[astro-ph/0606088] A re-analysis of the three-year WMAP temperature power spectrum and likelihood

Authors:  H. K. Eriksen, Greg Huey, R. Saha, F. K. Hansen, J. Dick, A. J. Banday, K. M. Gorski, P. Jain, J. B. Jewell, L. Knox, D. L. Larson, I. J. O'Dwyer, T. Souradeep, B. D. Wandelt
Abstract:  We analyze the three-year WMAP temperature anisotropy data seeking to confirm the power spectrum and likelihoods published by the WMAP team. We apply five independent implementations of four algorithms to the power spectrum estimation and two implementations to the parameter estimation. Our single most important result is that we broadly confirm the WMAP power spectrum and analysis. Still, we do find two small but potentially important discrepancies: On large angular scales there is a small power excess in the WMAP spectrum (5-10% at l<~30) primarily due to likelihood approximation issues between 13 <= l <~30. On small angular scales there is a systematic difference between the V- and W-band spectra (few percent at l>~300). Recently, the latter discrepancy was explained by Huffenberger et al. (2006) in terms of over-subtraction of unresolved point sources. As far as the low-l bias is concerned, most parameters are affected by a few tenths of a sigma. The most important effect is seen in n_s. For the combination of WMAP, Acbar and BOOMERanG, the significance of n_s =/ 1 drops from ~2.7 sigma to ~2.3 sigma when correcting for this bias. We propose a few simple improvements to the low-l WMAP likelihood code, and introduce two important extensions to the Gibbs sampling method that allows for proper sampling of the low signal-to-noise regime. Finally, we make the products from the Gibbs sampling analysis publically available, thereby providing a fast and simple route to the exact likelihood without the need of expensive matrix inversions.
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Hans Kristian Eriksen
Posts: 60
Joined: September 25 2004
Affiliation: ITA, University of Oslo

[astro-ph/0606088] A re-analysis of the three-year WMAP temp

Post by Hans Kristian Eriksen » October 04 2006

I just wanted to note that we have now published the Gibbs sampling data from the WMAP3 re-analysis at


under the "Research" tab. (Couldn't figure out how to link to a particular frame, so sorry for not having a direct link.. However, this will eventually all appear on Lambda, I think.)

These data form the basis of the low-l likelihood we use, and we also provide an F90 module to compute that likelihood easily. If you want to use any of this, please feel free. However, I would really appreciate it if you would send me an email if you can't make it work – I'm not sure if the README I wrote is sufficiently complete.. In fact, it would also be great if you would send me an email even if you can make it work, so that I know somebody is actually using this – if not, I'm not sure how much time I'll spend on making updates available.. :-)

Anyway, as described in the revised paper, the low-l WMAP likelihood part should be replaced by either this code or by an exact likelihood evaluation at Nside=16 and lmax=30, as the MASTER-based likelihood is not quite good enough in the l=13&#8722;30 range. Personally, I prefer the Gibbs+BR approach, since it's much faster, and significantly reduces the time spent on likelihood evaluations in the MCMC sampling process. But both are of course equivalent in terms of numerical results.

It is also worth noting that we make Gibbs sampled sky maps available at the above link. These may be useful for analyses that requires phase information. However, if you do use these for publications, I strongly recommend that 1) you make sure you really understand the properties of the Gibbs sampled sky maps properly, and 2) *really* check the convergence properties of your particular statistic! While the samples we provide give very good convergence characteristics for parameter estimation purposes up to lmax=30 or 50 or so, the story may be very different for some complicated non-Gaussianity statistic. So *please* check this carefully before going public with some funny effect :-)

Good luck!

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