# Existing likelihoods, and how to create new ones¶

This page is intended to explain in more concrete terms the information contained in the Likelihood class module documentation. More specifically, you should be able to write new likelihood files and understand the structure of existing ones.

## One likelihood is one directory, one .py and one .data file¶

We have seen already that cosmological parameters are passed directly from the input file to Class, and do not appear anywhere in the code itself, i.e. in the files located in the montepython/ directory. The situation is the same for likelihoods. You can write the name of a likelihood in the input file, and Monte Python will directly call one of the external likelihood codes implemented in the montepython/likelihoods/ directory. This means that when you add some new likelihoods, you don’t need to declare them in the code. You implement them in the likelihoods directory, and they are ready to be used if mentioned in the input file.

For This to work, a precise syntax must be respected. Each likelihood is associated to a name, e.g. hst, wmap, WiggleZ (the name is case-sensitive). This name is used:

• for calling the likelihood in the input file, e.g. data.experiments = ['hst', ...],
• for naming the directory of the likelihood, e.g. montepython/likelihoods/hst/,
• for naming the input data file describing the characteristics of the experiment, montepython/likelihoods/hst/hst.data (this file can point to raw data files located in the data directory)
• for naming the class declared in montepython/likelihoods/hst/__init__.py and used also in montepython/likelihoods/hst/hst.data

Warning

Note that since release 2.0.0, the likelihood python source is not called any longer hst.py, but __init__.py. The reason was for packaging and ease of use when calling from a Python console.

When implementing new likelihoods, you will have to follow this rule. You could already wish to have two Hubble priors/likelihoods in your folder. For instance, the distributed version of hst corresponds to a gaussian prior with standard deviation $$h=0.738\pm0.024$$. If you want to change these numbers, you can simply edit montepython/likelihoods/hst/hst.data. But you could also keep hst unchanged and create a new likelihood called e.g. spitzer. We will come back to the creation of likelihoods later, but just to illustrate the structure of likelihoods, let us see how to create such a prior/likelihood:

