InferenceModel
--------------------------------

For any inference task, the user must first create, for each model studied, an instance of the class :class:`.InferenceModel`
that defines the problem at hand. This class defines an inference model that will serve as input for all remaining
inference classes. A model can be defined in various ways. The following summarizes the four types of inference models
that are supported by :py:mod:`UQpy`. These four types are further summarized in the figure below.

* **Case 1a** - **Gaussian error model** powered by :class:`.RunModel`: In this case, the data is assumed to come form a
  model of the following form,  :math:`data \sim h(\theta) + \epsilon`, where :math:`\epsilon` is iid Gaussian and :math:`h` consists of a computational
  model executed using :class:`.RunModel`. Data is a 1D ndarray in this setting. In order to define such a inference model,
  the :class:`.ComputationalModel` class must be utilized.

* **Case 1b** - **Non-Gaussian error model** powered by :class:`.RunModel`: In this case, the user must provide a callable likelihood
  function in addition to a :class:`.RunModel` object. The data type is user-defined and must be consistent with the
  likelihood function definition. In order to define such a inference model, the :class:`.ComputationalModel` class must be utilized.

* **Case 2:** - **User-defined likelihood** without :class:`.RunModel`: Here, the likelihood function is user-defined and
  does not leverage :class:`.RunModel`. The data type must be consistent with the likelihood function definition.
  In order to define such a inference model, the :class:`.LogLikelihoodModel` class must be utilized.

* **Case 3:** - **Learn parameters of a probability distribution**: Here, the user must define an object of the
  :class:`.Distribution` class. Data is an :class:`numpy.ndarray` of shape :code:`(ndata, dim)` and consists in :code:`ndata` iid samples from the
  probability distribution. In order to define such a inference model, the :class:`.DistributionModel` class must be utilized.

.. image:: ../_static/Inference_models.png
   :scale: 30 %
   :align: left


Defining a Log-likelihood function
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
The critical component of the :class:`.InferenceModel` class, child classes is the evaluation of the log-likelihood function.
:class:`.InferenceModel` has been constructed to be flexible in how the user specifies the log-likelihood function.
The log-likelihood function can be specified as a user-defined callable method that is passed directly into the
:class:`.LogLikelihoodModel` or the :class:`.ComputationalModel` class. As the cases suggest, a user-defined log-likelihood function must take as input, at
minimum, both the parameters of the model and the data points at which to evaluate the log-likelihood. It may also
take additional keyword arguments. The method may compute the log-likelihood at the data points on its own, or it may
rely on a computational model defined through the :class:`.RunModel` class. If the log-likelihood function relies on a
:class:`.RunModel` object, this object is also passed into :class:`.InferenceModel` and the log-likelihood method should also take
as input, the output (`qoi_list`) of the :class:`.RunModel` object evaluated at the specified parameter values.

InferenceModel Class
^^^^^^^^^^^^^^^^^^^^^^

.. autoclass:: UQpy.inference.inference_models.baseclass.InferenceModel
   :members:

ComputationalModel Class
^^^^^^^^^^^^^^^^^^^^^^^^^

The :class:`.ComputationalModel` class is imported using the following command:

>>> from UQpy.inference.inference_models.ComputationalModel import ComputationalModel

.. autoclass:: UQpy.inference.inference_models.ComputationalModel

DistributionModel Class
^^^^^^^^^^^^^^^^^^^^^^^

The :class:`.DistributionModel` class is imported using the following command:

>>> from UQpy.inference.inference_models.DistributionModel import DistributionModel

.. autoclass:: UQpy.inference.inference_models.DistributionModel

LogLikelihoodModel Class
^^^^^^^^^^^^^^^^^^^^^^^^^^

The :class:`.LogLikelihoodModel` class is imported using the following command:

>>> from UQpy.inference.inference_models.LogLikelihoodModel import LogLikelihoodModel

.. autoclass:: UQpy.inference.inference_models.LogLikelihoodModel