gwkokab.analysis.utils.priors
=============================

.. py:module:: gwkokab.analysis.utils.priors


Functions
---------

.. autoapisummary::

   gwkokab.analysis.utils.priors.DirichletElement
   gwkokab.analysis.utils.priors.get_processed_priors


Module Contents
---------------

.. py:function:: DirichletElement(order: int, n_dimensions: int, validate_args: Optional[bool] = None, **kwargs) -> numpyro.distributions.Distribution

   Conditional Dirichlet Distribution.

   A `DirichletElement` is a distribution over the :math:`N`-dimensional simplex, where
   :math:`N` is the :code:`n_dimensions` parameter. The :math:`n`-th order Dirichlet
   distribution given by the :code:`order`. The distribution is defined as,

   .. math::
       \forall n \in \{0, N-2\}, p(x_n \mid x_0, \cdots, x_{n-1}) =
       \frac{(N-n-1)(1-\alpha_n-x_n)^{N-n-1}}{(1-\alpha_n)^{N-n-1}},
       \qquad x_n \in [0, \alpha_n]

   where :math:`\alpha_n = \sum_{i=0}^{n-1} \alpha_i` and :math:`x_n` is the
   :code:`order`-th element of the simplex.

   .. math::
       p(x_{N-1}\mid x_0, \cdots, x_{N-2}) = \frac{1}{1-\alpha_{N-1}},
       \qquad x_{N-1} \in [0,\alpha_{N-1}]

   :param order: order of the DirichletElement
   :type order: int
   :param n_dimensions: number of dimensions
   :type n_dimensions: int
   :param validate_args: whether to validate the arguments, by default None
   :type validate_args: Optional[bool], optional

   :returns: DirichletElement distribution
   :rtype: Distribution

   :raises KeyError: Missing concentration parameters for `DirichletElement` of order {order}


.. py:function:: get_processed_priors(params: List[str], priors: dict) -> dict

   Get the processed priors from a list of parameters.

   A processed prior is either an instantiated prior or a tuple of :code:`(jax.tree_util.Partial, lazy_vars)` where
   :code:`lazy_vars` is a dictionary of lazy variables.

   :param params: list of parameters
   :type params: List[str]
   :param priors: dictionary of priors
   :type priors: dict

   :returns: dictionary of processed priors
   :rtype: dict

   :raises ValueError: if the prior value is invalid