Power Spectrum Estimation from High-Resolution Maps by Gibbs Sampling

By H. Eriksen, Ian O'Dwyer, J. Jewell, Benjamin Dan Wandelt, D. Larson, K. G'orski, S. Levin, A. Banday, P. Lilje. 2004

182 citations recorded by the source corpus.

We revisit a recently introduced power spectrum estimation technique based on Gibbs sampling, with the goal of applying it to the high-resolution WMAP data. In order to facilitate this analysis, a number of sophistications have to be introduced, each of which is discussed in detail. We have implemented two independent versions of the algorithm to cross-check the computer codes and to verify that a particular solution to any given problem does not affect the scientific results. We then apply these programs to simulated data with known properties at intermediate (Nside = 128) and high (Nside = 512) resolutions, to study effects such as incomplete sky coverage and white versus correlated noise. From these simulations we also establish the Markov chain correlation length as a function of signal-to-noise ratio and give a few comments on the properties of the correlation matrices involved. Parallelization issues are also discussed, with emphasis on real-world limitations imposed by current supercomputer facilities. The scientific results from the analysis of the first-year WMAP data are presented in a companion letter.

Subfields: Astronomy and Astrophysics, Economics and Econometrics, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/fbaa470e15360a67558ff5f75d8b15f0dd538e5f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

In Economics and Econometrics

S. Galli

Citations in the corpus

SEVEN-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE (WMAP) OBSERVATIONS: POWER SPECTRA AND WMAP-DERIVED PARAMETERS (2010, background): “It is constructed from a set of Gibbs samples that contain power spectra and CMB maps that are statistically consistent with the data (Wandelt et al. 2004; Jewell et al. 2004; Eriksen et al. 2004).”
Planck 2015 results. XI. CMB power spectra, likelihoods, and robustness of parameters (2015, methodology): “1 shows the di↵erence between the Planck 2015 and 2013 Commander maximum-posterior maps, where the gray region now corresponds to the 2013 confidence mask.”
Planck intermediate results. LVII. Joint Planck LFI and HFI data processing (2020, methodology): “For further details, see Eriksen et al. (2004) and Thommesen et al. (2019).”
FIVE-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE OBSERVATIONS: COSMOLOGICAL INTERPRETATION (2008, unknown): “…et al. 2007; Park 2004; de Oliveira-Costa et al. 2004; Tegmark et al. 2003; Larson & Wandelt 2004; Eriksen et al. 2004; Eriksen et al. 2004; Eriksen et al. 2004, 2007a; Copi et al. 2004; Schwarz et al. 2004; Copi et al. 2006, 2007; Gordon et al. 2005; Bielewicz et al. 2005; Jaffe et al.…”
Bayesian physical reconstruction of initial conditions from large-scale structure surveys (2012, methodology): “…an observed sample of tracers given a survey mask and selection function (see e.g. Feldman et al. 1994; Tegmark & et al. 2004; Wandelt et al. 2004; Eriksen et al. 2004; Percival 2005; Jasche et al. 2010; Elsner & Wandelt 2012); and the much more difficult theoretical problem of modeling the power…”
A unified pseudo-Cℓ framework (2018, background): “…de Oliveira-Costa 2001; Vanneste et al. 2018) can recover the power spectrum with virtually no loss of information (see also the approaches of e.g. Eriksen et al. (2004); Taylor et al. (2008); Alsing et al. (2016), based on Bayesian sampling methods), their computational implementation is…”