[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).
[PDF]  [PS]  [BibTex]  [Bookmark]

Discussion related to specific recent arXiv papers
Post Reply
Thomas Dent
Posts: 26
Joined: November 14 2006
Affiliation: ITP Heidelberg
Contact:

[0710.2371] Probing Non-Gaussianity In The Cosmic Microwave

Post by Thomas Dent » October 16 2007

Jeong and Smoot claim to put f_NL = 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?

Ben Gold
Posts: 81
Joined: September 25 2004
Affiliation: University of Minnesota
Contact:

[0710.2371] Probing Non-Gaussianity In The Cosmic Microwave

Post by Ben Gold » October 23 2007

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?

alexandre amblard
Posts: 1
Joined: September 25 2004
Affiliation: UC, Irvine

[0710.2371] Probing Non-Gaussianity In The Cosmic Microwav

Post by alexandre amblard » October 29 2007

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.

Kate Land
Posts: 29
Joined: September 27 2004
Affiliation: Oxford University
Contact:

[0710.2371] Probing Non-Gaussianity In The Cosmic Microwav

Post by Kate Land » October 29 2007

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 \chi^2 upper limit such that P([tex]\chi^2<[/tex]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 < [tex]\chi^2[/tex] < 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...

Hans Kristian Eriksen
Posts: 58
Joined: September 25 2004
Affiliation: ITA, University of Oslo
Contact:

Re: [0710.2371] Probing Non-Gaussianity In The Cosmic Micr

Post by Hans Kristian Eriksen » October 29 2007

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 f_nl ~ 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 chi^2 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 chi^2 = 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 chi^2 "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 chi^2 curves in Figure 1, not on the minimum value. It might be useful if somebody with access to good f_nl simulations repeats this experiment, and see if they can reproduce the results..

Dominik Schwarz
Posts: 2
Joined: September 08 2005
Affiliation: University of Bielefeld

[0710.2371] Probing Non-Gaussianity In The Cosmic Microwave

Post by Dominik Schwarz » November 19 2007

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 f_NL. 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 N_side.

Post Reply