$mkdir likelihoods/spitzer$ cp likelihoods/hst/hst.data likelihoods/spitzer/spitzer.data
$cp likelihoods/hst/__init__.py likelihoods/spitzer/__init__.py  Then edit montepython/likelihoods/spitzer/__init__.py and replace in the initial declaration the class name hst by spitzer: class spitzer(Likelihood_prior):  Edit also montepython/likelihoods/spitzer/spitzer.data, replace the class name hst by spitzer, and the numbers by your constraint: spitzer.h = 0.743 spitzer.sigma = 0.021  You are done. You can simply add data.experiments = [...,'spitzer', ...] to the list of experiments in the input parameter file and the likelihood will be used. ## Existing likelihoods¶ We release the first version of Monte Python with the likelihoods: • spt, bicep, cbi, acbar, bicep, quad, the latest public versions of CMB data from SPT, Bicep, CBI, ACBAR, BICEP and Quad; for the SPT likelihoods we include three nuisance parameters obeying to gaussian priors, like in the original SPT paper, and for ACBAR one nuisance parameter with top-hat prior. These experiments are described by the very same files as in a ComsoMC implementation. They are located in the data/ directory. For each experiment, there is a master file xxx.dataset containing several variables and the names of other files with the raw data. In the files likelihoods/xxx/xxx.data, we just give the name of the different xxx.dataset files, that Monte Python is able to read just like CosmoMC. • wmap, original likelihood file accessed through the wmap wrapper. The file likelihoods/wmap/wmap.data allows you to call this likelihood with a few different options (e.g. switching on/off Gibbs sampling, choosing the minimum and maximum multipoles to include, etc.) As usual, we implemented the nuisance parameter A_SZ with a flat prior. In the input parameter file, you can decide to vary this parameter in the range 0-2, or to fix it to some value. • hst is the HST Key Project gaussian prior on $$h$$, • sn constains the luminosity distance-redhsift relation using the Union 2 data compilation, • WiggleZ constraints the matter power spectrum $$P(k)$$ in four different redshift bins using recent WiggleZ data, plus a few other likelihoods referring to future experiments, described in the next subsection. All these likelihoods are strictly equivalent to those in the CosmoMC patches released by the various experimental collaborations. ## Mock data likelihoods¶ We also release simplified likelihoods fake_planck_bluebook, euclid_lensing and euclid_pk for doing forecasts for Planck, Euclid (cosmic shear survey) and Euclid (redshift survey). In the case of Planck, we use a simple gaussian likelihood for TT, TE, EE (like in astro-ph/0606227 with no lensing extraction) with sensitivity parameters matching the numbers published in the Planck bluebook. In the case of Euclid, our likelihoods and sensitivity parameters are specified in the Euclid Red Book. The sensitivity parameters can always be modified by the user, by simply editing the .data files. These likelihoods compare theoretical spectra to a fiducial spectrum (and not to random data generated given the fiducial model: this approach is simpler and leads to the same forecast error bars, see this paper again). Let us illustrate the way in which this works with fake_planck_bluebook, although the two Euclid likelihoods obey exactly to the same logic. When you download the code, the file montepython/likelihoods/fake_planck_bluebook/fake_planck_bluebook.data has a field fake_planck_bluebook.fiducial_file pointing to the file 'fake_planck_bluebook_fiducial.dat'. You downloaded this file together with the code: it is located in data and it contains the TT/TE/EE spectrum of a particular fiducial model (with parameter values logged in the first line of the file). If you launch a run with this likelihood, it will work immediately and fit the various models to this fiducial spectrum. But you probably wish to choose your own fiducial model. This is extremely simple with Monte Python. You can delete the provided fiducial file\:code:‘fake_planck_bluebook_fiducial.dat’, or alternatively, you can change the name of the fiducial file in likelihoods/fake_planck_bluebook/fake_planck_bluebook.data. When you start the next run, the code will notice that there is no input fiducial spectrum. It will then generate one automatically, write it in the correct file with the correct location, and stop after this single step. Then, you can launch new chains, they will fit this fiducial spectrum. When you generate the fiducial model, you probably want to control exactly fiducial parameter values. If you start from an ordinary input file with no particular options, Monte Python will perform one random jump and generate the fiducial model. Fiducial parameter values will be logged in the first line of the fiducial file. But you did not choose them yourself. However, when you call Monte Python with the intention of generating a fiducial spectrum, you can pass the command line option -f 0. This sets the variance of the proposal density to zero. Hence the fiducial model will have precisely the parameter values specified in the input parameter file. The fiducial file is even logged in the log.param of all the runs that have been using it. ## Creating new likelihoods belonging to pre-defined category¶ A likelihood is a class (let’s call it generically xxx), declared and defined in montepython/likelihoods/xxx/__init__.py, using input numbers and input files names specified in montepython/likelihoods/xxx/xxx.data. The actual data files should usually be placed in the data/ folder (with the exception of WMAP data). Such a class will always inherit from the properties of the most generic class defined inside montepython/likelihoods_class.py. But it may fall in the category of some pre-defined likelihoods and inherit more properties. In this case the coding will be extremely simple, you won’t need to write a specific likelihood code. In the current version, pre-defined classes are: Likelihood_newdat suited for all CMB experiments described by a file in the .newdat format (same files as in CosmoMC). Likelihood_mock_cmb suited for all CMB experiments dexcribed with a simplified gaussian likelihood, like our fake_planck_bluebook likelihood. Likelihood_mpk suited for matter power spectrum data that would be described with a .dataset file in CosmoMC. This generic likelihood contains a piece of code following closely the routine mpk developped for CosmoMC. In the released version of Monte Python, this likelihood type is only used by each of the four redshift bins of the WiggleZ data, but it is almost ready for being used with other data set in this format. Suppose, for instance, that a new CMB dataset nextcmb is released in the .newdat format. You will then copy the .newdat file and other related files (with window functions, etc.) in the folder data/. You will then create a new likelihood, starting from an existing one, e.g cbi: $ mkdir likelihoods/nextcmb
$cp likelihoods/cbi/cbi.data likelihoods/nextcmb/nextcmb.data$ cp likelihoods/cbi/__init__.py likelihoods/nextcmb/__init__.py


