============
Priors
============
Redback uses :code:`bilby` under the hood for priors. See `here <https://lscsoft.docs.ligo.org/bilby/prior.html>`_ for general documentation of priors in :code:`bilby`.

Analytical priors
-------------------------

Thanks to :code:`bilby` there are several different priors already implemented.

- Beta
- Categorical
- Cauchy
- ChiSquared
- Cosine
- DeltaFunction
- Exponential
- FermiDirac
- Gamma
- Gaussian
- HalfGaussian
- LogGaussian
- LogUniform
- Logistic
- Lorentzian
- PowerLaw
- Sine
- StudentT
- SymmetricLogUniform
- TruncatedGaussian
- Uniform


Interpolated or from file
-------------------------

Users can also create a prior from a grid of values i.e., an interpolated_prior.
See documentation `here <https://lscsoft.docs.ligo.org/bilby/api/bilby.core.prior.interpolated.Interped.html#bilby.core.prior.interpolated.Interped>`_.

Constrained priors
-------------------------

Sometimes there are some additional constraints on the priors that are difficult to parameterise or not on a sampled parameter.

For example, the rotational energy of a neutron star cannot be exceeded in a super luminous supernova. Or that a numerical surrogate is only valid in a certain domain etc.
In redback, we have written several of these constraints which can be used by simply loading the particular constraint from redback.constraints and passing them to the bilby prior dictionary.

For example,

.. code:: python

    import redback
    from bilby.core.prior import PriorDict, Uniform, Constraint

    priors = PriorDict(conversion_function=redback.constraints.slsn_constraint)
    priors['erot_constraint'] = Constraint(minimum=0, maximum=100)
    priors['t_nebula_min'] = Constraint(minimum=0, maximum=100)

Then define our priors on all other parameters in the normal way. You can then check whether the constraints are set up correctly by sampling from the prior via

.. code:: python

    priors.sample(1000)

You can implement your own constraints by following the constraint templates and :code:`bilby` `documentation <https://lscsoft.docs.ligo.org/bilby/prior.html>`_.
We note that the default priors do not have constraints active so analysis with constraints must construct the prior dictionary as above.
This new prior dictionary can be updated to include the default prior via

.. code:: python

    model = 'slsn'
    priors.update(redback.priors.get_priors(model=model))

Adding sigma to the prior
-------------------------

One can also add a sigma to the prior by using the :code:`sigma` keyword in the prior dictionary.
For the default :code:`redback` likelihood, this will overwrite the sigma in the data and estimate a constant sigma.
For other likelihoods, this may be added in quadrature to the y_err from the data.
Or be a systematic offset proportional to the model that is added in quadrature to the measured noise.
Please look at the likelihood documentation for more details.