.. _SpaceDistribution2:


Space distribution
------------------


Probability distribution of design and environment parameters defined by distribution functions and constraints. The definition of the parameter distribution can have several effects:  

* In a call to the method ``get_statistics`` of the driver interface     the value of interest is averaged over samples drawn from the     space distribution.  

* In a call to the method ``run_mcmc`` of the driver interface     the space distribution acts as a prior distribution.  

* In a call to the method ``get_sobol_indices`` of the driver interface     the space distribution acts as a weighting factor for determining     expectation values.  

* In an :ref:`ActiveLearning` driver, one can access the value of the     log-probability density (up to an additive constant) by the name     ``'log_prob'`` in any expression, e.g. in     :ref:`ExpressionVariable`,     :ref:`LinearCombinationVariable`.

.. _BayesianLeastSquares.parameter_distribution.include_study_constraints:


include_study_constraints (bool)
""""""""""""""""""""""""""""""""
   If true, the constraints defined when creating the study are included in the distribution. 

   Default: ``False``

.. _BayesianLeastSquares.parameter_distribution.distributions:


distributions (list[dict])
""""""""""""""""""""""""""
   List of distributions for all or a subset of design and environment parameters. If not specified, the distributions are uniform over the specified domains. 

   Default: ``[]``

   .. admonition:: Example

      A multivariate normal distribution over two parameters ``'x1'``, ``'x2'`` and a uniform distribution over a third parameter ``'x3'``.

      .. code-block:: python

         [{'type': 'mvn', 'parameters': ['x1','x2'], 'mean': [0.0,0.0], 'covariance': [[1.0,0.4],
          [0.4,2.0]]},
          {'type': 'uniform', 'parameter': 'x2', 'domain': [-2.0,2.0]}]

   Each element of the list must be a dict. The dict entry ``type`` specifies the type of the element. The remaining entries  specify its properties. In the following, all possible  list element types are described:

      **Uniform distribution** (type ``'uniform'``): Uniform distribution in a specific domain.      
      
      See :ref:`uniform configuration <Uniform3>` for details.

      **Normal distribution** (type ``'normal'``): Normal distribution of specified mean and standard deviation.      
      
      See :ref:`normal configuration <Normal3>` for details.

      **Gamma distribution** (type ``'gamma'``): Gamma distribution defined by rate and shape parameter.      
      
      See :ref:`gamma configuration <Gamma3>` for details.

      **Distribution over discrete values** (type ``'discrete'``): Distribution over discrete values of a discrete or categorial parameter.      
      
      See :ref:`discrete configuration <DiscreteProbabilities3>` for details.

      **Multivariate normal distribution** (type ``'mvn'``): Multivariate normal defined my mean vector and covariance matrix.      
      
      See :ref:`mvn configuration <MultivariateNormal3>` for details.

.. toctree::
   :maxdepth: 100 
   :hidden:
   
   Uniform3
   Normal3
   Gamma3
   DiscreteProbabilities3
   MultivariateNormal3



.. _BayesianLeastSquares.parameter_distribution.constraints:


constraints (list[dict])
""""""""""""""""""""""""
   List of constraints on parameters. 

   Default: ``[]``

   .. admonition:: Example

      Constrain probability distribution to values :math:`\sqrt{x_1^2 + x_2^2} \leq 3`.

      .. code-block:: python

         [{'name': 'x1_constraint', 'expression': 'sqrt(x1^2 + x2^2) <= 3'}]

   Each element of the list must be a dict. In the following, the list elements are described:

   Inequality constraint on design end environment parameters.   
   
   See :ref:`constraint configuration <SpaceConstraint2>` for details.

.. toctree::
   :maxdepth: 100 
   :hidden:
   
   SpaceConstraint2