Basic cosmology runs

Sampling from a cosmological posterior works the same way as the examples at the beginning of the documentation, except that one usually needs to add a theory code, and possibly some of the cosmological likelihoods presented later.

You can sample or track any parameter that is understood by the theory code in use (or any dynamical redefinition of those). You do not need to modify Cobaya’s source to use new parameters that you have created by modifying CLASS or modifying CAMB, or to create a new cosmological likelihood and track its parameters.

Creating from scratch the input for a realistic cosmological case is quite a bit of work. But to make it simpler, we have created an automatic input generator, that you can run from the shell as:

$ cobaya-cosmo-generator
_images/cosmo_input_generator.png

Note

If PySide2 is not installed, this will fail. To fix it:

$ python -m pip install pyqt5 pyside2

Anaconda users should instead do:

$ conda install -c conda-forge pyside2

Installing PySide2 via pip, and sometime Anaconda, is often problematic. The most reliable solution seems to be to make a clean conda-forge environment and use that, e.g. install Anaconda or Miniconda and use the environment created with

$ conda create -n py39forge -c conda-forge python=3.9 scipy pandas matplotlib PyYAML PySide2

Start by choosing a preset, maybe modify some aspects using the options provided, and copy or save the generated input to a file, either in yaml form or as a python dictionary.

The parameter combinations and options included in the input generator are in general well-tested, but they are only suggestions: you can add by hand any parameter that your theory code or likelihood can understand, or modify any setting.

Don’t forget to add the installation path for the cosmological requisites packages_path: '/path/to/packages', and an output prefix if you wish.

As an example, here is the input for Planck 2015 base \(\Lambda\mathrm{CDM}\), both for CLASS and CAMB:

