{
  "id": "1202.4898",
  "version": "v2",
  "published": "2012-02-22T13:04:16.000Z",
  "updated": "2012-03-12T14:08:29.000Z",
  "title": "Fast calculation of the Fisher matrix for cosmic microwave background experiments",
  "authors": [
    "Franz Elsner",
    "Benjamin D. Wandelt"
  ],
  "comment": "4 pages, 1 figures. Accepted for publication in Astronomy and Astrophysics Letters. Replaced to match published version",
  "journal": "Astron.Astrophys. 540 (2012) L6",
  "doi": "10.1051/0004-6361/201218985",
  "categories": [
    "astro-ph.CO"
  ],
  "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.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-03-12T14:08:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cosmic microwave background experiments",
      "fisher matrix",
      "fast calculation",
      "optimal power spectrum estimation plays",
      "optimal quadratic power spectrum estimation"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Astronomy and Astrophysics",
      "year": 2012,
      "month": "Apr",
      "volume": 540
    },
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1090220,
      "adsabs": "2012A&A...540L...6E"
    }
  }
}