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[0710.2371] Probing Non-Gaussianity In The Cosmic Microwave Background Anisotropies: One Point Distribution Function
 
Authors:E. Jeong, G. F. Smoot
Abstract:We analyze WMAP 3 year data using the one-point distribution functions to probe the non-Gaussianity in the Cosmic Microwave Background (CMB) Anisotropy data. Computer simulations are performed to determine the uncertainties of the results. We report the non-Gaussianity parameter f_NL is constrained to 26<f_NL<82 for Q-band, 12<f_NL<67 for V-band, 7<f_NL<64 for W-band and 23<f_NL<75 for Q+V+W combined data at 95% confidence level (CL).
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Thomas Dent



Joined: 14 Nov 2006
Posts: 28
Affiliation: ITP Heidelberg

PostPosted: October 16 2007  Reply with quote

Jeong and Smoot claim to put fNL = 0 outside the 95% confidence level simply by looking at the one-point function, which appears to be sensitive at the level of O(100).

A number of questions arise. First, why are the results of their Fig.1 and Fig.2 so different, if the main errors do in fact arise from instrumental noise?
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Ben Gold



Joined: 25 Sep 2004
Posts: 97
Affiliation: University of Minnesota

PostPosted: October 23 2007  Reply with quote

I don't have an answer, just another question: why doesn't figure 1 seem to agree with the constraints listed in table 2? Aren't they supposed to be the same results?
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alexandre amblard



Joined: 25 Sep 2004
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Affiliation: UC, Irvine

PostPosted: October 29 2007  Reply with quote

I think Fig 1. numbers are in table 1 and Fig 2. numbers are in table 2, I think the difference between the two is that in Fig2/Table2 they take into account ("remove") non-Gaussianity from noise to estimate fNL.
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Kate Land



Joined: 27 Sep 2004
Posts: 29
Affiliation: Oxford University

PostPosted: October 29 2007  Reply with quote

Looks like they've done a one-tail rather than a two-tail probability on Figure 1. ie. the red 68% region is defined with a χ2 upper limit such that P(χ2 < limit)=68%. I would have thought that a two-tail probability was more meaningful, ie. the 68% confidence region is definied by upper and lower limits around the mean/mode/median such that P(limit1 < χ2 < limit2)=68%. This would widen those regions a little bit...

Another thought - the bestfitting f_NL values in Figure 1 are outside of the 68% region for the Q and the W band - indicting not a great goodness-of-fit. I'm wondering if the simulations generally found better fits...
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Hans Kristian Eriksen



Joined: 25 Sep 2004
Posts: 58
Affiliation: ITA, University of Oslo

PostPosted: October 29 2007  Reply with quote

Thomas Dent wrote:
A number of questions arise. First, why are the results of their Fig.1 and Fig.2 so different, if the main errors do in fact arise from instrumental noise?


Yes, I have the same feeling – I'm left with a number of questions after reading this paper. First and foremost, how is it possible that the 1D cumulative distribution can be competitive to the bi-spectrum in terms of sensitivity? All tests I've ever seen on this have turned out negative for the 1D cumulative distribution. In fact, the 1D distribution is often used as an illustration that fnl ~ O(100) is indeed a *tiny* effect, and more sophisticated methods are required..

Second, I'm wondering how they computed the confidence regions. One odd feature is that the Q-band confidence region is smaller than for Q+V+W, which isn't really very intuitive. In general, from Figure 1 it appears that a worse fit (= higher reduced chi2 at the minimum point) implies smaller error bars. Which again may perhaps suggest that the confidence regions are computed from the theoretical prediction only, as if the best-fit point was indeed perfect (with chi2 = 1) without first asking whether the fit is good in the first place. (In other words, a poor fit would automatically "imply" small error bars, because the total chi2 "rises" very rapidly – in fact, it starts out high..)

Still, even if this have been done correctly, it doesn't explain why the 1D distribution appears so sensitive, since this depends just on the width of the chi2 curves in Figure 1, not on the minimum value. It might be useful if somebody with access to good fnl simulations repeats this experiment, and see if they can reproduce the results..
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Dominik Schwarz



Joined: 08 Sep 2005
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Affiliation: University of Bielefeld

PostPosted: November 19 2007  Reply with quote

The test assumes that foreground subtraction is perfect in each pixel. Imagine that the foreground substraction is good on a typical pixel, but there are a few pixels (say 10%) in which it does not work. That would certainly mimic a fNL. It seems to me that we have no reason to believe that forground substraction works at the level of individual pixels. It would be interesting to see how this test changes as one plays with Nside.
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