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Demo 6: Getting a CFHTLens likelihood

Running

In this example we will generate a likelihood of a cosmology using the CFHTLens tomographic data from Heymans et al.

We will use the test sampler again, so just a single cosmology. I only just added the demo6.ini file, so if you can't see demos/demo6.ini then do "git pull" in your main directory to get these new files.

cosmosis demos/demo6.ini

You should see some output like this:

-- Setting up module camb --
-- Setting up module halofit --
-- Setting up module load_nz --
Found 6 samples and 72 bins in redshift in file cosmosis-standard-    library/likelihood/cfhtlens/combined_nz.txt
-- Setting up module shear_shear --
-- Setting up module 2pt --
-- Setting up module cfhtlens --
Need to check the Anderson Hartlap when cutting matrix - cut first?
xi_plus only? False
Cut low thetas? True
Setup all pipeline modules
Pipeline ran okay.
Likelihood -1.694817e+02
Prior      =  0
Likelihood =  -169.481692685
Posterior  =  -169.481692685

The last number is the CFHTLens log-posterior of the parameters in demos/values6.ini.

Now let's make some plots. For some variety, let's make them PDF plots instead of PNG:

postprocess  demos/demo6.ini -o plots -p demo6 -f pdf

You will get some nice new plots in plots/demo6*.pdf. Since we are now computing shear-shear functions we will have two new plots compared to demo 1: demo6_shear_power.pdf and demo6_shear_correlation.pdf. Here's the shear power plot:

shear_power.png

Understanding

The weak lensing case is an example where there is a longer sequence of different modules. The demos/demo6.ini file contains this line:

modules = consistency camb halofit  load_nz  shear_shear  2pt cfhtlens

We have already looked at the consistency, camb and halofit modules in demo one. The load_nz module just loads a simple text file containing n(z) in its setup, and then each time it is executed provides the same n(z).

The shear_shear module computes the Limber integral to go from P(k,z) and n(z) to C_ell for the different bins and the correlations between them.

The 2pt module integrates the C_ell with bessel functions J0 and J4 to get correlation function xi+ and x-.

The CFHTLens module interpolates into the xi+ and xi- values to get their values at the CFHTLens observed values, and then gets a likelihood.

Updated