Fast calculation of the Fisher matrix for cosmic microwave background experiments
arXiv:1202.4898 · doi:10.1051/0004-6361/201218985
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.
4 pages, 1 figures. Accepted for publication in Astronomy and Astrophysics Letters. Replaced to match published version
References in corpus (4)
- Use and Abuse of the Fisher Information Matrix in the Assessment of Gravitational-Wave Parameter-Estimation Prospects
- Detection of Gravitational Lensing in the Cosmic Microwave Background
- Probing cosmological parameters with the CMB: Forecasts from full Monte Carlo simulations
- Information Content in the Galaxy Angular Power Spectrum from the Sloan Digital Sky Survey and Its Implication on Weak Lensing Analysis