Post
by **Loison Hoi** » June 23 2006

Hi,

Maybe the followings are related to this topic.

I accidentally found a best fit point of the running spectral inex model (6 parameters + tensor + running spectral index) which gives \chi^2 = 10604 when using cosmomc. Compared with the best fit non-running model (6 parameters) value \chi^2=11252, there is a \Delta\chi^2 = 648! This is a huge change in likelihood. The values of parameters of this special best fit point are very different from those of the usual best fit point, for example dn/dlnk is positive, and hence this special point does not seem physical. Here are the values of parameters of the special best fit point when using cosmomc (inflation_consistency=T, other settings are default):

Best fit sample -log(Like) = 5302.02880859375

param bestfit

1 0.168166E-01 \Omega_b h^2

2 0.133521E+00 \Omega_c h^2

3 0.104458E+01 \theta

4 0.644379E-01 \tau

8 0.593603E+00 n_s

10 0.676360E-01 n_{run}

11 0.270513E+01 log[10^{10} A_s]

12 0.948667E+00 r

With detailed investigation, I found that the main question is that the TT beam and point source correction is very close to the TT C_l's likelihood,

but with the opposite sign, and thus the total likelihood is reduced significantly. Here are the likelihoods:

likelihoods for the special best fit point:

-2*ln(L)_ttlike = 114373.747999890

-2*ln(L)_ttbeamlike = -114373.598731511

-2*ln(L)_ttlowlike = 602.164159554811

-2*ln(L)_ttlowdet = -10999.7907555282

-2*ln(L)_telike = 1197.98368076825

-2*ln(L)_tedet = 3401.19832251655

-2*ln(L)_lowlike = 1190.72692871094

-2*ln(L)_lowdet = 15211.7269109651

Likelihood: 5302.079

likelihoods for the usual running spectral index model:

-2*ln(L)_ttlike = 1052.37469675378

-2*ln(L)_ttbeamlike = 1.46484474064230

-2*ln(L)_ttlowlike = 640.235204763192

-2*ln(L)_ttlowdet = -11040.4322809536

-2*ln(L)_telike = 417.149844866212

-2*ln(L)_tedet = 3776.02275889830

-2*ln(L)_lowlike = 1180.03723144531

-2*ln(L)_lowdet = 15222.2984174593

Likelihood: 5624.575

Therefore, we can see that every thing looks normal except for the beam and point source corrections. Michael Nolta, the author of the code WMAP_3yr_tt_beam_and_ptsrc_corr.f90, informed me that to fix this problem, we can try using the following options:

beam_diagonal_sigma = .false.

beam_gaussian_likelihood = .false.

This will integrate the beam module into the gaussian+lognormal form for the likelihood used for the TT spectrum, instead of using a gaussian approximation. Anyway, maybe the gaussian approximation for the likelihood is not valid in some regions, for example dn/dlnk>0 as in the above example.

By the way, there is a bug in the function "compute_tt_beam_and_ptsrc_chisq" in WMAP_3yr_tt_beam_and_ptsrc_corr.f90. This function defines the dimensions of C_l's arrays and the fisher matrix through the input lmin and lmax, which makes the C_l's and the fisher matrix inside the function different from those of the input values if lmin/=2 and lmax/=1000. For example, if lmin=3 and lmax=1000, according to the Fortran data passing rule, we have

cl(2) = cl(3)

cl(3) = cl(4)

cl(4) = cl(5)

fisher(2,2) = fisher(3,3)

fisher(3,3) = fisher(5,4)

fisher(4,3) = fisher(6,4)

where values in the left hand side are values outside the function (e.g. in the subroutine pass2_compute_likelihood), and values in the right hand

side are values inside the function compute_tt_beam_and_ptsrc_chisq. Problems will occur in the beam and point source corrections in TT data if

ttmin and ttmax are not set to the default values, 2 and 1000. To avoid this problem, just set the dimensions of the arrays and matrix:

real(kind=8), dimension(2:1000), intent(in) :: cltt, cltt_dat, neff, fsky, clps, z, zbar

real(kind=8), dimension(2:1000,2:1000), intent(in) :: fisher

Loison Hoi

22 Jun 2006