Click to toggle CAMB/CLASS
CAMB parameter names:
theory:
  camb:
    extra_args:
      halofit_version: mead
      bbn_predictor: PArthENoPE_880.2_standard.dat
      lens_potential_accuracy: 1
      num_massive_neutrinos: 1
      nnu: 3.046
      theta_H0_range:
      - 20
      - 100
likelihood:
  planck_2018_lowl.TT: null
  planck_2018_lowl.EE: null
  planck_2018_highl_plik.TTTEEE: null
  planck_2018_lensing.clik: null
params:
  logA:
    prior:
      min: 1.61
      max: 3.91
    ref:
      dist: norm
      loc: 3.05
      scale: 0.001
    proposal: 0.001
    latex: \log(10^{10} A_\mathrm{s})
    drop: true
  As:
    value: 'lambda logA: 1e-10*np.exp(logA)'
    latex: A_\mathrm{s}
  ns:
    prior:
      min: 0.8
      max: 1.2
    ref:
      dist: norm
      loc: 0.965
      scale: 0.004
    proposal: 0.002
    latex: n_\mathrm{s}
  theta_MC_100:
    prior:
      min: 0.5
      max: 10
    ref:
      dist: norm
      loc: 1.04109
      scale: 0.0004
    proposal: 0.0002
    latex: 100\theta_\mathrm{MC}
    drop: true
    renames: theta
  cosmomc_theta:
    value: 'lambda theta_MC_100: 1.e-2*theta_MC_100'
    derived: false
  H0:
    latex: H_0
    min: 20
    max: 100
  ombh2:
    prior:
      min: 0.005
      max: 0.1
    ref:
      dist: norm
      loc: 0.0224
      scale: 0.0001
    proposal: 0.0001
    latex: \Omega_\mathrm{b} h^2
  omch2:
    prior:
      min: 0.001
      max: 0.99
    ref:
      dist: norm
      loc: 0.12
      scale: 0.001
    proposal: 0.0005
    latex: \Omega_\mathrm{c} h^2
  omegam:
    latex: \Omega_\mathrm{m}
  omegamh2:
    derived: 'lambda omegam, H0: omegam*(H0/100)**2'
    latex: \Omega_\mathrm{m} h^2
  mnu: 0.06
  omega_de:
    latex: \Omega_\Lambda
  YHe:
    latex: Y_\mathrm{P}
  Y_p:
    latex: Y_P^\mathrm{BBN}
  DHBBN:
    derived: 'lambda DH: 10**5*DH'
    latex: 10^5 \mathrm{D}/\mathrm{H}
  tau:
    prior:
      min: 0.01
      max: 0.8
    ref:
      dist: norm
      loc: 0.055
      scale: 0.006
    proposal: 0.003
    latex: \tau_\mathrm{reio}
  zre:
    latex: z_\mathrm{re}
  sigma8:
    latex: \sigma_8
  s8h5:
    derived: 'lambda sigma8, H0: sigma8*(H0*1e-2)**(-0.5)'
    latex: \sigma_8/h^{0.5}
  s8omegamp5:
    derived: 'lambda sigma8, omegam: sigma8*omegam**0.5'
    latex: \sigma_8 \Omega_\mathrm{m}^{0.5}
  s8omegamp25:
    derived: 'lambda sigma8, omegam: sigma8*omegam**0.25'
    latex: \sigma_8 \Omega_\mathrm{m}^{0.25}
  A:
    derived: 'lambda As: 1e9*As'
    latex: 10^9 A_\mathrm{s}
  clamp:
    derived: 'lambda As, tau: 1e9*As*np.exp(-2*tau)'
    latex: 10^9 A_\mathrm{s} e^{-2\tau}
  age:
    latex: '{\rm{Age}}/\mathrm{Gyr}'
  rdrag:
    latex: r_\mathrm{drag}
sampler:
  mcmc:
    drag: true
    oversample_power: 0.4
    proposal_scale: 1.9
    covmat: auto
    Rminus1_stop: 0.01
    Rminus1_cl_stop: 0.2
CLASS parameter names:
theory:
  classy:
    extra_args:
      non linear: hmcode
      hmcode_min_k_max: 20
      N_ncdm: 1
      N_ur: 2.0328
likelihood:
  planck_2018_lowl.TT: null
  planck_2018_lowl.EE: null
  planck_2018_highl_plik.TTTEEE: null
  planck_2018_lensing.clik: null
params:
  logA:
    prior:
      min: 1.61
      max: 3.91
    ref:
      dist: norm
      loc: 3.05
      scale: 0.001
    proposal: 0.001
    latex: \log(10^{10} A_\mathrm{s})
    drop: true
  A_s:
    value: 'lambda logA: 1e-10*np.exp(logA)'
    latex: A_\mathrm{s}
  n_s:
    prior:
      min: 0.8
      max: 1.2
    ref:
      dist: norm
      loc: 0.965
      scale: 0.004
    proposal: 0.002
    latex: n_\mathrm{s}
  theta_s_1e2:
    prior:
      min: 0.5
      max: 10
    ref:
      dist: norm
      loc: 1.0416
      scale: 0.0004
    proposal: 0.0002
    latex: 100\theta_\mathrm{s}
    drop: true
  100*theta_s:
    value: 'lambda theta_s_1e2: theta_s_1e2'
    derived: false
  H0:
    latex: H_0
  omega_b:
    prior:
      min: 0.005
      max: 0.1
    ref:
      dist: norm
      loc: 0.0224
      scale: 0.0001
    proposal: 0.0001
    latex: \Omega_\mathrm{b} h^2
  omega_cdm:
    prior:
      min: 0.001
      max: 0.99
    ref:
      dist: norm
      loc: 0.12
      scale: 0.001
    proposal: 0.0005
    latex: \Omega_\mathrm{c} h^2
  Omega_m:
    latex: \Omega_\mathrm{m}
  omegamh2:
    derived: 'lambda Omega_m, H0: Omega_m*(H0/100)**2'
    latex: \Omega_\mathrm{m} h^2
  m_ncdm:
    value: 0.06
    renames: mnu
  Omega_Lambda:
    latex: \Omega_\Lambda
  YHe:
    latex: Y_\mathrm{P}
  tau_reio:
    prior:
      min: 0.01
      max: 0.8
    ref:
      dist: norm
      loc: 0.055
      scale: 0.006
    proposal: 0.003
    latex: \tau_\mathrm{reio}
  z_reio:
    latex: z_\mathrm{re}
  sigma8:
    latex: \sigma_8
  s8h5:
    derived: 'lambda sigma8, H0: sigma8*(H0*1e-2)**(-0.5)'
    latex: \sigma_8/h^{0.5}
  s8omegamp5:
    derived: 'lambda sigma8, Omega_m: sigma8*Omega_m**0.5'
    latex: \sigma_8 \Omega_\mathrm{m}^{0.5}
  s8omegamp25:
    derived: 'lambda sigma8, Omega_m: sigma8*Omega_m**0.25'
    latex: \sigma_8 \Omega_\mathrm{m}^{0.25}
  A:
    derived: 'lambda A_s: 1e9*A_s'
    latex: 10^9 A_\mathrm{s}
  clamp:
    derived: 'lambda A_s, tau_reio: 1e9*A_s*np.exp(-2*tau_reio)'
    latex: 10^9 A_\mathrm{s} e^{-2\tau}
  age:
    latex: '{\rm{Age}}/\mathrm{Gyr}'
  rs_drag:
    latex: r_\mathrm{drag}
sampler:
  mcmc:
    drag: true
    oversample_power: 0.4
    proposal_scale: 1.9
    covmat: auto
    Rminus1_stop: 0.01
    Rminus1_cl_stop: 0.2

Note

Note that Planck likelihood parameters (or nuisance parameters) do not appear in the input: they are included automatically at run time. The same goes for all internal likelihoods (i.e. those listed below in the table of contents).

