.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_probabilistic_modeling/distributions/plot_bayes_distribution.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_auto_probabilistic_modeling_distributions_plot_bayes_distribution.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_probabilistic_modeling_distributions_plot_bayes_distribution.py:


Create a Joint by Conditioning  distribution
============================================

.. GENERATED FROM PYTHON SOURCE LINES 7-17

In this example we are going to build the distribution of the random vector:

.. math::
   (Y, \vect{X}|\vect{\Theta})

with :math:`\vect{X}` conditioned by the random vector :math:`\vect{\Theta}` obtained with the random variable :math:`Y` through a function :math:`f`:

.. math::
   \vect{\Theta} = f(\vect{Y})


.. GENERATED FROM PYTHON SOURCE LINES 19-23

.. code-block:: Python

    import openturns as ot
    import openturns.viewer as viewer









.. GENERATED FROM PYTHON SOURCE LINES 24-28

We consider the following case: :math:`X|\vect{\Theta} \sim \cN(\vect{\Theta})`
with :math:`\vect{\Theta} = (Y, 0.1 + Y^2)` and :math:`Y \sim \cN(0,1)`.

We first create the :math:`Y` distribution:

.. GENERATED FROM PYTHON SOURCE LINES 28-30

.. code-block:: Python

    YDist = ot.Normal(0.0, 1.0)








.. GENERATED FROM PYTHON SOURCE LINES 31-32

Then we create the link function :math:`f: y \rightarrow (y, 0.1+y^2)`:

.. GENERATED FROM PYTHON SOURCE LINES 32-34

.. code-block:: Python

    f = ot.SymbolicFunction(["y"], ["y", "0.1 + y^2"])








.. GENERATED FROM PYTHON SOURCE LINES 35-36

Then, we create the :math:`\vect{X}|\vect{\Theta}` distribution:

.. GENERATED FROM PYTHON SOURCE LINES 36-38

.. code-block:: Python

    XgivenThetaDist = ot.Normal()








.. GENERATED FROM PYTHON SOURCE LINES 39-40

At last, we create the distribution of :math:`(Y,X)`:

.. GENERATED FROM PYTHON SOURCE LINES 40-44

.. code-block:: Python

    XDist = ot.JointByConditioningDistribution(XgivenThetaDist, YDist, f)
    XDist.setDescription(["Y", r"$X|\mathbf{\boldsymbol{\Theta}} = f(Y)$"])
    XDist






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    JointByConditioningDistribution
    <ul>
      <li>name=JointByConditioningDistribution</li>
      <li>dimension=2</li>
      <li>weight=1</li>
      <li>range=]-inf (-7.65063), (7.65063) +inf[
    ]-inf (-396.355), (396.355) +inf[</li>
      <li>description=[Y,$X|\mathbf{\boldsymbol{\Theta}} = f(Y)$]</li>
      <li>isParallel=false</li>
      <li>isCopula=false</li>
    </ul>

    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 45-46

Get a sample:

.. GENERATED FROM PYTHON SOURCE LINES 46-48

.. code-block:: Python

    sample = XDist.getSample(100)








.. GENERATED FROM PYTHON SOURCE LINES 49-50

Draw the PDF:

.. GENERATED FROM PYTHON SOURCE LINES 50-59

.. code-block:: Python

    ot.ResourceMap.SetAsString("Contour-DefaultColorMapNorm", "rank")
    graph = XDist.drawPDF(sample.getMin(), sample.getMax(), [256] * 2)
    graph.setTitle(r"$(Y,X)$ iso-PDF")
    cloud = ot.Cloud(sample)
    cloud.setColor("red")
    cloud.setLegend("sample")
    graph.add(cloud)
    view = viewer.View(graph)




.. image-sg:: /auto_probabilistic_modeling/distributions/images/sphx_glr_plot_bayes_distribution_001.svg
   :alt: $(Y,X)$ iso-PDF
   :srcset: /auto_probabilistic_modeling/distributions/images/sphx_glr_plot_bayes_distribution_001.svg
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 60-61

.. code-block:: Python

    view.ShowAll()








.. _sphx_glr_download_auto_probabilistic_modeling_distributions_plot_bayes_distribution.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_bayes_distribution.ipynb <plot_bayes_distribution.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_bayes_distribution.py <plot_bayes_distribution.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_bayes_distribution.zip <plot_bayes_distribution.zip>`