observations of the CMB Power Spectrum with ACBAR
- Myths and Truths Concerning Estimation of Power Spectra
- Global, Exact Cosmic Microwave Background Data Analysis Using Gibbs Sampling
- Planck early results: first assessment of the High Frequency Instrument in-flight performance
- The Pseudo- method: Cosmic microwave background anisotropy power spectrum statistics for high precision cosmology
- Cosmic microwave background anisotropy power spectrum statistics for high precision cosmology
- Weak Lensing: Prospects for Measuring Cosmological Parameters
- An Efficient Technique to Determine the Power Spectrum from Cosmic Microwave Background Sky Maps
- Planck early results. III. First assessment of the Low Frequency Instrument in-flight performance
- The Atacama Cosmology Telescope
- Information content of the non-linear matter power spectrum
- The Planck-LFI instrument: analysis of the 1/f noise and implications for the scanning strategy
- Fast Pixel Space Convolution for CMB Surveys with Asymmetric Beams and Complex Scan Strategies: FEBeCoP
- CMB-slow, or How to Estimate Cosmological Parameters by Hand
- New estimates of the CMB angular power spectra from the WMAP 5 yrs low resolution data
- Fast, exact CMB power spectrum estimation for a certain class of observational strategies
- Information Content in the Galaxy Angular Power Spectrum from the Sloan Digital Sky Survey and Its Implication on Weak Lensing Analysis
- Power Spectrum Estimators For Large CMB Datasets
- Beam deconvolution in noisy CMB maps
- Fast calculation of the Fisher matrix for cosmic microwave background experiments
Cited by in corpus (9)
- Planck 2018 results. V. CMB power spectra and likelihoods
- Planck 2015 results. XI. CMB power spectra, likelihoods, and robustness of parameters
- Efficient Wiener filtering without preconditioning
- Using inpainting to construct accurate cut-sky CMB estimators
- Bayesian angular power spectrum analysis of interferometric data
- Exact joint likelihood of pseudo- estimates from correlated Gaussian cosmological fields
- Optimal and fast E/B separation with a dual messenger field
- Bayesian Inference of Polarized CMB Power Spectra from Interferometric Data
- Towards efficient and optimal analysis of CMB anisotropies on a masked sky