You can still add them to the input, if you want to redefine any of their properties (its prior, label, etc.). See Changing and redefining parameters; inheritance.

Save the input generated to a file and run it with cobaya-run [your_input_file_name.yaml]. This will create output files as explained here, and, after some time, you should be able to run getdist-gui to generate some plots.

Note

You may want to start with a test run, adding --test to cobaya-run. It will initialise all components (cosmological theory code and likelihoods, and the sampler) and exit.

Typical running times for MCMC when using computationally heavy likelihoods (e.g. those involving \(C_\ell\), or non-linear \(P(k,z)\) for several redshifts) are ~10 hours running 4 MPI processes with 4 OpenMP threads per process, provided that the initial covariance matrix is a good approximation to the one of the real posterior (Cobaya tries to select it automatically from a database; check the [mcmc] output towards the top to see if it succeeded), or a few hours on top of that if the initial covariance matrix is not a good approximation.

It is much harder to provide typical PolyChord running times. We recommend starting with a low number of live points and a low convergence tolerance, and build up from there towards PolyChord’s default settings (or higher, if needed).

Post-processing cosmological samples

Let’s suppose that we want to importance-reweight a Planck sample, in particular the one we just generated with the input above, with some late time LSS data from BAO. To do that, we add the new BAO likelihoods. We would also like to increase the theory code’s precision with some extra arguments: we will need to re-add it, and set the new precision parameter under extra_args (the old extra_args will be inherited, unless specifically redefined). For his example let’s say we do not need to recompute the CMB likelihoods, so power spectra do not need to be recomputed, but we do want to add a new derived parameter.

Assuming we saved the sample at chains/planck, we need to define the following input file, which we can run with $ cobaya-run:

# Path the original sample
output: chains/planck

# Post-processing information
post:
  suffix: BAO  # the new sample will be called "chains\planck_post_des*"
  # If we want to skip the first third of the chain as burn in
  skip: 0.3
  # Now let's add the DES likelihood,
  # increase the precision (remember to repeat the extra_args)
  # and add the new derived parameter
  add:
    likelihood:
      sixdf_2011_bao:
      sdss_dr7_mgs:
      sdss_dr12_consensus_bao:
    theory:
      # Use *only* the theory corresponding to the original sample
      classy:
        extra_args:
          # New precision parameter
          # [option]: [value]
      camb:
        extra_args:
          # New precision parameter
          # [option]: [value]
    params:
      # h = H0/100. (nothing to add: CLASS/CAMB knows it)
      h:
      # A dynamic derived parameter (change omegam to Omega_m for classy)
      # note that sigma8 itself is not recomputed unless we add+remove it
      S8:
        derived: 'lambda sigma8, omegam: sigma8*(omegam/0.3)**0.5'
        latex: \sigma_8 (\Omega_\mathrm{m}/0.3)^{0.5}

Getting help and bibliography for a component

If you want to get the available options with their default values for a given component, use

$ cobaya-doc [component_name]

If the component name is not unique (i.e. there are more than one component with the same name but different kinds), use the option --kind [component_kind] to specify its kind: sampler, theory or likelihood.

Call $ cobaya-doc with a kind instead of a component name (e.g. $ cobaya-doc likelihood) to get a list of components of that kind. Call with no arguments to get all available components of all kinds.

If you would like to cite the results of a run in a paper, you would need citations for all the different parts of the process. In the example above that would be this very sampling framework, the MCMC sampler, the CAMB or CLASS cosmological code and the Planck 2018 likelihoods.

The bibtex for those citations, along with a short text snippet for each element, can be easily obtained and saved to some output_file.tex with

$ cobaya-bib [your_input_file_name.yaml] > output_file.tex

You can pass multiple input files this way, or even a (list of) component name(s), as in cobaya-doc.

You can also do this interactively, by passing your input info, as a python dictionary, to the function get_bib_info():

from cobaya.bib import get_bib_info
get_bib_info(info)

Note

Both defaults and bibliography are available in the GUI (menu Show defaults and bibliography for a component ...).

Bibliography for preset input files is displayed in the bibliography tab.