Cosmomc: the reduced \chi^2

Use of Healpix, camb, CLASS, cosmomc, compilers, etc.
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Loison Hoi
Posts: 23
Joined: February 21 2006
Affiliation: McGill University

Cosmomc: the reduced \\chi^2

Post by Loison Hoi » April 22 2006

Hi,

I am sorry if my question does not make sense.

The WMAP3 paper, Spergel et al. astro-ph/0603449 page 7, says: "that the reduced \chi_{\rm eff}^2 is 1.041 for the combined TT and TE data (1410 D.O.F., including TE l=24-450), quarter of the detected EE signal." So I would expect that the \chi^2 is 1.041*1410=1467.81. But I usually get the \chi^2=11266. I think I misunderstand something. What is wrong here?

I set the num_cls=3 as default. So cosmomc should include TT, TE, and EE. Is it the reason why I got a large number of \chi^2? However, I also set num_cls=3 in July 2005 version of cosmomc and WMAP1 data; in that case, I got best fit values and \chi^2 very close to those given by WMAP1 paper.

I use the \Lambda CDM model; most parameters and options are default. I am using April 2006 version.

Thanks!

Loison Hoi
21 Apr 2006

Antony Lewis
Posts: 1522
Joined: September 23 2004
Affiliation: University of Sussex
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Re: Cosmomc: the reduced \\\\chi^2

Post by Antony Lewis » April 22 2006

It depends on what you mean by the chi-squared. The chi-squared over pixels is different from the chi-squared over C_l. Since the WMAP3 likelihood code mixes pixel-space and C_l likelihood approximations, the absolute value of -2log(Liklihood) doesn't have a very obvious interpretation. See the readme.txt supplied with the WMAP likelihood code for the breakdown.

I guess the quoted chi-squareds are using some C_l likelihood approximation for all l?

Loison Hoi
Posts: 23
Joined: February 21 2006
Affiliation: McGill University

Cosmomc: the reduced \\chi^2

Post by Loison Hoi » April 23 2006

Hi Antony,

Thanks for your clarification!

Loison Hoi
22 Apr 2006

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