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[1103.3505]
Bias in lowmultipole CMB reconstructions

Authors:  Craig J. Copi, Dragan Huterer, Dominik J. Schwarz, Glenn D. Starkman 
Abstract:  The largeangle, low multipole cosmic microwave background (CMB) provides a
unique view of the largest angular scales in the Universe. Study of these
scales is hampered by the facts that we have only one Universe to observe, only
a few independent samples of the underlying statistical distribution of these
modes, and an incomplete sky to observe due to the interposing Galaxy.
Techniques for reconstructing a full sky from partial sky data are well known
and have been applied to the large angular scales. In this work we critically
study the reconstruction process and show that, in practise, the reconstruction
is biased due to leakage of information from the region obscured by foregrounds
to the region used for the reconstruction. We conclude that, despite being
suboptimal in a technical sense, using the unobscured region without
reconstructing is the most robust measure of the true CMB sky. 

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Syksy Rasanen
Joined: 02 Mar 2005 Posts: 128 Affiliation: University of Helsinki

Posted: March 25 2011 


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 largeangle properties should be studied on the cut sky, not on a reconstructed full sky. 

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Hiranya Peiris
Joined: 28 Sep 2004 Posts: 54 Affiliation: University College London

Posted: July 29 2011 


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 selfconsistent 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. 

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Syksy Rasanen
Joined: 02 Mar 2005 Posts: 128 Affiliation: University of Helsinki

Posted: July 29 2011 


Thanks, I'll have a look. 

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Syksy Rasanen
Joined: 02 Mar 2005 Posts: 128 Affiliation: University of Helsinki

Posted: August 23 2011 


It seems to me that the theorydependence 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". 

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Hiranya Peiris
Joined: 28 Sep 2004 Posts: 54 Affiliation: University College London

Posted: September 20 2011 


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 MLextraction 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. 

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