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Chatterjee indices
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
These examples serve as a guide for using the Chatterjee sensitivity module. They have been taken from various papers to enable validation of the implementation and have been referenced accordingly.

1. **Ishigami function**

    In addition to the Pick and Freeze scheme, the Sobol indices can be estimated using the rank statistics approach :cite:`gamboa2020global`. We demonstrate this estimation of the Sobol indices using the Ishigami function.

2. **Exponential function**

    For the Exponential model, analytical Cramér-von Mises indices are available :cite:`CVM` and since they are equivalent to the Chatterjee indices in the sample limit, they are shown here.

3. **Sobol function**

    This example was considered in :cite:`gamboa2020global` (page 18) to compare the Pick and Freeze scheme with the rank statistics approach for estimating the Sobol indices.



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    <div class="sphx-glr-thumbcontainer" tooltip="The exponential function was used in [1]_ to demonstrate the  Cramér-von Mises indices. Chatter...">

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  :ref:`sphx_glr_auto_examples_sensitivity_chatterjee_chatterjee_exponential.py`

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  :ref:`sphx_glr_auto_examples_sensitivity_chatterjee_chatterjee_ishigami.py`

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  :ref:`sphx_glr_auto_examples_sensitivity_chatterjee_chatterjee_sobol_func.py`

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      <div class="sphx-glr-thumbnail-title">Sobol function</div>
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.. toctree::
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   /auto_examples/sensitivity/chatterjee/chatterjee_exponential
   /auto_examples/sensitivity/chatterjee/chatterjee_ishigami
   /auto_examples/sensitivity/chatterjee/chatterjee_sobol_func


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      :download:`Download all examples in Python source code: chatterjee_python.zip </auto_examples/sensitivity/chatterjee/chatterjee_python.zip>`

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

      :download:`Download all examples in Jupyter notebooks: chatterjee_jupyter.zip </auto_examples/sensitivity/chatterjee/chatterjee_jupyter.zip>`


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    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_