The python file should only be there to tell the code that nextcmb is in the .newdat format. Hence it should only contain:

from montepython.likelihood_class import Likelihood_newdat
class nextcmb(Likelihood_newdat):
pass


This is enough: the likelihood is fully defined. The data file should only contain the name of the .newdat file:

nextcmb.data_directory  = data.path['data']
nextcmb.file            = 'next-cmb-file.newdat'


Once you have edited these few lines, you are done! No need to tell Monte Python that there is a new likelihood! Just call it in your next run by adding data.experiments = [...,'nextcmb', ...] to the list of experiments in the input parameter file, and the likelihood will be used.

You can also define nuisance parameters, contamination spectra and nuisance priors for this likelihood, as explained in the next section.

## Creating new likelihoods from scratch¶

The likelihood sn is an example of individual likelihood code: the actual code is explicitly written in sn.py. To create your own likelihood files, the best to is look at such examples and follow them. We do not provide a full tutorial here, and encourage you to ask for help if needed. Here are however some general indications.

Your customised likelihood should inherit from generic likelihood properties through:

from montepython.likelihood_class import Likelihood
class my-likelihood(Likelihood):


Implementing the likelihood amounts in developing in the python file my-likelihood.py the properties of two essential functions, __init__ and loglkl. But you don’t need to code everything from scratch, because the generic likelihood already knows the most generic steps. The previous link will give you all the functions defined from this base class, that your daughter class will inherit from. Here follows a detailled explanation about how to use these.

One thing is that you don’t need to write from scratch the parser reading the .data file: this will be done automatically at the beginning of the initialization of your likelihood. Consider that any field defined with a line in the .data file, e.g. my-likelihood.variance = 5, are known in the likelihood code: in this example you could write in the python code something like chi2+=result**2/self.variance.

You don’t need either to write from scratch an interface with Class. You just need to write somewhere in the initialization function some specific parameters that should be passed to Class. For instance, if you need the matter power spectrum, write

self.need_cosmo_arguments(data,{'output':'mPk'})


that uses the method need_cosmo_arguments. If this likelihood is used, the field mPk will be appended to the list of output fields (e.g. output=tCl,pCl,mPk), unless it was already there. If you write

self.need_cosmo_arguments(data,{'l_max_scalars':3300})


the code will check if l_max_scalars was already set at least to 3300, and if not, it will increase it to 3300. But if another likelihood needs more it will be more.

You don’t need to redefine functions like for instance those defining the role of nuisance parameters (especially for CMB experiments). If you write in the .data file

my-likelihood.use_nuisance           = ['N1','N2']


the code will know that this likelihood cannot work if these two nuisance parameters are not specified in the parameter input file (they can be varying or fixed; fix them by writing a 0 in the sigma entry). If you try to run without them, the code will stop with an explicit error message. If the parameter N1 has a top-hat prior, no need to write it: just specify prior edges in the input parameter file. If N2 has a gaussian prior, specify it in the .data file, e.g.:

my-likelihood.N2_prior_center  = 1
my-likelihood.N2_prior_variance = 2


Since these fields refer to pre-defined properties of the likelihood, you don’t need to write explicitly in the code something like chi2 += (N2-center)**2/variance, adding the prior is done automatically. Finally, if these nuisance parameters are associated to a CMB dataset, they may stand for a multiplicative factor in front of a contamination spectrum to be added to the theoretical $$C_{\ell}$$‘s. This is the case for the nuisance parameters of the acbar, spt and wmap likelihoods delivered with the code, so you can look there for concrete examples. To assign this role to these nuisance parameters, you just need to write

my-likelihood.N1_file = 'contamination_corresponding_to_N1.data'


and the code will understand what it should do with the parameter N1 and the file data/contamination_corresponding_to_N1.data. Optionally, the factor in front of the contamination spectrum can be rescaled by a constant number using the syntax:

my-likelihood.N1_scale = 0.5


Creating new likelihoods requires a basic knowledge of python. If you are new in python, once you know the basics, you will realise how concise a code can be. You can compare the length of the likelihood codes that we provide with their equivalent in Fortran in the CosmoMC package.