CosmoCoffee

[Syksy Rasanen]

The most conspicuous anomalies in the CMB are the deviations from statistical homogeneity and isotropy on large angles. There has been debate about their significance and the best method for evaluating them. (See http://cosmocoffee.info/viewtopic.php?t=1582. and http://cosmocoffee.info/viewtopic.php?t=1601&highlight= ).

In particular, the masked CMB sky shows almost zero large angle correlation function, at a level which is here quoted as 99.975% unlikely. However, if you do the analysis on the ILC map, the unlikeliness is only at the 95% level, which is not significant. It seems to me that this result alone shows that something funny is going on: the regions inside and outside the mask seem to behave rather differently!

The present paper argues that the procedures for reconstructing the full sky from a masked sky in fact involve assumptions about what lies behind the mask to such an extent that the reconstruction is significantly biased by the contents of the cut region. The authors therefore conclude (in agreement with their previous work) that the large-angle properties should be studied on the cut sky, not on a reconstructed full sky.

[Hiranya Peiris]

You'd probably be interested in http://arxiv.org/abs/1107.5466 - it shows how to get rid of this "smoothing bias" in alm reconstruction, proposes a self-consistent criterion by which to choose a particular estimator for a given reconstruction problem, and shows that the related Quadratic Maximum Likelihood estimator for the angular power spectrum is not affected by this smoothing bias.

[Syksy Rasanen]

Thanks, I'll have a look.

[Syksy Rasanen]

It seems to me that the theory-dependence of the method in your paper provides support for the statement "the procedures for reconstructing the full sky from a masked sky in fact involve assumptions about what lies behind the mask to such an extent that the reconstruction is significantly biased by the contents of the cut region".

[Hiranya Peiris]

Hi, sorry I did not see this before. The theory dependence is just a consequence of Bayes' theorem. This statement: "the reconstruction is significantly biased by the contents of the cut region" is ambiguous; you haven't explained what you mean by biased.

I pointed out our paper as a detailed analysis of the "smoothing bias" discussed by the Copi et al paper, not as a response to the statement above. The smoothing bias does affect the standard technique for ML-extraction of a_lm s, but it is quite easily mitigated by changing the way you smooth. However, the S1/2 statistic discussed by Copi in the context of "what's behind the Galactic plane" is based on C_l extraction, not a_lm extraction. The standard QML estimator is not affected by this smoothing bias.