Added documentation Chatterjee sensitivity

docs/code/sensitivity/chatterjee/README.rst

@@ -0,0 +1,15 @@
+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
+
+2. Exponential function
+
+For the Exponential model, analytical Cramer-von Mises indices are available, since they are equivalent to the Chatterjee indices, they are shown here.
+
+3. Sobol function
+
+This example was considered in [1] page 18.
+
+.. [1] Fabrice Gamboa, Pierre Gremaud, Thierry Klein, and Agnès Lagnoux. (2020). Global Sensitivity Analysis: a new generation of mighty estimators based on rank statistics.

docs/source/conf.py

@@ -93,6 +93,7 @@
         "../code/sensitivity/morris",
         "../code/sensitivity/sobol",
         "../code/sensitivity/cramer_von_mises",
+        "../code/sensitivity/chatterjee",
         "../code/stochastic_processes/bispectral",
         "../code/stochastic_processes/karhunen_loeve",
         "../code/stochastic_processes/spectral",
@@ -129,6 +130,7 @@
         "auto_examples/sensitivity/morris",
         "auto_examples/sensitivity/sobol",
         "auto_examples/sensitivity/cramer_von_mises",
+        "auto_examples/sensitivity/chatterjee",
         "auto_examples/stochastic_processes/bispectral",
         "auto_examples/stochastic_processes/karhunen_loeve",
         "auto_examples/stochastic_processes/spectral",

docs/source/sensitivity/chatterjee.rst

@@ -0,0 +1,41 @@
+Chatterjee indices
+----------------------------------------
+
+The Chatterjee index measures the strength of the relationship between :math:`X` and :math:`Y` using rank statistics.
+
+Consider :math:`n` samples of random variables :math:`X` and :math:`Y`, with :math:`(X_{(1)}, Y_{(1)}), \ldots,(X_{(n)}, Y_{(n)})` such that :math:`X_{(1)} \leq \cdots \leq X_{(n)}`. Here, random variable :math:`X` can be one of the inputs of a model and :math:`Y` be the model response. If :math:`X_{i}`'s have no ties, there is a unique way of doing this (case of ties is also taken into account in the implementation, see [1]_). Let :math:`r_{i}`` be the rank of :math:`Y_{(i)}`, that is, the number of :math:`j` such that :math:`Y_{(j)} \leq Y_{(i)}`.The Chatterjee index :math:`\xi_{n}(X, Y)` is defined as:
+
+.. math::
+
+   \xi_{n}(X, Y):=1-\frac{3 \sum_{i=1}^{n-1}\left|r_{i+1}-r_{i}\right|}{n^{2}-1}
+
+The Chatterjee index converges for :math:`n \rightarrow \infty` to the Cramér-von Mises index and is faster to estimate than using the Pick and Freeze approach in the Cramer-von Mises index.
+
+.. [1] Sourav Chatterjee (2021) A New Coefficient of Correlation, Journal of the American Statistical Association, 116:536, 2009-2022, DOI: 10.1080/01621459.2020.1758115 (`Link <https://doi.org/10.1080/01621459.2020.1758115>`_)
+
+Chatterjee Class
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+The :class:`Chatterjee` class is imported using the following command:
+
+>>> from UQpy.sensitivity.chatterjee import Chatterjee
+
+Methods
+"""""""
+.. autoclass:: UQpy.sensitivity.Chatterjee
+   :members: run, compute_chatterjee_indices, rank_analog_to_pickfreeze, compute_Sobol_indices
+
+Attributes
+""""""""""
+.. autoattribute:: UQpy.sensitivity.Chatterjee.chatterjee_i
+.. autoattribute:: UQpy.sensitivity.Chatterjee.sobol_i
+.. autoattribute:: UQpy.sensitivity.Chatterjee.CI_chatterjee_i
+.. autoattribute:: UQpy.sensitivity.Chatterjee.num_vars
+.. autoattribute:: UQpy.sensitivity.Chatterjee.n_samples
+
+Examples
+""""""""""
+
+.. toctree::
+
+   Chatterjee Examples <../auto_examples/sensitivity/chatterjee/index>

docs/source/sensitivity/index.rst

@@ -5,6 +5,7 @@ This module contains functionality for all the sampling methods supported in :py
 
 The module currently contains the following classes:
 
+- :py:class:`.CramervonMises`: Class to compute Chatterjee sensitivity indices.
 - :py:class:`.CramervonMises`: Class to compute Cramér-von Mises sensitivity indices.
 - :py:class:`.MorrisSensitivity`: Class to perform Morris.
 - :py:class:`.PceSensitivity`: Class to compute the sensitivity indices using the :class:`.PolynomialChaosExpansion` method.
@@ -18,6 +19,7 @@ Sensitivity analysis comprises techniques focused on determining how the variati
    :hidden:
    :caption: Sensitivity
 
+    Chatterjee <chatterjee>
     Cramér-von Mises Sensitivity <cramer_von_mises>
     Morris Sensitivity <morris>
     Polynomial Chaos Sensitivity <pce>