Likelihood for low ell Planck data (Commander)

 Posts: 12
 Joined: May 03 2021
 Affiliation: Naresuan University
Likelihood for low ell Planck data (Commander)
Hi All,
I am curious if anyone here could answer my question.
I have had a look at commander_dx12_v3_2_29.clik/clik/lkl_0/_external/sigma.fits which I believe it contains the likelihood for lowl (2 < ell < 29). It contains an array of shape
3 x 249 x 1000
I believe the first axis is for TT, EE and BB and the second axis is for ells from 2  250. I believe the third axis is the tabulated g_ell(C_ell^theory) from
Equation 12 in Planck 2018 05  CMB and likelihoods paper
https://doi.org/10.1051/00046361/201936386
The data only contains the tabulated values of log likelihood for C_ell^theory by the the values of C_ell^theory itself. I am wondering if I could somehow find the value of C_ell^theory to match the values of the log likelihood in the file.
Best,
Teera
I am curious if anyone here could answer my question.
I have had a look at commander_dx12_v3_2_29.clik/clik/lkl_0/_external/sigma.fits which I believe it contains the likelihood for lowl (2 < ell < 29). It contains an array of shape
3 x 249 x 1000
I believe the first axis is for TT, EE and BB and the second axis is for ells from 2  250. I believe the third axis is the tabulated g_ell(C_ell^theory) from
Equation 12 in Planck 2018 05  CMB and likelihoods paper
https://doi.org/10.1051/00046361/201936386
The data only contains the tabulated values of log likelihood for C_ell^theory by the the values of C_ell^theory itself. I am wondering if I could somehow find the value of C_ell^theory to match the values of the log likelihood in the file.
Best,
Teera

 Posts: 12
 Joined: May 03 2021
 Affiliation: Naresuan University
Re: Likelihood for low ell Planck data (Commander)
The data only contains the tabulated values of log likelihood for C_ell^theory but not the the values of C_ell^theory itself.The data only contains the tabulated values of log likelihood for C_ell^theory by the the values of C_ell^theory itself.
Sorry for not proof read before.
Teera

 Posts: 1
 Joined: October 24 2022
 Affiliation: Perimeter Institute
Re: Likelihood for low ell Planck data (Commander)
Hello,
I would like to followup on the first part of this question and confirm if this is indeed the correct description for the dimensions of this 3 x 249 x 1000 array? I have also been looking at this sigma.fits file and am unsure what each axis of this array corresponds to.
Thank you for your help,
Jordan
I would like to followup on the first part of this question and confirm if this is indeed the correct description for the dimensions of this 3 x 249 x 1000 array? I have also been looking at this sigma.fits file and am unsure what each axis of this array corresponds to.
Thank you for your help,
Jordan

 Posts: 1
 Joined: March 17 2023
 Affiliation: University of Oslo
Re: Likelihood for low ell Planck data (Commander)
Hey Teera and Jordan,
The first dimension, with 3 elements, correspond to the spline information required to recreated a gaussianized CL_TT given input CLs. I.e. this is only for temperature Cls, from l=2 to 250, and the last dimension are 1000 distinct points the be able to spline input cls to give the output gaussianized Cls.
Then, the gaussianized Cls output from this can be used to evaluate the gaussian likelihood given the mean and covariance matrix, which also is found in sigma.fits in the other extensions.
This was recently reimplemented in Cobaya: https://github.com/CobayaSampler/cobaya/blob/master/cobaya/likelihoods/planck_2018_lowl/TT_native.py
so have a look at this to see how it works.
Eirik
The first dimension, with 3 elements, correspond to the spline information required to recreated a gaussianized CL_TT given input CLs. I.e. this is only for temperature Cls, from l=2 to 250, and the last dimension are 1000 distinct points the be able to spline input cls to give the output gaussianized Cls.
Then, the gaussianized Cls output from this can be used to evaluate the gaussian likelihood given the mean and covariance matrix, which also is found in sigma.fits in the other extensions.
This was recently reimplemented in Cobaya: https://github.com/CobayaSampler/cobaya/blob/master/cobaya/likelihoods/planck_2018_lowl/TT_native.py
so have a look at this to see how it works.
Eirik