Fast calculation of the Fisher matrix for cosmic microwave background experiments

Abstract

The Fisher information matrix of the cosmic microwave background (CMB) radiation power spectrum coefficients is a fundamental quantity that specifies the information content of a CMB experiment. In the most general case, its exact calculation scales with the third power of the number of data points N and is therefore computationally prohibitive for state-of-the-art surveys. Applicable to a very large class of CMB experiments without special symmetries, we show how to compute the Fisher matrix in only O(N^2 log N) operations as long as the inverse noise covariance matrix can be applied to a data vector in time O(l_max^3 log l_max). This assumption is true to a good approximation for all CMB data sets taken so far. The method takes into account common systematics such as arbitrary sky coverage and realistic noise correlations. As a consequence, optimal quadratic power spectrum estimation also becomes feasible in O(N^2 log N) operations for this large group of experiments. We discuss the relevance of our findings to other areas of cosmology where optimal power spectrum estimation plays a role.

arXiv comment4 pages, 1 figures. Accepted for publication in Astronomy and Astrophysics Letters. Replaced to match published version

References in corpus (27)

• Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Preliminary Maps and Basic Results
• A measurement by BOOMERANG of multiple peaks in the angular power spectrum of the cosmic microwave background
• Probing Dark Energy with Baryonic Acoustic Oscillations from Future Large Galaxy Redshift Surveys
• MASTER of the CMB Anisotropy Power Spectrum: A Fast Method for Statistical Analysis of Large and Complex CMB Data Sets
• Use and Abuse of the Fisher Information Matrix in the Assessment of Gravitational-Wave Parameter-Estimation Prospects
• 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 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
• Cosmological parameters from lensing power spectrum and bispectrum tomography
• Detection of Gravitational Lensing in the Cosmic Microwave Background
• High Resolution Observations of the CMB Power Spectrum with ACBAR
• Probing cosmological parameters with the CMB: Forecasts from full Monte Carlo simulations
• The Pseudo-$C_l$ 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
• Dark Energy Constraints from Weak Lensing Cross-Correlation Cosmography
• Algorithms for bispectra: forecasting, optimal analysis, and simulation
• Information content of the non-linear matter power spectrum
• Systematic effects on dark energy from 3D weak shear
• Decorrelating the Power Spectrum of Galaxies
• 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

Cited by in corpus (8)

• Bayesian physical reconstruction of initial conditions from large scale structure surveys
• Efficient Wiener filtering without preconditioning
• Using inpainting to construct accurate cut-sky CMB estimators
• Describing variations of the Fisher-matrix across parameter space
• Likelihood, Fisher information, and systematics of cosmic microwave background experiments
• Optimal and fast E/B separation with a dual messenger field
• Towards efficient and optimal analysis of CMB anisotropies on a masked sky
• Partition function approach to non-Gaussian likelihoods: Formalism and expansions for weakly non-Gaussian cosmological inference