Likelihood Function for exact likelihood approximation

[Junsong Cang]

Hi Antony and All,

I have been using makePerfectForecastDataset.py included in CosmoMC/python directory (October 2019 Version) to produce dataset for my forecast study, I noticed in the *.dataset file that this python script produces dataset files in "exact likelihood approximation". I have been reading the Fortran source codes myself but I would really appreciate it if you could also refer me to a reference where I can find detailed description of the likelihood function of this approximation.

An example of my forecast dataset is as follows:

binned=F
cl_hat_file=LiteBird.dat
cl_hat_includes_noise=F
cl_lmax=1350
cl_lmin=2
cl_noise_file =LiteBird_Noise.dat
dataset_format=CMBLike2
fields_use=T E
fullsky_exact_fksy=0.7
like_approx=exact

PS: I used to assume that approximation described in Section IIIE of arXiv: 0801.0554 is the "exact likelihood approximation", but Line 124 of CosmoMC/source/CMBlikes.f90 says that this paper also describes HL approximation (eg. used in BK15 likelihood) so I am a bit confused.


Cheers

Junsong

[Junsong Cang]

I think I found it in arXiv: 0801.0554, under the Section II: EXACT FULL-SKY LIKELIHOOD FUNCTION, I didn't realize this until I dug further into CMBlike.f90. Thanks mates.